topics for mathematics research paper

251+ Math Research Topics [2024 Updated]

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

• Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
• Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
• Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
• Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
• Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
• Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
• Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
• Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
• Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

• Prime Number Distribution in Arithmetic Progressions
• Diophantine Equations and their Solutions
• Applications of Modular Arithmetic in Cryptography
• The Riemann Hypothesis and its Implications
• Graph Theory: Exploring Connectivity and Coloring Problems
• Knot Theory: Unraveling the Mathematics of Knots and Links
• Fractal Geometry: Understanding Self-Similarity and Dimensionality
• Differential Equations: Modeling Physical Phenomena and Dynamical Systems
• Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
• Combinatorial Optimization: Algorithms for Solving Optimization Problems
• Computational Complexity: Analyzing the Complexity of Algorithms
• Game Theory: Mathematical Models of Strategic Interactions
• Number Theory: Exploring Properties of Integers and Primes
• Algebraic Topology: Studying Topological Invariants and Homotopy Theory
• Analytic Number Theory: Investigating Properties of Prime Numbers
• Algebraic Geometry: Geometry Arising from Algebraic Equations
• Galois Theory: Understanding Field Extensions and Solvability of Equations
• Representation Theory: Studying Symmetry in Linear Spaces
• Harmonic Analysis: Analyzing Functions on Groups and Manifolds
• Mathematical Logic: Foundations of Mathematics and Formal Systems
• Set Theory: Exploring Infinite Sets and Cardinal Numbers
• Real Analysis: Rigorous Study of Real Numbers and Functions
• Complex Analysis: Analytic Functions and Complex Integration
• Measure Theory: Foundations of Lebesgue Integration and Probability
• Topological Groups: Investigating Topological Structures on Groups
• Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
• Differential Geometry: Curvature and Topology of Smooth Manifolds
• Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
• Ramsey Theory: Investigating Structure in Large Discrete Structures
• Analytic Geometry: Studying Geometry Using Analytic Methods
• Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
• Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
• Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
• Topological Vector Spaces: Vector Spaces with Topological Structure
• Representation Theory of Finite Groups: Decomposition of Group Representations
• Category Theory: Abstract Structures and Universal Properties
• Operator Theory: Spectral Theory and Functional Analysis of Operators
• Algebraic Number Theory: Study of Algebraic Structures in Number Fields
• Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
• Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
• Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
• Population Dynamics: Mathematical Models of Population Growth and Interaction
• Epidemiology: Mathematical Modeling of Disease Spread and Control
• Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
• Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
• Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
• Mathematical Physics: Mathematical Models in Physical Sciences
• Quantum Mechanics: Foundations and Applications of Quantum Theory
• Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
• Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
• Mathematical Finance: Stochastic Models in Finance and Risk Management
• Option Pricing Models: Black-Scholes Model and Beyond
• Portfolio Optimization: Maximizing Returns and Minimizing Risk
• Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
• Financial Time Series Analysis: Modeling and Forecasting Financial Data
• Operations Research: Optimization of Decision-Making Processes
• Linear Programming: Optimization Problems with Linear Constraints
• Integer Programming: Optimization Problems with Integer Solutions
• Network Flow Optimization: Modeling and Solving Flow Network Problems
• Combinatorial Game Theory: Analysis of Games with Perfect Information
• Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
• Fair Division: Methods for Fairly Allocating Resources Among Parties
• Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
• Voting Theory: Mathematical Models of Voting Systems and Social Choice
• Social Network Analysis: Mathematical Analysis of Social Networks
• Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
• Machine Learning: Statistical Learning Algorithms and Data Mining
• Deep Learning: Neural Network Models with Multiple Layers
• Reinforcement Learning: Learning by Interaction and Feedback
• Natural Language Processing: Statistical and Computational Analysis of Language
• Computer Vision: Mathematical Models for Image Analysis and Recognition
• Computational Geometry: Algorithms for Geometric Problems
• Symbolic Computation: Manipulation of Mathematical Expressions
• Numerical Analysis: Algorithms for Solving Numerical Problems
• Finite Element Method: Numerical Solution of Partial Differential Equations
• Monte Carlo Methods: Statistical Simulation Techniques
• High-Performance Computing: Parallel and Distributed Computing Techniques
• Quantum Computing: Quantum Algorithms and Quantum Information Theory
• Quantum Information Theory: Study of Quantum Communication and Computation
• Quantum Error Correction: Methods for Protecting Quantum Information from Errors
• Topological Quantum Computing: Using Topological Properties for Quantum Computation
• Quantum Algorithms: Efficient Algorithms for Quantum Computers
• Quantum Cryptography: Secure Communication Using Quantum Key Distribution
• Topological Data Analysis: Analyzing Shape and Structure of Data Sets
• Persistent Homology: Topological Invariants for Data Analysis
• Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
• Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
• Tropical Geometry: Geometric Methods for Studying Polynomial Equations
• Model Theory: Study of Mathematical Structures and Their Interpretations
• Descriptive Set Theory: Study of Borel and Analytic Sets
• Ergodic Theory: Study of Measure-Preserving Transformations
• Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
• Additive Combinatorics: Study of Additive Properties of Sets
• Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
• Proof Theory: Study of Formal Proofs and Logical Inference
• Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
• Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
• Computable Analysis: Study of Computable Functions and Real Numbers
• Graph Theory: Study of Graphs and Networks
• Random Graphs: Probabilistic Models of Graphs and Connectivity
• Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
• Algebraic Graph Theory: Study of Algebraic Structures in Graphs
• Metric Geometry: Study of Geometric Structures Using Metrics
• Geometric Measure Theory: Study of Measures on Geometric Spaces
• Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
• Algebraic Coding Theory: Study of Error-Correcting Codes
• Information Theory: Study of Information and Communication
• Coding Theory: Study of Error-Correcting Codes
• Cryptography: Study of Secure Communication and Encryption
• Finite Fields: Study of Fields with Finite Number of Elements
• Elliptic Curves: Study of Curves Defined by Cubic Equations
• Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
• Modular Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Number Theory
• Zeta Functions: Analytic Functions with Special Properties
• Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
• Dirichlet Series: Analytic Functions Represented by Infinite Series
• Euler Products: Product Representations of Analytic Functions
• Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
• Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
• Julia Sets: Fractal Sets Associated with Dynamical Systems
• Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
• Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
• Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
• Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
• Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
• Galois Representations: Study of Representations of Galois Groups
• Automorphic Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Automorphic Forms
• Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
• Langlands Program: Program to Unify Number Theory and Representation Theory
• Hodge Theory: Study of Harmonic Forms on Complex Manifolds
• Riemann Surfaces: One-dimensional Complex Manifolds
• Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
• Modular Curves: Algebraic Curves Associated with Modular Forms
• Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
• Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
• Mirror Symmetry: Duality Between Calabi-Yau Manifolds
• Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
• Algebraic Groups: Linear Algebraic Groups and Their Representations
• Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
• Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
• Quantum Groups: Deformation of Lie Groups and Lie Algebras
• Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
• Homotopy Theory: Study of Continuous Deformations of Spaces
• Homology Theory: Study of Algebraic Invariants of Topological Spaces
• Cohomology Theory: Study of Dual Concepts to Homology Theory
• Singular Homology: Homology Theory Defined Using Simplicial Complexes
• Sheaf Theory: Study of Sheaves and Their Cohomology
• Differential Forms: Study of Multilinear Differential Forms
• De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
• Morse Theory: Study of Critical Points of Smooth Functions
• Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
• Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
• Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
• Mirror Symmetry: Duality Between Symplectic and Complex Geometry
• Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
• Moduli Spaces: Spaces Parameterizing Geometric Objects
• Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
• Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
• Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
• Derived Categories: Categories Arising from Homological Algebra
• Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
• Model Categories: Categories with Certain Homotopical Properties
• Higher Category Theory: Study of Higher Categories and Homotopy Theory
• Higher Topos Theory: Study of Higher Categorical Structures
• Higher Algebra: Study of Higher Categorical Structures in Algebra
• Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
• Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
• Higher Category Theory: Study of Higher Categorical Structures
• Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
• Homotopical Groups: Study of Groups with Homotopical Structure
• Homotopical Categories: Study of Categories with Homotopical Structure
• Homotopy Groups: Algebraic Invariants of Topological Spaces
• Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

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In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

• 🏫 Math Topics for High School
• 🎓 College Math Topics
• 🤔 Advanced Math
• 📚 Math Research
• ✏️ Math Education
• 💵 Business Math

🔍 References

• Number theory in everyday life.
• Logicist definitions of mathematics.
• Multivariable vs. vector calculus.
• 4 conditions of functional analysis.
• Random variable in probability theory.
• How is math used in cryptography?
• The purpose of homological algebra.
• Concave vs. convex in geometry.
• The philosophical problem of foundations.
• Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

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• Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

• The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
• An evaluation of Georg Cantor’s set theory.
• The best approaches to learning math facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use of mathematics in recreational activities.
• The five types of math used in computer science .
• Real-life applications of the Pythagorean Theorem .
• A study of the different theories of mathematical logic .
• The use of game theory in social science.
• Mathematical definitions of infinity and how to measure it.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and median using classroom math grades.
• The properties and geometry of a Möbius strip.
• Using truth tables to present the logical validity of a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Theorem.
• The use of different number types: the history.
• The application of differential geometry in modern architecture.
• A mathematical approach to the solution of a Rubik’s Cube.
• Comparison of predictive and prescriptive statistical analyses.
• Explaining the iterations of the Koch snowflake.
• The importance of limits in calculus.
• Hexagons as the most balanced shape in the universe.
• The emergence of patterns in chaos theory.
• What were Euclid’s contributions to the field of mathematics?
• The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

• Explain what we need Pythagoras’ theorem for. 
• What is a hyperbola? 
• Describe the difference between algebra and arithmetic. 
• When is it unnecessary to use a calculator ? 
• Find a connection between math and the arts. 
• How do you solve a linear equation? 
• Discuss how to determine the probability of rolling two dice. 
• Is there a link between philosophy and math? 
• What types of math do you use in your everyday life? 
• What is the numerical data? 
• Explain how to use the binomial theorem. 
• What is the distributive property of multiplication? 
• Discuss the major concepts in ancient Egyptian mathematics . 
• Why do so many students dislike math? 
• Should math be required in school? 
• How do you do an equivalent transformation? 
• Why do we need imaginary numbers? 
• How can you calculate the slope of a curve? 
• What is the difference between sine, cosine, and tangent? 
• How do you define the cross product of two vectors? 
• What do we use differential equations for? 
• Investigate how to calculate the mean value. 
• Define linear growth. 
• Give examples of different number types. 
• How can you solve a matrix? 

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

• What do we need n-dimensional spaces for?
• Explain how card counting works.
• Discuss the difference between a discrete and a continuous probability distribution .
• How does encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math problem unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?  
• Discuss the core problems of computational geometry. 
• Explain the use of set theory . 
• What do we need Boolean functions for? 
• Describe the main topological concepts in modern mathematics. 
• Investigate the properties of a rotation matrix. 
• Analyze the practical applications of game theory.  
• How can you solve a Rubik’s cube mathematically? 
• Explain the math behind the Koch snowflake. 
• Describe the paradox of Gabriel’s Horn. 
• How do fractals form? 
• Find a way to solve Sudoku using math. 
• Why is the Riemann hypothesis still unsolved? 
• Discuss the Millennium Prize Problems. 
• How can you divide complex numbers? 
• Analyze the degrees in polynomial functions. 
• What are the most important concepts in number theory? 
• Compare the different types of statistical methods . 

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

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• What is an abelian group?
• Explain the orbit-stabilizer theorem.
• Discuss what makes the Burnside problem influential.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
• How do the two Picard theorems relate to each other?
• When is a trigonometric series called a Fourier series?
• Give an example of an algorithm used for machine learning .
• Compare the different types of knapsack problems.
• What is the minimum overlap problem?
• Describe the Bernoulli scheme.
• Give a formal definition of the Chinese restaurant process.
• Discuss the logistic map in relation to chaos .
• What do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of the Fibonacci sequence.
• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• How can you use elementary embeddings in model theory?
• Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
• How is Lie algebra used in physics ?
• Define various cases of algebraic cycles.
• Why do we need étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Why are unsolved math problems significant?
• Find reasons for the gender gap in math students.
• What are the toughest mathematical questions asked today?
• Examine the notion of operator spaces.
• How can we design a train schedule for a whole country?
• What makes a number big?

