undergraduate mathematics research papers

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On the Singular Pebbling Number of a Graph Authors: Harmony R. Morris Faculty Sponsor: Joy Morris

Optimizing Buying Strategies in Dominion Authors: Nikolas A. Koutroulakis Faculty Sponsor: Dr. Tricia Muldoon Brown

Wang Tilings in Arbitrary Dimensions Authors: Ian Tassin Faculty Sponsor: Huck Bennett

The Basel Problem and Summing Rational Functions over Integers Authors: Pranjal Jain Faculty Sponsor: Dr. Chandrasheel Bhagwat

Modeling an infection outbreak with quarantine: The SIBKR Model Authors: Mikenna Dew, Amanda Langosch, and Theadora Baker-Wallerstein Faculty Sponsor: King-Yeung Lam

Are All Weakly Convex and Decomposable Polyhedral Surfaces Infinitesimally Rigid? Authors: Jilly Kevo Faculty Sponsor: Jean-Marc Schlenker

Approximating Equilibria in Restricted Games Authors: Jack W. Doyle Faculty Sponsor: Benoît Legat

Modeling Virus Diffusion on Social Media Networks with the SMIRQ Model Authors: Justin Browning, Arnav Mazumder, and Gowri Nanda Faculty Sponsor: Noelle West

Uniformly Distributing Points On A Sphere Authors: Flavio Arrigoni Faculty Sponsor: Peter Grabner

Modeling the Effect of Human Behavior on Disease Transmission Authors: Katie Yan Faculty Sponsor: Rachel Roe-Dale

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About the Journal

Aims and Scope

The primary goal of the Columbia Journal of Undergraduate Mathematics is to provide undergraduate readers with high-quality, accessible articles on challenging topics, or novel approaches to teaching more familiar concepts. Articles published are purely expository; we do not accept research papers. Most range from 5 to 15 pages in length, with the primary exceptions being senior theses written by students at Columbia and other universities alike. The journal also accepts and publishes mathematical artwork with clear pedagogical value.

Math differs from other disciplines in that it is much harder for undergraduates to perform and publish novel research. However, there is plenty of high quality expository work being produced by undergraduates through coursework, REUs, and senior theses. These pieces are made better by the fact that the authors are undergraduates themselves, granting them insight into how other undergraduates think. Undergraduate-written expository work can be an invaluable supplement to textbooks when it can be accessed, however, there are few active academic journals publishing expository work by undergraduates, so this work largely vanishes, to the detriment of both undergraduate authors and the mathematical community. The Columbia Journal of Undergraduate Mathematics is a math journal by undergraduates, for undergraduates seeking to fill this gap in resources within the mathematical community.

Open Access

CJUM is an open access journal, which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. Authors retain their copyright and agree to license their articles with a CC BY-NC-ND 4.0 license. You can read more about Creative Commons licenses at creativecommons.org.

CJUM is a no-fee journal. Authors are not charged for the publication of their articles. 

CJUM is a Diamond Open Access journal.

Peer Review

CJUM uses a double-anonymous peer review process for expository work. Peer reviewers are graduate students from the Columbia Department of Mathematics, along with undergraduate reviewers who read for style and language. The CJUM Executive Editorial Board and Chief Confidentiality Officer mediates between peer reviewers and authors during the editorial process, whose identities are not revealed to one another. 

CJUM does not use peer review for creative submissions such as pedagogical artwork, which are directly published in the journal if accepted, pending minor edits suggested by the CJUM Executive Editorial Board.

Diversity and Inclusion 

CJUM is committed to increasing the diversity of voices that is represented in mathematical spaces. This diversity includes differences in race, ethnicity, sexual orientation, gender identity, country of origin, religious or spiritual beliefs, ability, and socioeconomic status. Our double-anonymous peer review coupled with the mediating role of our editorial board represents CJUM’s commitment to a fair and respectful review process for all submissions. We also actively recruit editorial board members from a variety of backgrounds and identities in order to have diverse perspectives in our peer review process and to provide more opportunities for marginalized groups in math.

CJUM upholds a zero-tolerance policy for plagiarism by prospective authors. Any concerns should be directly addressed to the Editors-in-Chief of CJUM. In the interest of a fair deliberation process, CJUM requires all members of its editorial board to report conflicts of interest.

Journal Archiving

CJUM is archived in Columbia University’s Academic Commons . Academic Commons is Columbia University’s institutional repository, offering long-term public access to research shared by the Columbia community. A program of the Columbia University Libraries, Academic Commons provides secure, replicated storage for files in multiple formats. Academic Commons assigns a DOI and accurate metadata to each work to enhance discoverability.

Undergraduate Journals

• Math Horizons (MAA) Math Horizons is a vibrant and accessible forum for practitioners, students, educators, and enthusiasts of mathematics, dedicated to exploring the folklore, characters, and current happenings in mathematical culture.
• Rose-Hulman Institute of Technology Undergraduate Math Journal The Rose-Hulman Undergraduate Mathematics Journal is devoted entirely to papers written by undergraduates on topics related to mathematics.
• Involve: A Journal of Mathematics Involve is dedicated to showcasing and encouraging high quality mathematical research involving students (at all levels). The editorial board consists of mathematical scientists each of whom is personally committed to nurturing student participation in research.
• SIAM Undergraduate Research Online (SIURO) SIAM Undergraduate Research Online (SIURO) is a web based publication devoted to undergraduate research in applied and computational mathematics. The publication represents a wide range of applied topics, including but not limited to, analysis, discrete mathematics, statistics, operations research, optimization, dynamical systems, modeling, and computation. Typical areas of application include but are not limited to physical, life, financial, and management sciences and engineering.