• How can infinities have various sizes?
• What is the best mathematical strategy to win a game of Go?
• Analyze natural occurrences of random walks in biology.
• Explain what kind of mathematics was used in ancient Persia.
• Discuss how the Iwasawa theory relates to modular forms.
• What role do prime numbers play in encryption ?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How can you use them?
• What is the best mathematical way to find someone who is lost in a maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Describe how barcodes function.
• Study some real-life examples of chaos theory. How do you define them mathematically?
• Compare the impact of various ground-breaking mathematical equations .
• Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
• Discuss Fisher’s fundamental theorem of natural selection.
• How does quantum computing work?
• Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

• Compare traditional methods of teaching math with unconventional ones.
• How can you improve mathematical education in the U.S.?
• Describe ways of encouraging girls to pursue careers in STEM fields.
• Should computer programming be taught in high school?
• Define the goals of mathematics education .
• Research how to make math more accessible to students with learning disabilities .
• At what age should children begin to practice simple equations?
• Investigate the effectiveness of gamification in algebra classes.
• What do students gain from taking part in mathematics competitions?
• What are the benefits of moving away from standardized testing ?
• Describe the causes of “ math anxiety .” How can you overcome it?
• Explain the social and political relevance of mathematics education.
• Define the most significant issues in public school math teaching.
• What is the best way to get children interested in geometry?
• How can students hone their mathematical thinking outside the classroom?
• Discuss the benefits of using technology in math class.
• In what way does culture influence your mathematical education?
• Explore the history of teaching algebra .
• Compare math education in various countries.

• How does dyscalculia affect a student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standards ?
• What are the advantages of following an integrated curriculum in math?
• Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

• Give an example of an induction proof.
• What are F-algebras used for?
• What are number problems?
• Show the importance of abstract algebraic thinking .
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of Boolean algebra?
• Explore the relationship between algebra and geometry.
• Compare the differences between commutative and noncommutative algebra.
• Why is Brun’s constant relevant?
• How do you factor quadratics?
• Explain Descartes’ Rule of Signs.
• What is the quadratic formula?
• Compare the four types of sequences and define them.
• Explain how partial fractions work.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and eigenvalues.
• Analyze the Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in algebra.
• What can you do with determinants?
• Learn about the origin of the distance formula.
• Find the best way to solve math word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory .

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids? 
• Find real-life uses for a rhombicosidodecahedron. 
• What is studied in projective geometry? 
• Compare the most common types of transformations. 
• Explain how acute square triangulation works. 
• Discuss the Borromean ring configuration. 
• Investigate the solutions to Buffon’s needle problem. 
• What is unique about right triangles? 

• Describe the notion of Dirac manifolds.
• Compare the various relationships between lines.
• What is the Klein bottle?
• How does geometry translate into other disciplines, such as chemistry and physics?
• Explore Riemannian manifolds in Euclidean space.
• How can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden ratio .
• Describe the importance of circles.
• Investigate what the ancient Greeks knew about geometry.
• What does congruency mean?
• Study the uses of Euler’s formula.
• How do CT scans relate to geometry?
• Why do we need n-dimensional vectors?
• How can you solve Heesch’s problem?
• What are hypercubes?
• Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

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• What are the differences between trigonometry, algebra, and calculus?
• Explain the concept of limits.
• Describe the standard formulas needed for derivatives.
• How can you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How do you define the area between curves?
• What is the foundation of calculus?

• How does multivariate calculus work?
• Discuss the use of Stokes’ theorem.
• What does Leibniz’s integral rule state?
• What is the Itô stochastic integral?
• Explore the influence of nonstandard analysis on probability theory.
• Research the origins of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explain the extreme value theorem.
• What do we need predicate calculus for?
• What are linear approximations?
• When does an integral become improper?
• Describe the Ratio and Root Tests.
• How does the method of rings work?
• Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

• What are the essential skills needed for business math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is a discount factor?
• How do you know that an investment is reasonable?
• When does it make sense to pay a loan with another loan?
• Find useful financing techniques that everyone can use.
• How does critical path analysis work?
• Explain how loans work.
• Which areas of work utilize operations research?
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Compare the uses of different chart types.
• What causes a stock market crash?
• How can you calculate the net present value?
• Explore the history of revenue management .
• When do you use multi-period models?
• Explain the consequences of depreciation.
• Are annuities a good investment?
• Would the U.S. financially benefit from discontinuing the penny?
• What caused the United States housing crash in 2008?
• How do you calculate sales tax?
• Describe the notions of markups and markdowns.
• Investigate the math behind debt amortization.
• What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

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• The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
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Mathematics Research Paper Topics

See our list of mathematics research paper topics . Mathematics is the science that deals with the measurement, properties, and relationships of quantities, as expressed in either numbers or symbols. For example, a farmer might decide to fence in a field and plant oats there. He would have to use mathematics to measure the size of the field, to calculate the amount of fencing needed for the field, to determine how much seed he would have to buy, and to compute the cost of that seed. Mathematics is an essential part of every aspect of life—from determining the correct tip to leave for a waiter to calculating the speed of a space probe as it leaves Earth’s atmosphere.

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• Boolean algebra
• Chaos theory
• Complex numbers
• Correlation
• Fraction, common
• Game theory
• Graphs and graphing
• Imaginary number
• Multiplication
• Natural numbers
• Number theory
• Numeration systems
• Probability theory
• Proof (mathematics)
• Pythagorean theorem
• Trigonometry

Mathematics undoubtedly began as an entirely practical activity— measuring fields, determining the volume of liquids, counting out coins, and the like. During the golden era of Greek science, between about the sixth and third centuries B.C., however, mathematicians introduced a new concept to their study of numbers. They began to realize that numbers could be considered as abstract concepts. The number 2, for example, did not necessarily have to mean 2 cows, 2 coins, 2 women, or 2 ships. It could also represent the idea of “two-ness.” Modern mathematics, then, deals both with problems involving specific, concrete, and practical number concepts (25,000 trucks, for example) and with properties of numbers themselves, separate from any practical meaning they may have (the square root of 2 is 1.4142135, for example).

Fields of Mathematics

Mathematics can be subdivided into a number of special categories, each of which can be further subdivided. Probably the oldest branch of mathematics is arithmetic, the study of numbers themselves. Some of the most fascinating questions in modern mathematics involve number theory. For example, how many prime numbers are there? (A prime number is a number that can be divided only by 1 and itself.) That question has fascinated mathematicians for hundreds of years. It doesn’t have any particular practical significance, but it’s an intriguing brainteaser in number theory.

Geometry, a second branch of mathematics, deals with shapes and spatial relationships. It also was established very early in human history because of its obvious connection with practical problems. Anyone who wants to know the distance around a circle, square, or triangle, or the space contained within a cube or a sphere has to use the techniques of geometry.

Algebra was established as mathematicians recognized the fact that real numbers (such as 4 and 5.35) can be represented by letters. It became a way of generalizing specific numerical problems to more general situations.

Analytic geometry was founded in the early 1600s as mathematicians learned to combine algebra and geometry. Analytic geometry uses algebraic equations to represent geometric figures and is, therefore, a way of using one field of mathematics to analyze problems in a second field of mathematics.

Over time, the methods used in analytic geometry were generalized to other fields of mathematics. That general approach is now referred to as analysis, a large and growing subdivision of mathematics. One of the most powerful forms of analysis—calculus—was created almost simultaneously in the early 1700s by English physicist and mathematician Isaac Newton (1642–1727) and German mathematician Gottfried Wilhelm Leibniz (1646–1716). Calculus is a method for analyzing changing systems, such as the changes that take place as a planet, star, or space probe moves across the sky.

Statistics is a field of mathematics that grew in significance throughout the twentieth century. During that time, scientists gradually came to realize that most of the physical phenomena they study can be expressed not in terms of certainty (“A always causes B”), but in terms of probability (“A is likely to cause B with a probability of XX%”). In order to analyze these phenomena, then, they needed to use statistics, the field of mathematics that analyzes the probability with which certain events will occur.

Each field of mathematics can be further subdivided into more specific specialties. For example, topology is the study of figures that are twisted into all kinds of bizarre shapes. It examines the properties of those figures that are retained after they have been deformed.

Back to Science Research Paper Topics .

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Applied mathematics articles from across Nature Portfolio

Applied mathematics is the application of mathematical techniques to describe real-world systems and solve technologically relevant problems. This can include the mechanics of a moving body, the statistics governing the atoms in a gas or developing more efficient algorithms for computational analysis. These ideas are closely linked with those of theoretical physics.

Latest Research and Reviews

Quantitative analysis and stochastic modeling of osteophyte formation and growth process on human vertebrae based on radiographs: a follow-up study

• Changxi Wang

A comparative study of J–A and Preisach improved models for core loss calculation under DC bias

• Zhichao Luo

Medical equipment effectiveness evaluation model based on cone-constrained DEA and attention-based bi-LSTM

• Luying Huang

Pulsatile nanofluid flow with variable pressure gradient and heat transfer in wavy channel

• A. S. Dawood
• Faisal A. Kroush
• Islam M. Eldesoky

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

• Muhammad Nadeem
• Yahya Alsayaad

Long ties accelerate noisy threshold-based contagions

How is contagion affected by changes to network structure? Recent work has claimed a ‘weakness of long ties’ for complex contagions that rely on social reinforcement, unlike biological contagions. Eckles et al. substantially revise this conclusion.

• Dean Eckles
• Elchanan Mossel
• Subhabrata Sen

News and Comment

The curious case of the test set AUROC

The area under the receiver operating characteristic curve (AUROC) of the test set is used throughout machine learning (ML) for assessing a model’s performance. However, when concordance is not the only ambition, this gives only a partial insight into performance, masking distribution shifts of model outputs and model instability.

• Michael Roberts
• Carola-Bibiane Schönlieb

The role of computational science in digital twins

Digital twins hold immense promise in accelerating scientific discovery, but the publicity currently outweighs the evidence base of success. We summarize key research opportunities in the computational sciences to enable digital twin technologies, as identified by a recent National Academies of Sciences, Engineering, and Medicine consensus study report.

• Karen Willcox
• Brittany Segundo

Distilling data into code

One of the greatest limitations of deep neural networks is the difficulty of interpreting what they learn from the data. Deep distilling addresses this problem by extracting human-comprehensible and executable code from observations.

• Joseph Bakarji

Why even specialists struggle with black hole proofs

Mathematical proofs of black hole physics are becoming too complex even for specialists.

• Alejandro Penuela Diaz

Packing finite numbers of spheres efficiently

A paper in Nature Communications reports experiments and simulations of spherical particles that help show how finite numbers of spheres pack in practice.

• Zoe Budrikis

Graph theory captures hard-core exclusion

Physical networks, composed of nodes and links that occupy a spatial volume, are hard to study with conventional techniques. A meta-graph approach that elucidates the impact of physicality on network structure has now been introduced.

• Zoltán Toroczkai

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Writing math research papers: a guide for students and instructors.

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Robert Gerver

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Writing Math Research Papers  is primarily a guide for high school students that describes how to write aand present mathematics research papers. But it’s really much more than that: it’s a systematic presentation of a philosophy that writing about math helps many students to understand it, and a practical method to move students from the relatively passive role of someone doing what is assigned to them, to creative thinkers and published writers who contribute to the mathematical literature.

As experienced writers know, the actual writing is not the half of it. William Zinsser once taught a writing class at the New School for Social Research which involved no writing at all: students talked through their ideas in class and through that process discovered the real story which could be written from their tangle of experiences, hopes and dreams. The actual writing was secondary, once they understood how to find the story and organize it.

Gerver, an experienced high school mathematics teacher, takes a similar approach. The primary audience is high school students who want to prepare formal papers or presentations, for contests or for a “math day” at their high school. But the discovery, research and organizational processes involved in writing an original paper, as opposed to rehashing information from a reference book, can help any student learn and understand math, and the experience will be useful even if the paper is never written.

Gerver leads students through a discovery process beginning with examining their own knowledge of mathematics and reviewing the basics of problem solving. The “math annotation” project follows next, in which students organize their class notes for one topic for presentation to their peers, resulting in a product similar to a section of a textbook or handbook, complete with illustrations and the necessary background and review material. Practical advice about finding a topic, developing it by keeping a research journal, and creating a final product, either a research paper or oral presentation, follows.

Writing Math Research Papers  is directed primarily to students, and could be assigned as a supplementary textbook for high school mathematics classes. It will also be useful to teachers who incorporate writing into their classes or who serve as mentors to the math club, and for student teachers in similar situations. An appendix for teachers includes practical advice about helping students through the research and writing process, organizing consultations, and grading the student papers and presentations. Excerpts from student research papers are included as well, and more materials are available from the web site www.keypress.com/wmrp .

Robert Gerver, PhD, is a mathematics instructor at North Shore High School in New York. He received the Presidential Award for Excellence in Mathematical Teaching in 1988 and the Tandy Prize and Chevron Best Practices Award in Education in 1997. He has been publishing mathematics. Dr. Gerver has written eleven mathematics textbooks and numerous articles, and holds two U.S. patents for educational devices.

Sarah Boslaugh, ( [email protected] ) is a Performance Review Analyst for BJC HealthCare and an Adjunct Instructor in the Washington University School of Medicine, both in St. Louis, MO. Her books include An Intermediate Guide to SPSS Programming: Using Syntax for Data Management  (Sage, 2004), Secondary Data Sources for Public Health: A Practical Guide (Cambridge, 2007), and Statistics in a Nutshell (O'Reilly, forthcoming), and she is Editor-in-Chief of The Encyclopedia of Epidemiology (Sage, forthcoming).

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Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2023 2023.

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field , Nolberto Rezola

ALGEBRA 1 STUDENTS’ ABILITY TO RELATE THE DEFINITION OF A FUNCTION TO ITS REPRESENTATIONS , Sarah A. Thomson

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166 Extraordinary Math Research Topics For Your Papers

Math research topics cover various genres from which students can choose. Many people think that a research project on a math topic is dull. However, mathematics can be a wonderful and vivid field. Since it’s a universal language, mathematics can describe anything and everything, from galaxies that orbit each other to music. However, the broad nature of this study field also makes selecting a research paper difficult. That’s because learners want to pick interesting topics that will impress educators to award them top scores. This article lists the best math research paper topics. It’s useful because it inspires students to select or customize topics for their academic essays without much struggle.

What Are The Different Types Of Math?

As hinted, math covers several genres. Here are the primary types of mathematics:

Geometry: It’s a math branch that deals with the shapes, size, and relative position of figures. Many people consider geometry a practical math branch because it examines figures, shapes, sizes, and features of various entities, including parts like solids, lines, surfaces, lines, and angles. Algebra: It assists in solving equations and manipulating symbols. This branch helps students represent unknown quantities with alphabets and use them alongside numbers. Calculus: This area is vital in determining rates of change, such as velocity and acceleration. Arithmetic: Arithmetic is the most common and oldest math branch, encompassing basis number operations. These operations include subtraction, addition, divisions, and multiplications, and some schools shorten it as BODMAS. Statistics and Probability: They help analyze numerical data to make predictions. Probability is about chances, while statistics entails handling different data using various techniques. Trigonometry: It assists in calculating angles and distances between points. It mainly deals with triangles’ relationships, sides, and curves.

Now that you understand the types of mathematics, it’s easier to select a suitable research topic. The following are some of the best topic ideas in math. 

 Undergraduate Math Research Topics

Maybe you’re pursuing your undergraduate studies. However, you have challenges comprehending math topics, yet the professor expects you to write a superior paper. In that case, here’s a list of engaging research topics in math to consider for your essays.

• An in-depth comprehension of the meaning of discrete random variables in math and their identification
• Math evolution- Comprehending the Gauss-Markov
• Primary math theorems- Investigating how they work
• Continuous stochastic process- Exploring its role in the math process
• Analyzing the Dempster-Shafer theory
• The application of the transferable belief model
• Exploring the use of math in artificial intelligence
• The application of mathematics in daily life
• Algebra and its history
• Math and culture- What’s the relationship?
• How drawing and painting could help with mathematics
• Ways to boost math interest among learners
• The social and political significance of learning mathematics
• Circles and their relevance in mathematics
• Challenges to math learning in public schools
• Prove the use of F-Algebras
• Understanding the meaning of abstract algebra
• Discuss geometry and algebra
• How acute square triangulation works
• Discuss the essence of right triangles
• Why non-Euclidean geometry should be compulsory for math students
• Investigating number problems
• Discuss the meaning of Dirac manifolds
• How geometry influences chemistry and physics
• Riemannian manifolds’ application in the Euclidean space

These are exciting math topics for undergraduate students. Nevertheless, prepare adequate time and resources to investigate any of these titles to draft a winning essay. You might have to provide theoretical and practical assessments when writing your essay.

Math Research Topics for High School Learners

Maybe your high school teacher asked you to write a research paper. Choosing a familiar topic is an excellent way to get a high grade. Here are some of the best math research paper topics for high school.

• How to draw a chart representing the financial analysis of a prominent company over the last five years
• How to solve a matrix- The vital principles and formulas to embrace
• Exploring various techniques for solving finance and mathematical gaps
• Discount factor- Why it’s crucial for learners and ways to achieve it
• Calculating the interest rate and its essence in the banking industry
• Why imaginary numbers are important
• Investigating the application of math in the workplace
• Explain why learners hate mathematics teachers
• What makes math a complex subject?
• Is making math compulsory in high school a good thing?
• How to solve a dice question from a probability perspective
• Understanding the Binomial theorem and its essence
• Investigating Egyptian mathematics
• Hyperbola- Understanding it and its use in math
• When should students use calculators in class?
• How to solve linear equations
• Is the Pythagoras theorem important in math?
• The interdependence between math and art
• Philosophy’s role in math
• Numerical data overview

High school learners can pick any of these titles and develop them into an essay. Nevertheless, they should prepare to spend some time investigating their topics to write pieces that will impress their educators. Titles that address math history and its influence on education can also suit high school students. However, learners should select titles that fulfil the academic requirements set by the educators.

Applied Math Research Topics

As a branch, applied math deals with mathematical methods and their real-life applications. These methods are manifest in engineering, finance, medicine, biology, physics, and others. Here are some of the exciting topics in this field.

• Dimensions for examining fingerprints
• Computer tomography and its significance
• Step-stress modelling- What is its importance?
• Explain the essence of data mining- How does it benefit the banking sector?
• A detailed examination of nonlinear models
• How genes discovery helps determine unhealthy and healthy patients
• Algorithms and their role in probabilistic modelling
• Mathematicians and their importance in robots’ development
• Mathematicians’ role in crime prevention and data analysis
• The essence of Law of Motion by Isaac in real life
• The importance of math in energy conservation
• Math and its role in quantum theory
• Analyzing the Lorentz symmetry features
• Evaluating the processing of the statistical signal in detail
• Explain the achievement of Galilean Transformation

These are exciting ideas to explore when writing a research paper in applied math. Nevertheless, take your time to carefully and extensively research your preferred title to write a high-quality essay. Students should also note that some topics in this category require specialized knowledge to write superior papers.

It’s a challenge to write a paper for a high grade. Sometimes every student need a professional help with college paper writing. Therefore, don’t be afraid to hire a writer to complete your assignment. Just write a message “Please, write custom research paper for me” and get time to relax. Contact us today and get a 100% original paper. 

Interesting Math Research Topics

Maybe you’re among the learners that prefer working with exciting ideas. In that case, this category has topics that will interest you.

• The uses of numerical analysis in machine learning
• Foundations and philosophical problems
• Convex versus Concave in geometry
• Homological algebra- What is its purpose?
• Is math useful in cryptography
• Probability theory and random variable
• Functional analysis- What are its four conditions?
• Vector calculus versus multivariable
• Mathematics and logicist definitions
• Ways to apply the number theory in daily life
• Studying complex math equations
• How to calculate mode, median, and mean
• Understanding the meaning of the Scholz conjecture
• The definition of the past correspondence problem
• Computational maths- What are its classes?
• Multiplication table and its importance
• What the Boolean satisfiability problem means for a learner
• Understanding the linear speedup theory in mathematics
• The Turing machine description
• Understanding the Markov algorithm
• Investigating the similarities and differences between Buchi automation and Pushdown automation
• What is the meaning of Tree automation?
• Describing the enclosing sphere method and its use in combinations
• Egyptian pyramids and calculus
• Analyzing De Finetti theorem in statistics and probability
• Examining the congruence meaning in math
• Application and purpose of calculus in the banking industry
• Jean d’Alembert’s most famous works
• Boolean algebra- What are its essential elements
• Isaac Newton- His contribution, life, and time in math
• Understanding the meaning of Sphericon
• What is the purpose of Martingales?
• Gauss times, energy, and contributions to math
• Jakob Bernoulli- Exploring his famous works
• A brief history of math

Some learners think writing a math essay is complex and tedious. However, you can find a topic you will enjoy working with throughout the project. These are exciting ideas to explore in research papers. However, prepare to spend sufficient time investigating your chosen title to write a winning paper, although these are generally relaxing titles for math papers and essays.

Math Research Topics for Middle School

Some middle school students worry about the math topics for their research. However, they can choose unique titles that will impress their teachers. Here are some of these ideas.

• The impacts of standard exam curriculum on math education
• Why is learning math so tricky?
• What is the meaning of the commutative ring in algebra?
• The Artin-Wedderburn theorem and its meaning
• How monopolists and epimorphisms differ
• Understanding the Jacobson density theorem
• How linear approximations work
• Root and ratio test definition
• Statistics role in business
• Economic lot scheduling- What does it mean?
• Causes of the stock market crash
• How many traders contribute to the New York Stock Exchange
• The history of revenue management
• Financial signs of an excellent investment
• Depreciation and its odds
• How a poor currency can benefit a country
• How math helps with debt amortization
• Ways to calculate a person’s net worth
• Distinctions in algebra, trigonometry, and calculus
• Discussing the beginning of calculus
• The essence of stochastic in math
• The meaning of limits in math
• Ways to identify a critical point in a graph
• Nonstandard analysis- What does it mean in the probability theory?
• Continuous function description and meaning
• Calculus- What are its primary principles?
• Pythagoras theorem- What are its central tenets?
• Calculus applications in finance
• Theorem value in math
• The application of linear approximations

This list has some of the best titles for middle school learners. But they also require some research to write superior essays. However, finding information on such topics is relatively easy, making them suitable for middle school students.

Math Research Topics for College Students

Maybe you’re pursuing college studies and need a title for a math research paper. In that case, here are exciting titles to consider for your essay.

• What is the purpose of n-dimensional spaces?
• Card counting- How does it work?
• How continuous probability and discrete distribution differ
• Understanding encryption- How Does it work?
• Extremal problems- Investigating them in discrete geometry
• The Mobius strip- Examining the topology
• Why can a math problem be unsolvable?
• Comparing different statistical methods
• Explain the vital number theory concepts
• Analyzing the polynomial functions’ degrees
• Ways to divide complex numbers
• Describe the prize problems with the millennium
• The reasons for the unsolved Riemann hypothesis
• Methods of solving Sudoku with math
• Explain the fractals formation
• Describe the evolution of math
• Explore different types of Tower of Hanoi solutions
• Discuss the uses of Napier’s bones
• With examples, explain the chaos theory
• Why are mathematical equations important all the time?
• Fisher’s fundamental theorem and natural selection- Why are they important?

College professors expect students to draft papers with relevant and valuable information. These are relevant titles for college students. However, they require extensive research to write winning papers.

Cool Math Topics to Research

Maybe you don’t need a complex topic for your research paper. In that case, consider any of these ideas for your essay. If you have a problem writing even with these topics and you’re thinking: “solve my math for me,” you can always reach out to our service.

• How contemporary architectural designs use geometry
• What makes some math equations complex?
• Ways to solve the Rubik’s cube
• Discuss the meaning of prescriptive statistical and predictive analysis
• Understanding the purpose of the chaos theory
• What limits calculus?- Provide relevant examples
• A comparison of universal and abstract algebra- How do they differ?
• The relationship between probability and card tricks
• Pascal’s Triangle- What does it mean?
• Mobius strip- What are its features in geometry?
• Multiple probability ideas- A brief overview
• Discuss the meaning of the Golden Ration in Renaissance period paintings
• How checkers and chess matter in understanding mathematics
• Ways to measure infinity
• Evaluating the Georg Contor theory
• Are hexagons the most balanced shapes in the world?
• The Koch snowflake- Explain the iterations
• The history of various number types and their use
• Game theory use in social science
• Five math types with significant benefits in computer science

These are some of the most excellent math education research topics. However, they also require extensive research to write high-quality papers.

Enlist the Best College Research Paper Writing Service

Perhaps, you have a topic for your paper but not the time to write a winning piece. Maybe you’re not confident in your research, analytical, and writing skills. Thus, you’re unsure that you can write an essay that will compel your educator to award you the highest grade in your class. Well, you’re not the only one. Many students seek cheap research papers due to varied reasons. Whether it’s limited time and resources or a lack of the necessary skills and experience in academic paper writing, our crew can help you. We offer affordable college paper writing services and help in various math branches. Our experts can assist you if you need help with math research topics for high school students, college, or undergraduates. We are a professional team with a reputation for providing the best-rated academic writing assistance. Whether in university, college, or high school, our crew will offer the service you need to excel academically. Contact us now for cheap and reliable help with your academic essays.

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Research Paper Topics on Mathematics

Research papers in mathematics usually have a set of basic requirements that apply to all students. As a rule, they relate to the format of the research work and the requirements for it. Students need to adhere to a specific font, spacing, and writing format. It is necessary to have a title page of the research paper and the project, as well as the correct text formatting with recommendations and pagination.

Students must adhere to a clear heading hierarchy in research work and adhere to the correct abbreviations and formulas in the design of the entire project. As a rule, research work associated with the use of certain drawings, tables, diagrams, and graphs. Also, there may be charts which must also be marked following the requirements.

Students must reveal the topic given to them and bring clear arguments in favor of their statements. It should be a full-fledged mathematics research topic that fully reveals the theme and provides the reader with real evidence of opinion. It's important to choose an interesting math research topic.

The main task for each student is to relate everything they plan to write with one Topic. It will allow the teacher not to waste time looking for information and get the opportunity to see holistic work that fully meets all the established requirements. Students should also check the practical part as mathematics is an exact science that does not tolerate assumptions. So, let's take a look at the math research topics for middle schools.

Algebra & Algebraic Geometry

Algebra and algebraic geometry are the oldest branches of this science. This section arose as a result of the need to solve arithmetic problems of the same type. Now, this is a huge branch of science, which is extremely important because of its ability to make accurate calculations and definitions in various areas of our life. Choose any research topic for mathematics that suits you well.

• Formality in Deformation Theory
• The World of P-adic Numbers
• Toric Geometry and Mirror Symmetry
• Algebraic Geometry and Singularity Theory
• P-adic Dynamics and Applications of P-adic Numbers in Other Sciences
• Algebraic Geometry New Trends: The height Functions in Modern Science
• Theory of Height Functions & in Math

Algebraic Topology

This section of typology studies topological spaces using the juxtaposition of algebraic objects. At the moment, it is one of the more popular offshoots that uses homotopy groups and homomorphism. Any research topic in mathematics is a chance to create a good paper. This area of mathematics is popular thanks to several scientific studies. Here is a list of paper themes, but you can also find math education research topics by yourself.

• Main Calculus Functions and How to Use it in Real Life
• The Calculus of Functors and Applications
• How to Use the Algebraic Models for Spaces in Real Life
• New Wave of Automorphisms in Math
• The Asymptotic Properties of Polynomials in Higher Dimensions
• Moduli Spaces Geometry: Main Features
• The Lefschetz Properties and Main Parameters
• The Group Theory in Mathematics: Main Benefits
• Automorphisms of Manifolds and Related Options
• Modern Trends in Algebraic Topology and How to Use it Properly

Analysis & PDEs

This list of topics can be especially interesting for those who want to develop methods for solving equations of mathematical physics. Let's proceed to researchable topics in mathematics. In particular, students can create their work based on the approximation of the differential operator and use numerical methods to solve the tasks and open the topic of scientific research.

• Regularity Theory for Linear, Semilinear, and Fully Nonlinear Elliptic and Parabolic Equation
• New Theory for Linear, Semilinear, and Nonlinear Functions
• Qualitative Properties of Solutions to Reaction-diffusion Equations
• The Analysis of Problems in Mathematical Physics and Mathematical Modeling
• Delay Equations Formulation of Structured Population Dynamics
• Fractional differential equations and Fractals
• Mathematical Modeling of Ecological Systems and Epidemic Systems
• Delay Differential Equations is One Best Research Area in Mathematics.

According to many historians, the foundations of geometry were laid by the ancient Greeks, who took over from the Egyptians some mathematical calculations and general principles. This section received such a name in 1822. Nevertheless, all the foundations and important stages of this science branch were laid many centuries ago. Here are the applied mathematics research topics.

• The Bending Active Approach In Lightweight Design
• The Need Of Geometry In Orthodontics
• Archimedes Theory of a Circle ABCD and a Triangle K
• Applications of Toric Geometry to Geometric Representation Theory
• Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations
• Geometric Constructions of Mapping Cones in the Fukaya Category
• Euclidean and Non-Euclidean Geometries. Going Beyond the Space, We Used to know

Mathematical Logic & Foundations

This branch of mathematics may be of interest to those who want to study the nature of mathematical proof in general and various mathematical judgments as a branch of informal logic. In many respects, the foundation of this science was laid by Aristotle. Nevertheless, mathematical logic is developing in our time. Therefore, this is a good basis for scientific work.

• Deductive Parsing of Visual Languages
• Reduction of the Yablo paradox
• Gödel's: Minds are not Machines
• Ways to use the Mathematical logic in data science
• Applied Propositional Logic and digital circuit design
• Category Theory and Model Theory of Constructive Systems
• Constructive Mathematics and Point-free Methods in Topology and Analysis
• Ways to Use Martin-Löf type Theory and Univalent Foundations in Real Life

Number Theory

This is one of the popular branches of mathematics, consisting of many areas such as the Euclidean algorithm, continued fractions, Diophantine equations, and farm theory. At the moment, this industry has a lot of interesting topics to write a research paper. That's why you can find interesting mathematical topics.

• Writing Pi As the Sum of Arctangents With Recurring Linear Sequences, the Golden Mean and Lucas Numbers
• Binary Options Winning Formula: Make Consistent Wins Every Time
• A Theory of Numbers and New Operations
• The Twin Prime Conjecture in a Number Theory
• Pythagorean Triplets (Alternative Approach, Algebraic Operations, Dual of Given Triplets, and New Observations)
• A New Theory of Numbers: The Latest Discoveries in Mathematics
• Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs
• A Clever Way To Factor One Less A Perfect Square
• How to use Number Theory to fight with gender stereotypes
• Goldbachs Twin Prime Conjecture

Probability & Statistics

By choosing this direction of mathematics, you can write a lot of interesting materials on modeling and data distribution and the study of two-dimensional numerical data. This is a particularly popular area of mathematics that will allow you to choose interesting topics for yourself with experiments and proofs. Let's check the research topics for mathematic paper.

• Highlighting Probability Issues in Simulated Annealing and Tabu Search
• Estimation of the Probability of Non-Response in Sampling Surveys Using Kernel Density Estimation Methods
• Importance of Statistical Tools and Methods in Data Science
• A Statistical Approach on Experimental Study for Determining Switching Frequency of Retro Reflector Sensor Using PLC
• The Statistics Analysis on Gender: Ain't ia Woman
• Quantitative Data Management, Statistical Analysis, and Graphics Using Stata
• The Data Science and Modern Statistics: the Symbiotic Connection
• Sei Shonagon's Pillow Book as an Example of Probability & Statistics Processes
• The Weibull Length Biased Exponential Distribution: Statistical Properties and Applications
• Univariate and Bivariate Transformations

Representation Theory

This branch of mathematics is especially interesting due to algebraic structures and linear transformations of vector spaces. Students can use Number Theory and Differential Geometry to describe certain nuances of Fourier theory or use topological groups to prove new theories. Here you can choose an undergraduate math research topic.

• Computing Modular Forms for the Weil Representation
• Combinatorics of the Asymmetric Simple Exclusion Process
• The Representation Theory & Asymmetric Simple Exclusion
• The Weil Representation in Tropical Mathematics
• Camel and Cactus Test in Representation Theory
• Combinatorics and Computations in Tropical Mathematics
• Quaternionic Representation and Its Use in Real Life
• The Modern Trends in Representation Theory of Diffeomorphism Groups

How to Write a Research Paper on Mathematics?

As we wrote earlier, teachers are very scrupulous about the correct design and writing of research papers. And interesting math research paper topics are a must. First of all, you need to write a clear introduction and structure of all your work. It is worth noting that you need formal and informal exposure, as well as bringing evidence of your work. One of the sections there will be special recommendations that depend on a particular educational institution.

You should understand that any such work requires a clear technical design and the ghost of the necessary graphs, tables, formulas, and calculations. The most important task of such research papers is to provide clear and evidence of your point of view to argue for each point and paragraph of your work. This is the key aspect, without which you do not get good grades.

That is why you should turn to professionals if you are not confident in your abilities or want to save a little time. Our company can help you write a research paper in mathematics and accompany you until you receive your final grade. It's important to choose good research topics in mathematics education, and we are ready to help you.

An Inspiration Sources List:

• Maths At Home
• The Holy Grail for Any Student
• The Mathunion Website
• Yahoo Mathematics Page
• Computer Algebra Group
• MacTutor History of Math
• Mathematics on the Web

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100+ Amazing Algebra Topics for Research Papers

Many students seek algebra topics when writing research papers in this mathematical field. Algebra is the study field that entails studying mathematical symbols and rules for their manipulation. Algebra is the unifying thread for most mathematics, including solving elementary equations to learning abstractions like rings, groups, and fields.

In most cases, people use algebra when unsure about the exact numbers. Therefore, they replace those numbers with letters. In business, algebra helps with sales prediction. While many students dislike mathematics, avoiding algebra research paper topics is almost impossible at an advanced study level.

Therefore, this article lists topics to consider when writing a research paper in this academic field. It’s helpful because many learners struggle to find suitable topics when writing research papers in this field.

How to Write Theses on Advanced Algebra Topics

A thesis on an algebra topic is an individual project that the learner writes after investigating and studying a specific idea. Here’s a step-by-step guide for writing a thesis on an algebra topic.

Pick a topic: Start by selecting a title for your algebra thesis. Your topic should relate to your research interests and your supervisor’s guidelines. Investigate your topic: Once you’ve chosen a topic, research it extensively to know the relevant theories, formulas, and texts. Your thesis should be an extension of a particular topic’s analysis and a report on your research. Write the thesis: Once you’ve explored the topic extensively, start writing your paper. Your dissertation should have an abstract, an introduction, the body, and a conclusion.

The abstract should summarise your thesis’ aims, scope, and conclusions. The introduction should introduce the topic, size, and significance while providing relevant literature and outlining the logical structure. The body should have several chapters with details and proofs of numerical implementations, while the conclusion should restate your main arguments and tell readers the effects. Also, it should suggest future work.

College Algebra Topics

You may need topics to consider if you’re in college and want to write an algebra research paper. Here’s a list of titles worth considering for your essay.

• Exploring the relationship between Rubik’s cube and the group theory
• Comparing the relationship between various equation systems
• Finding the most appropriate way to solve mathematical word problems
• Investigating the distance formula and its origin
• Exploring the things you can achieve with determinants
• Explaining what “domain” and “range” mean in algebra
• A two-dimension analysis of the Gram-Schmidt process
• Exploring the differences between eigenvalues and eigenvectors
• What the Cramer’s rule states, and why does it matter
• Describing the Gaussian elimination
• Provide an induction-proof example
• Describe the uses of F-algebras
• Understanding the number problems in algebra
• What’s the essence of abstract algebra?
• Investigating Fermat’s last theorem peculiarities
• Exploring the algebra essentials
• Investigating the relationship between geometry and algebra

These are exciting topics in college algebra. However, writing a winning paper about any of them requires careful research and analysis. Therefore, prepare to spend sufficient time working on any of these titles.

Cool Topics in Algebra

Perhaps, you want to write about an excellent topic in this mathematical field. If so, consider the following ideas for your algebra paper.

• Discussing a differential equation with illustrations
• Describing and analysing the Noetherian ring
• Explain the commutative ring from an algebra viewpoint
• Describe the Artin-Weddderburn theorem
• Studying the Jacobson density theorem
• Describe the four properties of any binary operation from an algebra viewpoint
• A detailed analysis of the unary operator
• Analysing the Abel-Ruffini theorem
• Monomorphisms versus Epimorphisms: Contrast and comparison
• Discus Morita duality with algebraic structures in mind
• Nilpotent versus Idempotent in Ring theory

Pick any idea from this list and develop it into a research topic. Your educator will love your paper and award you a good grade if you research it and write an informative essay.

Linear Algebra Topics

Linear algebra covers vector spaces and the linear mapping between them. Linear equation systems have unknowns, and mathematicians use vectors and matrices to represent them. Here are exciting topics in linear algebra to consider for your research paper.

• Decomposition of singular value
• Investigating linear independence and dependence
• Exploring projections in linear algebra
• What are linear transformations in linear algebra?
• Describe positive definite matrices
• What are orthogonal matrices?
• Describe Euclidean vector spaces with examples
• Explain how you can solve equation systems with matrices
• Determinants versus matrix inverses
• Describe mathematical operations using matrices
• Functional analysis of linear algebra
• Exploring linear algebra and its fundamentals

These are some of the exciting project topics in linear algebra. Nevertheless, prepare sufficient resources and time to investigate any of these titles to write a winning paper.

Pre Algebra Topics

Are you interested in a pre-algebra research topic? If so, this category has some of the most exciting ideas to explore.

• Investigating the importance of pre-algebra
• The best way to start pre-algebra for a beginner
• Pre-algebra and algebra- Which is the hardest and why?
• Core lessons in pre-algebra
• What follows pre-algebra?
• The first things to learn in pre-algebra
• Investigating the standard form in pre-algebra
• Provide pre-algebra examples using the basic rules to evaluate expressions
• Differentiate pre-algebra and algebra
• Describe five pre-algebra formulas

Consider exploring any of these ideas if you’re interested in pre-algebra. Nevertheless, choose a title you’re comfortable with to develop a winning paper.

Intermediate Algebra Topics for Research

Perhaps, you’re interested in intermediate algebra. If so, consider any of these ideas for your research paper.

• Reviewing absolute value and real numbers
• Investigating real numbers’ operations
• Exploring the cube and square roots of real numbers
• Analysing algebraic formulas and expressions
• What are the rules of scientific notation and exponents?
• How to solve a linear inequality with a single variable
• Exploring relations, functions, and graphics from an algebraic viewpoint
• Investigating linear systems with two variables and solutions
• How to solve a linear system with two variables
• Exploring linear systems applications with two variables
• How to solve a linear system with three variables
• Gaussian elimination and matrices
• How to simplify a radical expression
• How to add and subtract a radical expression
• How to multiply and divide a radical expression
• How to extract a square root and complete the square
• Investigating quadratic functions and graphs
• How to solve a polynomial and rational inequality
• How to solve logarithmic and exponential equations
• Exploring arithmetic series and sequences

These are exciting topics in intermediate algebra to consider for research papers. Nevertheless, learners should prepare to solve equations in their work.

Algebra Topics High School Students Can Explore

Are you in high school and want to explore algebra? If yes, consider these topics for your research, they could be a great coursework help to you.

• Crucial principles and formulas to embrace when solving a matrix
• Ways to create charts on a firm’s financial analysis for the past five years
• How to find solutions to finance and mathematical gaps
• Ways to solve linear equations
• What is a linear equation- Provide examples
• Describe the substitution and elimination methods for solving equations
• How to solve logarithmic equations
• What are partial fractions?
• Describe linear inequalities with examples
• How to solve a quadratic equation by factoring
• How to solve a quadratic equation by formula
• How to solve a quadratic equation with a square completion method
• How to frame a worksheet for a quadratic equation
• Explain the relationship between roots and coefficients
• Describe rational expressions and ways to simplify them
• Describe a cubic equation roots
• What is the greatest common factor- Provide examples
• What is the least common multiple- Provide examples
• Describe the remainder theorem with examples

Explore any of these titles for your high school paper. However, pick a title you’re comfortable working with from the beginning to the end to make your work easier.

Advanced Topics in Algebra and Geometry

Maybe you want to explore something more advanced in your paper. In that case, the following list has advanced topics in geometry and algebra worth considering.

• Arithmetical structures and their algorithmic aspects
• Fractional thermoentropy spaces in topological quantum fields
• Fractional thermoentripy spaces in large-scale systems
• Eigenpoints configurations
• Investigating the higher dimension aperiodic domino problem
• Exploring math anxiety, executive functions, and math performance
• Coherent quantiles and lifting elements
• Absolute values extension on two subfields
• Reviewing the laws of form and Majorana fermions
• Studying the specialisation and rational maps degree
• Investigating mathematical-pedagogical knowledge of prospective teachers in ECD programs
• The adeles I model theory
• Exploring logarithmic vector fields, arrangements, and divisors’ freeness
• How to reconstruct curves from Hodge classes
• Investigating Eigen points configuration

These are advanced topics in algebra and geometry worth investigating. However, please prepare to explore your topic extensively to write a strong essay.

Abstract Algebra Topics

Most people study abstract algebra in college. If you’re interested in research in this area, consider these topics for your project.

• Describe abstract algebra applications
• Why is abstract algebra essential?
• Describe ring theory and its application
• What is group theory, and why does it matter?
• Describe the critical conceptual algebra levels
• Describe the fundamental theorem of the finite Abelian groups
• Describe Sylow’s theorems
• What is Polya counting?
• Describe the RSA algorithm
• What are the homomorphisms and ideals of Rings?
• Describe integral domains and factorisation
• Describe Boolean algebra and its importance
• State and explain Cauchy’s Theorem- Why is it important?

This algebra topics list is not exhaustive. You can find more ideas worth exploring in your project. Nevertheless, pick an idea you will work with comfortably to deliver a winning paper.

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8. Appendices

In the appendices you should include any data or material that supported your research but that was too long to include in the body of your paper. Materials in an appendix should be referenced at some point in the body of the report.

Some examples:

• If you wrote a computer program to generate more data than you could produce by hand, you should include the code and some sample output.

• If you collected statistical data using a survey, include a copy of the survey.

• If you have lengthy tables of numbers that you do not want to include in the body of your report, you can put them in an appendix.

Sample Write-Up

Seating unfriendly customers, a combinatorics problem.

By Lisa Honeyman February 12, 2002

The Problem

In a certain coffee shop, the customers are grouchy in the early morning and none of them wishes to sit next to another at the counter.

1. Suppose there are ten seats at the counter. How many different ways can three early morning customers sit at the counter so that no one sits next to anyone else?

2. What if there are n seats at the counter?

3. What if we change the number of customers?

4. What if, instead of a counter, there was a round table and people refused to sit next to each other?

Assumptions

I am assuming that the order in which the people sit matters. So, if three people occupy the first, third and fifth seats, there are actually 6 (3!) different ways they can do this. I will explain more thoroughly in the body of my report.

Body of the Report

At first there are 10 seats available for the 3 people to sit in. But once the first person sits down, that limits where the second person can sit. Not only can’t he sit in the now-occupied seat, he can’t sit next to it either. What confused me at first was that if the first person sat at one of the ends, then there were 8 seats left for the second person to chose from. But if the 1 st person sat somewhere else, there were only 7 remaining seats available for the second person. I decided to look for patterns. By starting with a smaller number of seats, I was able to count the possibilities more easily. I was hoping to find a pattern so I could predict how many ways the 10 people could sit without actually trying to count them all. I realized that the smallest number of seats I could have would be 5. Anything less wouldn’t work because people would have to sit next to each other. So, I started with 5 seats. I called the customers A, B, and C.

With 5 seats there is only one configuration that works.

As I said in my assumptions section, I thought that the order in which the people sit is important. Maybe one person prefers to sit near the coffee maker or by the door. These would be different, so I decided to take into account the different possible ways these 3 people could occupy the 3 seats shown above. I know that ABC can be arranged in 3! = 6 ways. (ABC, ACB, BAC, BCA, CAB, CBA). So there are 6 ways to arrange 3 people in 5 seats with spaces between them. But, there is only one configuration of seats that can be used. (The 1 st , 3 rd , and 5 th ).

Next, I tried 6 seats. I used a systematic approach to show that there are 4 possible arrangements of seats. This is how my systematic approach works:

Assign person A to the 1 st seat. Put person B in the 3 rd seat, because he can’t sit next to person A. Now, person C can sit in either the 5 th or 6 th positions. (see the top two rows in the chart, below.) Next suppose that person B sits in the 4 th seat (the next possible one to the right.) That leaves only the 6 th seat free for person C. (see row 3, below.) These are all the possible ways for the people to sit if the 1 st seat is used. Now put person A in the 2 nd seat and person B in the 4 th . There is only one place where person C can sit, and that’s in the 6 th position. (see row 4, below.) There are no other ways to seat the three people if person A sits in the 2 nd seat. So, now we try putting person A in the 3 rd seat. If we do that, there are only 4 seats that can be used, but we know that we need at least 5, so there are no more possibilities.

Possible seats 3 people could occupy if there are 6 seats

Once again, the order the people sit in could be ABC, BAC, etc. so there are 4 * 6 = 24 ways for the 3 customers to sit in 6 seats with spaces between them.

I continued doing this, counting how many different groups of seats could be occupied by the three people using the systematic method I explained. Then I multiplied that number by 6 to account for the possible permutations of people in those seats. I created the following table of what I found.

Next I tried to come up with a formula. I decided to look for a formula using combinations or permutations. Since we are looking at 3 people, I decided to start by seeing what numbers I would get if I used n C 3 and n P 3 .

3 C 3 = 1   4 C 3 = 4   5 C 3 = 10   6 C 3 = 20

3 P 3 = 6   4 P 3 = 24   5 P 3 = 60   6 P 3 = 120

Surprisingly enough, these numbers matched the numbers I found in my table. However, the n in n P r and n C r seemed to be two less than the total # of seats I was investigating. 

Conjecture 1:

Given n seats at a lunch counter, there are n -2 C 3 ways to select the three seats in which the customers will sit such that no customer sits next to another one. There are n -2 P 3 ways to seat the 3 customers in such a way than none sits next to another.

After I found a pattern, I tried to figure out why n -2 C 3 works. (If the formula worked when order didn’t matter it could be easily extended to when the order did, but the numbers are smaller and easier to work with when looking at combinations rather than permutations.)

In order to prove Conjecture 1 convincingly, I need to show two things:

(1) Each n – 2 seat choice leads to a legal n seat configuration.

(2) Each n seat choice resulted from a unique n – 2 seat configuration.

To prove these two things I will show

And then conclude that these two procedures are both functions and therefore 1—1.

Claim (1): Each ( n – 2) -seat choice leads to a legal n seat configuration.

Suppose there were only n – 2 seats to begin with. First we pick three of them in which to put people, without regard to whether or not they sit next to each other. But, in order to guarantee that they don’t end up next to another person, we introduce an empty chair to the right of each of the first two people. It would look like this:

We don’t need a third “new” seat because once the person who is farthest to the right sits down, there are no more customers to seat. So, we started with n – 2 chairs but added two for a total of n chairs. Anyone entering the restaurant after this procedure had been completed wouldn’t know that there had been fewer chairs before these people arrived and would just see three customers sitting at a counter with n chairs. This procedure guarantees that two people will not end up next to each other. Thus, each ( n – 2)-seat choice leads to a unique, legal n seat configuration.

Therefore, positions s 1 ' s 2 ', and s 3 ' are all separated by at least one vacant seat.

This is a function that maps each combination of 3 seats selected from n – 2 seats onto a unique arrangement of n seats with 3 separated customers. Therefore, it is invertible.

Claim (2): Each 10-seat choice has a unique 8-seat configuration.

Given a legal 10-seat configuration, each of the two left-most diners must have an open seat to his/her right. Remove it and you get a unique 8-seat arrangement. If, in the 10-seat setting, we have q 1 > q 2 , q 3 ; q 3 – 1 > q 2 , and q 2 – 1 > q 1 , then the 8 seat positions are q 1 ' = q 2 , q 2 ' = q 2 – 1, and q 3 ' = q 3 – 2. Combining these equations with the conditions we have

q 2 ' = q 2 – 1 which implies q 2 ' > q 1 = q 1 '

q 3 ' = q 3 – 2 which implies q 3 ' > q 2 – 1 = q 2 '

Since q 3 ' > q 2 ' > q 1 ', these seats are distinct. If the diners are seated in locations q 1 , q 2 , and q 3 (where q 3 – 1 > q 2 and q 2 – 1 > q 1 ) and we remove the two seats to the right of q 1 and q 2 , then we can see that the diners came from q 1 , q 2 – 1, and q 3 – 2. This is a function that maps a legal 10-seat configuration to a unique 8-seat configuration.

The size of a set can be abbreviated s ( ). I will use the abbreviation S to stand for n separated seats and N to stand for the n – 2 non-separated seats.

therefore s ( N ) = s ( S ).

Because the sets are the same size, these functions are 1—1.

Using the technique of taking away and adding empty chairs, I can extend the problem to include any number of customers. For example, if there were 4 customers and 10 seats there would be 7 C 4 = 35 different combinations of chairs to use and 7 P 4 = 840 ways for the customers to sit (including the fact that order matters). You can imagine that three of the ten seats would be introduced by three of the customers. So, there would only be 7 to start with.

In general, given n seats and c customers, we remove c- 1 chairs and select the seats for the c customers. This leads to the formula n -( c -1) C c = n - c +1 C c for the number of arrangements.

Once the number of combinations of seats is found, it is necessary to multiply by c ! to find the number of permutations. Looking at the situation of 3 customers and using a little algebraic manipulation, we get the n P 3 formula shown below.

This same algebraic manipulation works if you have c people rather than 3, resulting in n - c +1 P c

Answers to Questions

• With 10 seats there are 8 P 3 = 336 ways to seat the 3 people.
• My formula for n seats and 3 customers is: n -2 P 3 .
• My general formula for n seats and c customers, is: n -( c -1) P c = n - c +1 P c

_________________________________________________________________ _

After I finished looking at this question as it applied to people sitting in a row of chairs at a counter, I considered the last question, which asked would happen if there were a round table with people sitting, as before, always with at least one chair between them.

I went back to my original idea about each person dragging in an extra chair that she places to her right, barring anyone else from sitting there. There is no end seat, so even the last person needs to bring an extra chair because he might sit to the left of someone who has already been seated. So, if there were 3 people there would be 7 seats for them to choose from and 3 extra chairs that no one would be allowed to sit in. By this reasoning, there would be 7 C 3 = 35 possible configurations of chairs to choose and 7 P 3 = 840 ways for 3 unfriendly people to sit at a round table.

Conjecture 2: Given 3 customers and n seats there are n -3 C 3 possible groups of 3 chairs which can be used to seat these customers around a circular table in such a way that no one sits next to anyone else.

My first attempt at a proof: To test this conjecture I started by listing the first few numbers generated by my formula:

When n = 6    6-3 C 3 = 3 C 3 = 1

When n = 7    7-3 C 3 = 4 C 3 = 4

When n = 8    8-3 C 3 = 5 C 3 = 10

When n = 9    9-3 C 3 = 6 C 3 = 20

Then I started to systematically count the first few numbers of groups of possible seats. I got the numbers shown in the following table. The numbers do not agree, so something is wrong — probably my conjecture!

I looked at a circular table with 8 people and tried to figure out the reason this formula doesn’t work. If we remove 3 seats (leaving 5) there are 10 ways to select 3 of the 5 remaining chairs. ( 5 C 3 ).

The circular table at the left in the figure below shows the n – 3 (in this case 5) possible chairs from which 3 will be randomly chosen. The arrows point to where the person who selects that chair could end up. For example, if chair A is selected, that person will definitely end up in seat #1 at the table with 8 seats. If chair B is selected but chair A is not, then seat 2 will end up occupied. However, if chair A and B are selected, then the person who chose chair B will end up in seat 3 . The arrows show all the possible seats in which a person who chose a particular chair could end. Notice that it is impossible for seat #8 to be occupied. This is why the formula 5 C 3 doesn’t work. It does not allow all seats at the table of 8 to be chosen.

The difference is that in the row-of-chairs-at-a-counter problem there is a definite “starting point” and “ending point.” The first chair can be identified as the one farthest to the left, and the last one as the one farthest to the right. These seats are unique because the “starting point” has no seat to the left of it and the “ending point” has no seat to its right. In a circle, it is not so easy.

Using finite differences I was able to find a formula that generates the correct numbers:

Proof: We need to establish a “starting point.” This could be any of the n seats. So, we select one and seat person A in that seat. Person B cannot sit on this person’s left (as he faces the table), so we must eliminate that as a possibility. Also, remove any 2 other chairs, leaving ( n – 4) possible seats where the second person can sit. Select another seat and put person B in it. Now, select any other seat from the ( n – 5) remaining seats and put person C in that. Finally, take the two seats that were previously removed and put one to the left of B and one to the left of C.

The following diagram should help make this procedure clear.

In a manner similar to the method I used in the row-of-chairs-at-a-counter problem, this could be proven more rigorously.

An Idea for Further Research:

Consider a grid of chairs in a classroom and a group of 3 very smelly people. No one wants to sit adjacent to anyone else. (There would be 9 empty seats around each person.) Suppose there are 16 chairs in a room with 4 rows and 4 columns. How many different ways could 3 people sit? What if there was a room with n rows and n columns? What if it had n rows and m columns?

References:

Abrams, Joshua. Education Development Center, Newton, MA. December 2001 - February 2002. Conversations with my mathematics mentor.

Brown, Richard G. 1994. Advanced Mathematics . Evanston, Illinois. McDougal Littell Inc. pp. 578-591

The Oral Presentation

Giving an oral presentation about your mathematics research can be very exciting! You have the opportunity to share what you have learned, answer questions about your project, and engage others in the topic you have been studying. After you finish doing your mathematics research, you may have the opportunity to present your work to a group of people such as your classmates, judges at a science fair or other type of contest, or educators at a conference. With some advance preparation, you can give a thoughtful, engaging talk that will leave your audience informed and excited about what you have done.

Planning for Your Oral Presentation

In most situations, you will have a time limit of between 10 and 30 minutes in which to give your presentation. Based upon that limit, you must decide what to include in your talk. Come up with some good examples that will keep your audience engaged. Think about what vocabulary, explanations, and proofs are really necessary in order for people to understand your work. It is important to keep the information as simple as possible while accurately representing what you’ve done. It can be difficult for people to understand a lot of technical language or to follow a long proof during a talk. As you begin to plan, you may find it helpful to create an outline of the points you want to include. Then you can decide how best to make those points clear to your audience.

You must also consider who your audience is and where the presentation will take place. If you are going to give your presentation to a single judge while standing next to your project display, your presentation will be considerably different than if you are going to speak from the stage in an auditorium full of people! Consider the background of your audience as well. Is this a group of people that knows something about your topic area? Or, do you need to start with some very basic information in order for people to understand your work? If you can tailor your presentation to your audience, it will be much more satisfying for them and for you.

No matter where you are presenting your speech and for whom, the structure of your presentation is very important. There is an old bit of advice about public speaking that goes something like this: “Tell em what you’re gonna tell ’em. Tell ’em. Then tell ’em what you told ’em.” If you use this advice, your audience will find it very easy to follow your presentation. Get the attention of the audience and tell them what you are going to talk about, explain your research, and then following it up with a re-cap in the conclusion.

Writing Your Introduction

Your introduction sets the stage for your entire presentation. The first 30 seconds of your speech will either capture the attention of your audience or let them know that a short nap is in order. You want to capture their attention. There are many different ways to start your speech. Some people like to tell a joke, some quote famous people, and others tell stories.

Here are a few examples of different types of openers.

You can use a quote from a famous person that is engaging and relevant to your topic. For example:

• Benjamin Disraeli once said, “There are three kinds of lies: lies, damn lies, and statistics.” Even though I am going to show you some statistics this morning, I promise I am not going to lie to you! Instead, . . .

• The famous mathematician, Paul Erdös, said, “A Mathematician is a machine for turning coffee into theorems.” Today I’m here to show you a great theorem that I discovered and proved during my mathematics research experience. And yes, I did drink a lot of coffee during the project!

• According to Stephen Hawking, “Equations are just the boring part of mathematics.” With all due respect to Dr. Hawking, I am here to convince you that he is wrong. Today I’m going to show you one equation that is not boring at all!

Some people like to tell a short story that leads into their discussion.

“Last summer I worked at a diner during the breakfast shift. There were 3 regular customers who came in between 6:00 and 6:15 every morning. If I tell you that you didn’t want to talk to these folks before they’ve had their first cup of coffee, you’ll get the idea of what they were like. In fact, these people never sat next to each other. That’s how grouchy they were! Well, their anti-social behavior led me to wonder, how many different ways could these three grouchy customers sit at the breakfast counter without sitting next to each other? Amazingly enough, my summer job serving coffee and eggs to grouchy folks in Boston led me to an interesting combinatorics problem that I am going to talk to you about today.”

A short joke related to your topic can be an engaging way to start your speech.

It has been said that there are three kinds of mathematicians: those who can count and those who can’t.

All joking aside, my mathematics research project involves counting. I have spent the past 8 weeks working on a combinatorics problem.. . .

To find quotes to use in introductions and conclusions try: http://www.quotationspage.com/

To find some mathematical quotes, consult the Mathematical Quotation Server: http://math.furman.edu/~mwoodard/mquot.html

To find some mathematical jokes, you can look at the “Profession Jokes” web site: http://www.geocities.com/CapeCanaveral/4661/projoke22.htm

There is a collection of math jokes compiled by the Canadian Mathematical Society at http://camel.math.ca/Recreation/

After you have the attention of your audience, you must introduce your research more formally. You might start with a statement of the problem that you investigated and what lead you to choose that topic. Then you might say something like this,

“Today I will demonstrate how I came to the conclusion that there are n ( n  – 4)( n  – 5) ways to seat 3 people at a circular table with n seats in such a way that no two people sit next to each other. In order to do this I will first explain how I came up with this formula and then I will show you how I proved it works. Finally, I will extend this result to tables with more than 3 people sitting at them.”

By providing a brief outline of your talk at the beginning and reminding people where you are in the speech while you are talking, you will be more effective in keeping the attention of your audience. It will also make it much easier for you to remember where you are in your speech as you are giving it.

The Middle of Your Presentation

Because you only have a limited amount of time to present your work, you need to plan carefully. Decide what is most important about your project and what you want people to know when you are finished. Outline the steps that people need to follow in order to understand your research and then think carefully about how you will lead them through those steps. It may help to write your entire speech out in advance. Even if you choose not to memorize it and present it word for word, the act of writing will help you clarify your ideas. Some speakers like to display an outline of their talk throughout their entire presentation. That way, the audience always knows where they are in the presentation and the speaker can glance at it to remind him or herself what comes next.

An oral presentation must be structured differently than a written one because people can’t go back and “re-read” a complicated section when they are at a talk. You have to be extremely clear so that they can understand what you are saying the first time you say it. There is an acronym that some presenters like to remember as they prepare a talk: “KISS.” It means, “Keep It Simple, Student.” It may sound silly, but it is good advice. Keep your sentences short and try not to use too many complicated words. If you need to use technical language, be sure to define it carefully. If you feel that it is important to present a proof, remember that you need to keep things easy to understand. Rather than going through every step, discuss the main points and the conclusion. If you like, you can write out the entire proof and include it in a handout so that folks who are interested in the details can look at them later. Give lots of examples! Not only will examples make your talk more interesting, but they will also make it much easier for people to follow what you are saying.

It is useful to remember that when people have something to look at, it helps to hold their attention and makes it easier for them to understand what you are saying. Therefore, use lots of graphs and other visual materials to support your work. You can do this using posters, overhead transparencies, models, or anything else that helps make your explanations clear.

Using Materials

As you plan for your presentation, consider what equipment or other materials you might want use. Find out what is available in advance so you don’t spend valuable time creating materials that you will not be able to use. Common equipment used in talks include an over-head projector, VCR, computer, or graphing calculator. Be sure you know how to operate any equipment that you plan to use. On the day of your talk, make sure everything is ready to go (software loaded, tape at the right starting point etc.) so that you don’t have “technical difficulties.”

Visual aides can be very useful in a presentation. (See Displaying Your Results for details about poster design.) If you are going to introduce new vocabulary, consider making a poster with the words and their meanings to display throughout your talk. If people forget what a term means while you are speaking, they can refer to the poster you have provided. (You could also write the words and meanings on a black/white board in advance.) If there are important equations that you would like to show, you can present them on an overhead transparency that you prepare prior to the talk. Minimize the amount you write on the board or on an overhead transparency during your presentation. It is not very engaging for the audience to sit watching while you write things down. Prepare all equations and materials in advance. If you don’t want to reveal all of what you have written on your transparency at once, you can cover up sections of your overhead with a piece of paper and slide it down the page as you move along in your talk. If you decide to use overhead transparencies, be sure to make the lettering large enough for your audience to read. It also helps to limit how much you put on your transparencies so they are not cluttered. Lastly, note that you can only project approximately half of a standard 8.5" by 11" page at any one time, so limit your information to displays of that size.

Presenters often create handouts to give to members of the audience. Handouts may include more information about the topic than the presenter has time to discuss, allowing listeners to learn more if they are interested. Handouts may also include exercises that you would like audience members to try, copies of complicated diagrams that you will display, and a list of resources where folks might find more information about your topic. Give your audience the handout before you begin to speak so you don’t have to stop in the middle of the talk to distribute it. In a handout you might include:

• A proof you would like to share, but you don’t have time to present entirely.

• Copies of important overhead transparencies that you use in your talk.

• Diagrams that you will display, but which may be too complicated for someone to copy down accurately.

• Resources that you think your audience members might find useful if they are interested in learning more about your topic.

The Conclusion

Ending your speech is also very important. Your conclusion should leave the audience feeling satisfied that the presentation was complete. One effective way to conclude a speech is to review what you presented and then to tie back to your introduction. If you used the Disraeli quote in your introduction, you might end by saying something like,

I hope that my presentation today has convinced you that . . . Statistical analysis backs up the claims that I have made, but more importantly, . . . . And that’s no lie!

Getting Ready

After you have written your speech and prepared your visuals, there is still work to be done.

• Prepare your notes on cards rather than full-size sheets of paper. Note cards will be less likely to block your face when you read from them. (They don’t flop around either.) Use a large font that is easy for you to read. Write notes to yourself on your notes. Remind yourself to smile or to look up. Mark when to show a particular slide, etc.
• Practice! Be sure you know your speech well enough that you can look up from your notes and make eye contact with your audience. Practice for other people and listen to their feedback.
• Time your speech in advance so that you are sure it is the right length. If necessary, cut or add some material and time yourself again until your speech meets the time requirements. Do not go over time!
• Anticipate questions and be sure you are prepared to answer them.
• Make a list of all materials that you will need so that you are sure you won’t forget anything.
• If you are planning to provide a handout, make a few extras.
• If you are going to write on a whiteboard or a blackboard, do it before starting your talk.

The Delivery

How you deliver your speech is almost as important as what you say. If you are enthusiastic about your presentation, it is far more likely that your audience will be engaged. Never apologize for yourself. If you start out by saying that your presentation isn’t very good, why would anyone want to listen to it? Everything about how you present yourself will contribute to how well your presentation is received. Dress professionally. And don’t forget to smile!

Here are a few tips about delivery that you might find helpful.

• Make direct eye contact with members of your audience. Pick a person and speak an entire phrase before shifting your gaze to another person. Don’t just “scan” the audience. Try not to look over their heads or at the floor. Be sure to look at all parts of the room at some point during the speech so everyone feels included.
• Speak loudly enough for people to hear and slowly enough for them to follow what you are saying.
• Do not read your speech directly from your note cards or your paper. Be sure you know your speech well enough to make eye contact with your audience. Similarly, don’t read your talk directly off of transparencies.
• Avoid using distracting or repetitive hand gestures. Be careful not to wave your manuscript around as you speak.
• Move around the front of the room if possible. On the other hand, don’t pace around so much that it becomes distracting. (If you are speaking at a podium, you may not be able to move.)
• Keep technical language to a minimum. Explain any new vocabulary carefully and provide a visual aide for people to use as a reference if necessary.
• Be careful to avoid repetitive space-fillers and slang such as “umm”, “er”, “you know”, etc. If you need to pause to collect your thoughts, it is okay just to be silent for a moment. (You should ask your practice audiences to monitor this habit and let you know how you did).
• Leave time at the end of your speech so that the audience can ask questions.

Displaying Your Results

When you create a visual display of your work, it is important to capture and retain the attention of your audience. Entice people to come over and look at your work. Once they are there, make them want to stay to learn about what you have to tell them. There are a number of different formats you may use in creating your visual display, but the underlying principle is always the same: your work should be neat, well-organized, informative, and easy to read.

It is unlikely that you will be able to present your entire project on a single poster or display board. So, you will need to decide which are the most important parts to include. Don’t try to cram too much onto the poster. If you do, it may look crowded and be hard to read! The display should summarize your most important points and conclusions and allow the reader to come away with a good understanding of what you have done.

A good display board will have a catchy title that is easy to read from a distance. Each section of your display should be easily identifiable. You can create posters such as this by using headings and also by separating parts visually. Titles and headings can be carefully hand-lettered or created using a computer. It is very important to include lots of examples on your display. It speeds up people’s understanding and makes your presentation much more effective. The use of diagrams, charts, and graphs also makes your presentation much more interesting to view. Every diagram or chart should be clearly labeled. If you include photographs or drawings, be sure to write captions that explain what the reader is looking at.

In order to make your presentation look more appealing, you will probably want to use some color. However, you must be careful that the color does not become distracting. Avoid florescent colors, and avoid using so many different colors that your display looks like a patch-work quilt. You want your presentation to be eye-catching, but you also want it to look professional.

People should be able to read your work easily, so use a reasonably large font for your text. (14 point is a recommended minimum.) Avoid writing in all-capitals because that is much harder to read than regular text. It is also a good idea to limit the number of different fonts you use on your display. Too many different fonts can make your poster look disorganized.

Notice how each section on the sample poster is defined by the use of a heading and how the various parts of the presentation are displayed on white rectangles. (Some of the rectangles are blank, but they would also have text or graphics on them in a real presentation.) Section titles were made with pale green paper mounted on red paper to create a boarder. Color was used in the diagrams to make them more eye-catching. This poster would be suitable for hanging on a bulletin board.

If you are planning to use a poster, such as this, as a visual aid during an oral presentation, you might consider backing your poster with foam-core board or corrugated cardboard. A strong board will not flop around while you are trying to show it to your audience. You can also stand a stiff board on an easel or the tray of a classroom blackboard or whiteboard so that your hands will be free during your talk. If you use a poster as a display during an oral presentation, you will need to make the text visible for your audience. You can create a hand-out or you can make overhead transparencies of the important parts. If you use overhead transparencies, be sure to use lettering that is large enough to be read at a distance when the text is projected.

If you are preparing your display for a science fair, you will probably want to use a presentation board that can be set up on a table. You can buy a pre-made presentation board at an office supply or art store or you can create one yourself using foam-core board. With a presentation board, you can often use the space created by the sides of the board by placing a copy of your report or other objects that you would like people to be able to look at there. In the illustration, a black trapezoid was cut out of foam-core board and placed on the table to make the entire display look more unified. Although the text is not shown in the various rectangles in this example, you will present your information in spaces such as these.

Don’t forget to put your name on your poster or display board. And, don’t forget to carefully proof-read your work. There should be no spelling, grammatical or typing mistakes on your project. If your display is not put together well, it may make people wonder about the quality of the work you did on the rest of your project.

For more information about creating posters for science fair competitions, see

http://school.discovery.com/sciencefaircentral/scifairstudio/handbook/display.html ,

http://www.siemens-foundation.org/science/poster_guidelines.htm ,

Robert Gerver’s book, Writing Math Research Papers , (published by Key Curriculum Press) has an excellent section about doing oral presentations and making posters, complete with many examples.

References Used

American Psychological Association . Electronic reference formats recommended by the American Psychological Association . (2000, August 22). Washington, DC: American Psychological Association. Retrieved October 6, 2000, from the World Wide Web: http://www.apastyle.org/elecsource.html

Bridgewater State College. (1998, August 5 ). APA Style: Sample Bibliographic Entries (4th ed) . Bridgewater, MA: Clement C. Maxwell Library. Retrieved December 20, 2001, from the World Wide Web: http://www.bridgew.edu/dept/maxwell/apa.htm

Crannell, Annalisa. (1994). A Guide to Writing in Mathematics Classes . Franklin & Marshall College. Retrieved January 2, 2002, from the World Wide Web: http://www.fandm.edu/Departments/Mathematics/writing_in_math/guide.html

Gerver, Robert. 1997. Writing Math Research Papers . Berkeley, CA: Key Curriculum Press.

Moncur, Michael. (1994-2002 ). The Quotations Page . Retrieved April 9, 2002, from the World Wide Web: http://www.quotationspage.com/

Public Speaking -- Be the Best You Can Be . (2002). Landover, Hills, MD: Advanced Public Speaking Institute. Retrieved April 9, 2002, from the World Wide Web: http://www.public-speaking.org/

Recreational Mathematics. (1988) Ottawa, Ontario, Canada: Canadian Mathematical Society. Retrieved April 9, 2002, from the World Wide Web: http://camel.math.ca/Recreation/

Shay, David. (1996). Profession Jokes — Mathematicians. Retrieved April 5, 2001, from the World Wide Web: http://www.geocities.com/CapeCanaveral/4661/projoke22.htm

Sieman’s Foundation. (2001). Judging Guidelines — Poster . Retrieved April 9, 2002, from the World Wide Web: http://www.siemens-foundation.org/science/poster_guidelines.htm ,

VanCleave, Janice. (1997). Science Fair Handbook. Discovery.com. Retrieved April 9, 2002, from the World Wide Web: http://school.discovery.com/sciencefaircentral/scifairstudio/handbook/display.html ,

Woodward, Mark. (2000) . The Mathematical Quotations Server . Furman University. Greenville, SC. Retrieved April 9, 2002, from the World Wide Web: http://math.furman.edu/~mwoodard/mquot.html

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Choose Your Test

Sat / act prep online guides and tips, 113 great research paper topics.

General Education

One of the hardest parts of writing a research paper can be just finding a good topic to write about. Fortunately we've done the hard work for you and have compiled a list of 113 interesting research paper topics. They've been organized into ten categories and cover a wide range of subjects so you can easily find the best topic for you.

In addition to the list of good research topics, we've included advice on what makes a good research paper topic and how you can use your topic to start writing a great paper.

What Makes a Good Research Paper Topic?

Not all research paper topics are created equal, and you want to make sure you choose a great topic before you start writing. Below are the three most important factors to consider to make sure you choose the best research paper topics.

#1: It's Something You're Interested In

A paper is always easier to write if you're interested in the topic, and you'll be more motivated to do in-depth research and write a paper that really covers the entire subject. Even if a certain research paper topic is getting a lot of buzz right now or other people seem interested in writing about it, don't feel tempted to make it your topic unless you genuinely have some sort of interest in it as well.

#2: There's Enough Information to Write a Paper

Even if you come up with the absolute best research paper topic and you're so excited to write about it, you won't be able to produce a good paper if there isn't enough research about the topic. This can happen for very specific or specialized topics, as well as topics that are too new to have enough research done on them at the moment. Easy research paper topics will always be topics with enough information to write a full-length paper.

Trying to write a research paper on a topic that doesn't have much research on it is incredibly hard, so before you decide on a topic, do a bit of preliminary searching and make sure you'll have all the information you need to write your paper.

#3: It Fits Your Teacher's Guidelines

Don't get so carried away looking at lists of research paper topics that you forget any requirements or restrictions your teacher may have put on research topic ideas. If you're writing a research paper on a health-related topic, deciding to write about the impact of rap on the music scene probably won't be allowed, but there may be some sort of leeway. For example, if you're really interested in current events but your teacher wants you to write a research paper on a history topic, you may be able to choose a topic that fits both categories, like exploring the relationship between the US and North Korea. No matter what, always get your research paper topic approved by your teacher first before you begin writing.

113 Good Research Paper Topics

Below are 113 good research topics to help you get you started on your paper. We've organized them into ten categories to make it easier to find the type of research paper topics you're looking for.

Arts/Culture

• Discuss the main differences in art from the Italian Renaissance and the Northern Renaissance .
• Analyze the impact a famous artist had on the world.
• How is sexism portrayed in different types of media (music, film, video games, etc.)? Has the amount/type of sexism changed over the years?
• How has the music of slaves brought over from Africa shaped modern American music?
• How has rap music evolved in the past decade?
• How has the portrayal of minorities in the media changed?

Current Events

• What have been the impacts of China's one child policy?
• How have the goals of feminists changed over the decades?
• How has the Trump presidency changed international relations?
• Analyze the history of the relationship between the United States and North Korea.
• What factors contributed to the current decline in the rate of unemployment?
• What have been the impacts of states which have increased their minimum wage?
• How do US immigration laws compare to immigration laws of other countries?
• How have the US's immigration laws changed in the past few years/decades?
• How has the Black Lives Matter movement affected discussions and view about racism in the US?
• What impact has the Affordable Care Act had on healthcare in the US?
• What factors contributed to the UK deciding to leave the EU (Brexit)?
• What factors contributed to China becoming an economic power?
• Discuss the history of Bitcoin or other cryptocurrencies  (some of which tokenize the S&P 500 Index on the blockchain) .
• Do students in schools that eliminate grades do better in college and their careers?
• Do students from wealthier backgrounds score higher on standardized tests?
• Do students who receive free meals at school get higher grades compared to when they weren't receiving a free meal?
• Do students who attend charter schools score higher on standardized tests than students in public schools?
• Do students learn better in same-sex classrooms?
• How does giving each student access to an iPad or laptop affect their studies?
• What are the benefits and drawbacks of the Montessori Method ?
• Do children who attend preschool do better in school later on?
• What was the impact of the No Child Left Behind act?
• How does the US education system compare to education systems in other countries?
• What impact does mandatory physical education classes have on students' health?
• Which methods are most effective at reducing bullying in schools?
• Do homeschoolers who attend college do as well as students who attended traditional schools?
• Does offering tenure increase or decrease quality of teaching?
• How does college debt affect future life choices of students?
• Should graduate students be able to form unions?

• What are different ways to lower gun-related deaths in the US?
• How and why have divorce rates changed over time?
• Is affirmative action still necessary in education and/or the workplace?
• Should physician-assisted suicide be legal?
• How has stem cell research impacted the medical field?
• How can human trafficking be reduced in the United States/world?
• Should people be able to donate organs in exchange for money?
• Which types of juvenile punishment have proven most effective at preventing future crimes?
• Has the increase in US airport security made passengers safer?
• Analyze the immigration policies of certain countries and how they are similar and different from one another.
• Several states have legalized recreational marijuana. What positive and negative impacts have they experienced as a result?
• Do tariffs increase the number of domestic jobs?
• Which prison reforms have proven most effective?
• Should governments be able to censor certain information on the internet?
• Which methods/programs have been most effective at reducing teen pregnancy?
• What are the benefits and drawbacks of the Keto diet?
• How effective are different exercise regimes for losing weight and maintaining weight loss?
• How do the healthcare plans of various countries differ from each other?
• What are the most effective ways to treat depression ?
• What are the pros and cons of genetically modified foods?
• Which methods are most effective for improving memory?
• What can be done to lower healthcare costs in the US?
• What factors contributed to the current opioid crisis?
• Analyze the history and impact of the HIV/AIDS epidemic .
• Are low-carbohydrate or low-fat diets more effective for weight loss?
• How much exercise should the average adult be getting each week?
• Which methods are most effective to get parents to vaccinate their children?
• What are the pros and cons of clean needle programs?
• How does stress affect the body?
• Discuss the history of the conflict between Israel and the Palestinians.
• What were the causes and effects of the Salem Witch Trials?
• Who was responsible for the Iran-Contra situation?
• How has New Orleans and the government's response to natural disasters changed since Hurricane Katrina?
• What events led to the fall of the Roman Empire?
• What were the impacts of British rule in India ?
• Was the atomic bombing of Hiroshima and Nagasaki necessary?
• What were the successes and failures of the women's suffrage movement in the United States?
• What were the causes of the Civil War?
• How did Abraham Lincoln's assassination impact the country and reconstruction after the Civil War?
• Which factors contributed to the colonies winning the American Revolution?
• What caused Hitler's rise to power?
• Discuss how a specific invention impacted history.
• What led to Cleopatra's fall as ruler of Egypt?
• How has Japan changed and evolved over the centuries?
• What were the causes of the Rwandan genocide ?

• Why did Martin Luther decide to split with the Catholic Church?
• Analyze the history and impact of a well-known cult (Jonestown, Manson family, etc.)
• How did the sexual abuse scandal impact how people view the Catholic Church?
• How has the Catholic church's power changed over the past decades/centuries?
• What are the causes behind the rise in atheism/ agnosticism in the United States?
• What were the influences in Siddhartha's life resulted in him becoming the Buddha?
• How has media portrayal of Islam/Muslims changed since September 11th?

Science/Environment

• How has the earth's climate changed in the past few decades?
• How has the use and elimination of DDT affected bird populations in the US?
• Analyze how the number and severity of natural disasters have increased in the past few decades.
• Analyze deforestation rates in a certain area or globally over a period of time.
• How have past oil spills changed regulations and cleanup methods?
• How has the Flint water crisis changed water regulation safety?
• What are the pros and cons of fracking?
• What impact has the Paris Climate Agreement had so far?
• What have NASA's biggest successes and failures been?
• How can we improve access to clean water around the world?
• Does ecotourism actually have a positive impact on the environment?
• Should the US rely on nuclear energy more?
• What can be done to save amphibian species currently at risk of extinction?
• What impact has climate change had on coral reefs?
• How are black holes created?
• Are teens who spend more time on social media more likely to suffer anxiety and/or depression?
• How will the loss of net neutrality affect internet users?
• Analyze the history and progress of self-driving vehicles.
• How has the use of drones changed surveillance and warfare methods?
• Has social media made people more or less connected?
• What progress has currently been made with artificial intelligence ?
• Do smartphones increase or decrease workplace productivity?
• What are the most effective ways to use technology in the classroom?
• How is Google search affecting our intelligence?
• When is the best age for a child to begin owning a smartphone?
• Has frequent texting reduced teen literacy rates?

How to Write a Great Research Paper

Even great research paper topics won't give you a great research paper if you don't hone your topic before and during the writing process. Follow these three tips to turn good research paper topics into great papers.

#1: Figure Out Your Thesis Early

Before you start writing a single word of your paper, you first need to know what your thesis will be. Your thesis is a statement that explains what you intend to prove/show in your paper. Every sentence in your research paper will relate back to your thesis, so you don't want to start writing without it!

As some examples, if you're writing a research paper on if students learn better in same-sex classrooms, your thesis might be "Research has shown that elementary-age students in same-sex classrooms score higher on standardized tests and report feeling more comfortable in the classroom."

If you're writing a paper on the causes of the Civil War, your thesis might be "While the dispute between the North and South over slavery is the most well-known cause of the Civil War, other key causes include differences in the economies of the North and South, states' rights, and territorial expansion."

#2: Back Every Statement Up With Research

Remember, this is a research paper you're writing, so you'll need to use lots of research to make your points. Every statement you give must be backed up with research, properly cited the way your teacher requested. You're allowed to include opinions of your own, but they must also be supported by the research you give.

#3: Do Your Research Before You Begin Writing

You don't want to start writing your research paper and then learn that there isn't enough research to back up the points you're making, or, even worse, that the research contradicts the points you're trying to make!

Get most of your research on your good research topics done before you begin writing. Then use the research you've collected to create a rough outline of what your paper will cover and the key points you're going to make. This will help keep your paper clear and organized, and it'll ensure you have enough research to produce a strong paper.

What's Next?

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Want to know the fastest and easiest ways to convert between Fahrenheit and Celsius? We've got you covered! Check out our guide to the best ways to convert Celsius to Fahrenheit (or vice versa).

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Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.

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Researchers detect a new molecule in space

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New research from the group of MIT Professor Brett McGuire has revealed the presence of a previously unknown molecule in space. The team's open-access paper, “ Rotational Spectrum and First Interstellar Detection of 2-Methoxyethanol Using ALMA Observations of NGC 6334I ,” appears in April 12 issue of The Astrophysical Journal Letters .

Zachary T.P. Fried , a graduate student in the McGuire group and the lead author of the publication, worked to assemble a puzzle comprised of pieces collected from across the globe, extending beyond MIT to France, Florida, Virginia, and Copenhagen, to achieve this exciting discovery. 

“Our group tries to understand what molecules are present in regions of space where stars and solar systems will eventually take shape,” explains Fried. “This allows us to piece together how chemistry evolves alongside the process of star and planet formation. We do this by looking at the rotational spectra of molecules, the unique patterns of light they give off as they tumble end-over-end in space. These patterns are fingerprints (barcodes) for molecules. To detect new molecules in space, we first must have an idea of what molecule we want to look for, then we can record its spectrum in the lab here on Earth, and then finally we look for that spectrum in space using telescopes.”

Searching for molecules in space

The McGuire Group has recently begun to utilize machine learning to suggest good target molecules to search for. In 2023, one of these machine learning models suggested the researchers target a molecule known as 2-methoxyethanol. 

“There are a number of 'methoxy' molecules in space, like dimethyl ether, methoxymethanol, ethyl methyl ether, and methyl formate, but 2-methoxyethanol would be the largest and most complex ever seen,” says Fried. To detect this molecule using radiotelescope observations, the group first needed to measure and analyze its rotational spectrum on Earth. The researchers combined experiments from the University of Lille (Lille, France), the New College of Florida (Sarasota, Florida), and the McGuire lab at MIT to measure this spectrum over a broadband region of frequencies ranging from the microwave to sub-millimeter wave regimes (approximately 8 to 500 gigahertz). 

The data gleaned from these measurements permitted a search for the molecule using Atacama Large Millimeter/submillimeter Array (ALMA) observations toward two separate star-forming regions: NGC 6334I and IRAS 16293-2422B. Members of the McGuire group analyzed these telescope observations alongside researchers at the National Radio Astronomy Observatory (Charlottesville, Virginia) and the University of Copenhagen, Denmark. 

“Ultimately, we observed 25 rotational lines of 2-methoxyethanol that lined up with the molecular signal observed toward NGC 6334I (the barcode matched!), thus resulting in a secure detection of 2-methoxyethanol in this source,” says Fried. “This allowed us to then derive physical parameters of the molecule toward NGC 6334I, such as its abundance and excitation temperature. It also enabled an investigation of the possible chemical formation pathways from known interstellar precursors.”

Looking forward

Molecular discoveries like this one help the researchers to better understand the development of molecular complexity in space during the star formation process. 2-methoxyethanol, which contains 13 atoms, is quite large for interstellar standards — as of 2021, only six species larger than 13 atoms were detected outside the solar system , many by McGuire’s group, and all of them existing as ringed structures.  

“Continued observations of large molecules and subsequent derivations of their abundances allows us to advance our knowledge of how efficiently large molecules can form and by which specific reactions they may be produced,” says Fried. “Additionally, since we detected this molecule in NGC 6334I but not in IRAS 16293-2422B, we were presented with a unique opportunity to look into how the differing physical conditions of these two sources may be affecting the chemistry that can occur.”

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Partisan divides over K-12 education in 8 charts

K-12 education is shaping up to be a key issue in the 2024 election cycle. Several prominent Republican leaders, including GOP presidential candidates, have sought to limit discussion of gender identity and race in schools , while the Biden administration has called for expanded protections for transgender students . The coronavirus pandemic also brought out partisan divides on many issues related to K-12 schools .

Today, the public is sharply divided along partisan lines on topics ranging from what should be taught in schools to how much influence parents should have over the curriculum. Here are eight charts that highlight partisan differences over K-12 education, based on recent surveys by Pew Research Center and external data.

Pew Research Center conducted this analysis to provide a snapshot of partisan divides in K-12 education in the run-up to the 2024 election. The analysis is based on data from various Center surveys and analyses conducted from 2021 to 2023, as well as survey data from Education Next, a research journal about education policy. Links to the methodology and questions for each survey or analysis can be found in the text of this analysis.

Most Democrats say K-12 schools are having a positive effect on the country , but a majority of Republicans say schools are having a negative effect, according to a Pew Research Center survey from October 2022. About seven-in-ten Democrats and Democratic-leaning independents (72%) said K-12 public schools were having a positive effect on the way things were going in the United States. About six-in-ten Republicans and GOP leaners (61%) said K-12 schools were having a negative effect.

About six-in-ten Democrats (62%) have a favorable opinion of the U.S. Department of Education , while a similar share of Republicans (65%) see it negatively, according to a March 2023 survey by the Center. Democrats and Republicans were more divided over the Department of Education than most of the other 15 federal departments and agencies the Center asked about.

In May 2023, after the survey was conducted, Republican lawmakers scrutinized the Department of Education’s priorities during a House Committee on Education and the Workforce hearing. The lawmakers pressed U.S. Secretary of Education Miguel Cardona on topics including transgender students’ participation in sports and how race-related concepts are taught in schools, while Democratic lawmakers focused on school shootings.

Partisan opinions of K-12 principals have become more divided. In a December 2021 Center survey, about three-quarters of Democrats (76%) expressed a great deal or fair amount of confidence in K-12 principals to act in the best interests of the public. A much smaller share of Republicans (52%) said the same. And nearly half of Republicans (47%) had not too much or no confidence at all in principals, compared with about a quarter of Democrats (24%).

This divide grew between April 2020 and December 2021. While confidence in K-12 principals declined significantly among people in both parties during that span, it fell by 27 percentage points among Republicans, compared with an 11-point decline among Democrats.

Democrats are much more likely than Republicans to say teachers’ unions are having a positive effect on schools. In a May 2022 survey by Education Next , 60% of Democrats said this, compared with 22% of Republicans. Meanwhile, 53% of Republicans and 17% of Democrats said that teachers’ unions were having a negative effect on schools. (In this survey, too, Democrats and Republicans include independents who lean toward each party.)

The 38-point difference between Democrats and Republicans on this question was the widest since Education Next first asked it in 2013. However, the gap has exceeded 30 points in four of the last five years for which data is available.

Republican and Democratic parents differ over how much influence they think governments, school boards and others should have on what K-12 schools teach. About half of Republican parents of K-12 students (52%) said in a fall 2022 Center survey that the federal government has too much influence on what their local public schools are teaching, compared with two-in-ten Democratic parents. Republican K-12 parents were also significantly more likely than their Democratic counterparts to say their state government (41% vs. 28%) and their local school board (30% vs. 17%) have too much influence.

On the other hand, more than four-in-ten Republican parents (44%) said parents themselves don’t have enough influence on what their local K-12 schools teach, compared with roughly a quarter of Democratic parents (23%). A larger share of Democratic parents – about a third (35%) – said teachers don’t have enough influence on what their local schools teach, compared with a quarter of Republican parents who held this view.

Republican and Democratic parents don’t agree on what their children should learn in school about certain topics. Take slavery, for example: While about nine-in-ten parents of K-12 students overall agreed in the fall 2022 survey that their children should learn about it in school, they differed by party over the specifics. About two-thirds of Republican K-12 parents said they would prefer that their children learn that slavery is part of American history but does not affect the position of Black people in American society today. On the other hand, 70% of Democratic parents said they would prefer for their children to learn that the legacy of slavery still affects the position of Black people in American society today.

Parents are also divided along partisan lines on the topics of gender identity, sex education and America’s position relative to other countries. Notably, 46% of Republican K-12 parents said their children should not learn about gender identity at all in school, compared with 28% of Democratic parents. Those shares were much larger than the shares of Republican and Democratic parents who said that their children should not learn about the other two topics in school.

Many Republican parents see a place for religion in public schools , whereas a majority of Democratic parents do not. About six-in-ten Republican parents of K-12 students (59%) said in the same survey that public school teachers should be allowed to lead students in Christian prayers, including 29% who said this should be the case even if prayers from other religions are not offered. In contrast, 63% of Democratic parents said that public school teachers should not be allowed to lead students in any type of prayers.

In June 2022, before the Center conducted the survey, the Supreme Court ruled in favor of a football coach at a public high school who had prayed with players at midfield after games. More recently, Texas lawmakers introduced several bills in the 2023 legislative session that would expand the role of religion in K-12 public schools in the state. Those proposals included a bill that would require the Ten Commandments to be displayed in every classroom, a bill that would allow schools to replace guidance counselors with chaplains, and a bill that would allow districts to mandate time during the school day for staff and students to pray and study religious materials.

Mentions of diversity, social-emotional learning and related topics in school mission statements are more common in Democratic areas than in Republican areas. K-12 mission statements from public schools in areas where the majority of residents voted Democratic in the 2020 general election are at least twice as likely as those in Republican-voting areas to include the words “diversity,” “equity” or “inclusion,” according to an April 2023 Pew Research Center analysis .

Also, about a third of mission statements in Democratic-voting areas (34%) use the word “social,” compared with a quarter of those in Republican-voting areas, and a similar gap exists for the word “emotional.” Like diversity, equity and inclusion, social-emotional learning is a contentious issue between Democrats and Republicans, even though most K-12 parents think it’s important for their children’s schools to teach these skills . Supporters argue that social-emotional learning helps address mental health needs and student well-being, but some critics consider it emotional manipulation and want it banned.

In contrast, there are broad similarities in school mission statements outside of these hot-button topics. Similar shares of mission statements in Democratic and Republican areas mention students’ future readiness, parent and community involvement, and providing a safe and healthy educational environment for students.

• Education & Politics
• Partisanship & Issues
• Politics & Policy

Jenn Hatfield is a writer/editor at Pew Research Center

About 1 in 4 U.S. teachers say their school went into a gun-related lockdown in the last school year

About half of americans say public k-12 education is going in the wrong direction, what public k-12 teachers want americans to know about teaching, what’s it like to be a teacher in america today, race and lgbtq issues in k-12 schools, most popular.

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