Undergraduate Research Papers

Here are a few recent undergraduate publications (byu undergraduate coauthors are in all caps):.

Network Specialization: A Topological Mechanism for the Emergence of Cluster Synchronization – Webb, B. Z., Walker, E., SELLERS, JORDAN, HANNESSON, ERIK, published in Physica A,  2022

A Simple Stability Criteria for Dynamical Systems with Stochastic Switching and/or Stochastic Time-Delays – Webb, B. Z., Reber, D., Carter, C., MURRI, JACOB, published in Nonlinearity,  2022

Nilpotent polynomials and nilpotent coefficients – DRAPER, THOMAS L., Nielsen, P. P., Ster, J., published in Journal of Algebra,  2022

Prime factors of Phi_3(x) of the same form  – HANSEN, CODY S., Nielsen, P. P., published in   Integers,  2022 A 1-separation formula for the graph Kemeny constant and Braess edges – Kempton, M., FAUGHT, NOLAN, KNUDSON, ADAM, published in Journal of Mathematical Chemistry,  2022

A general algorithm for calculating the irreducible Brillouin zone – Jorgensen, J. J., CHRISTENSEN, JOHN C., Jarvis, T. J., Hart, G. L., published in Communications in Computational Physics,  2022

Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations – Parkinson, S. S., Ringer, H., WALL, KATE, Parkinson, E., ERIKSON, LUKAS, CHRISTENSEN, DANIEL, Jarvis, T. J., published in Journal of Computational and Applied Mathematics,  2022

Mathematical Analysis of Redistricting  in Utah – KING, ANNIKA, MURRI, JACOB, Callahan, J., RUSSELL, ADRIENNE, Jarvis, T. J., published in Statistics and Public Policy,  2022

Miura-ori Inspired Smooth Sheet Attachments for Zipper-coupled Tubes – WEBB DYLAN C., REYNOLDS, ELISSA, Halverson, D. M., Howell, L. L. published in Mathematics,  2022

Deployable Space-Filling Mechanisms: Asymmetric Zipper-Coupled Tubes and Smooth Sheet Attachments – WEBB, DYLAN C., REYNOLDS, ELISSA, Halverson, D., Howell, L. L. published in ASME 2022 International Design Engineering Technical Conferences,  2022

Applications of Origami Principles in Deployable Childcare Furniture – Ames, D. C., JONES, JACKSON KADE, MITTELMAN, ALIYA, Halverson, D. M., Bateman, T. C., Magleby, S. P., Howell, L. L., published in ASME 2022 International Design Engineering Technical Conferences,  2022

Using social networks to improve group transition prediction in professional sports – Evans, E. J., Jones, R., LEUNG, JOSEPH, Webb, B. Z., published in 2022

How structural features of a spring-based model of fibrous collagen tissue govern the overall Young’s Modulus – NUEBERT, Evans, E. J., Dallon, J. C. published in Journal of Biomechanical Engineering,  2022

Strong Gelfand pairs of  SL – BARTON, ANDREA, Humphries, S. P. published in Journal of Algebra and Its Applications,  2022

Utilizing nonequilibrium isotope enrichments to dramatically increase turnover measurement ranges in single biopsy samples from humans – Naylor, B. C., Anderson, C. K., HADFIELD, MARCUS, Parkinson, D., AHLSTROM, AUSTIN, HANNAMANN, AUSTIN, QUILLING, CHAD, CUTLER, KYLE, DENTON, RUSSELL, Adamson, R., Burlett, R., Angel, T., Dallon, J. C., Transtrum, M. K., Hyldahl, R. D., Price, J. C. published in Utilizing nonequilibrium isotope enrichments to dramatically increase turnover measurement ranges in single biopsy samples from humans,  2022

A note on the 4- color theorem –  Chahal, J. S., CANIZALES, JENNIFER, published in aequationes mathematicae (online),  2022

Zeros of a family of complex-valued harmonic trinomials –  Dorff, M., Brooks, J., HUDSON, ALEXANDRA, PITTS, ERIN, CLAY, WHIFFEN, AMY, WOODALL, published in Bulletin of the Malaysian Mathematical Sciences Society,  2022

Odd, spoof perfect factorizations –  Andersen, N., DURHAM, SPENCER, Griffin, M. J., Hales, J., Jenkins, P., Keck, R., Ko, H., Molnar, G., Moss, E., Nielsen, P. P., NIENDORF, KYLE, Tombs, V., WARNICK, MERRILL, Wu, D. published in Journal of Number Theory,  2022

Fourier decompositions of graphs with symmetries and equitable partitions – Webb, B. Z., Lund, D., DRAPEAU, JOSEPH, published in Linear Algebra and its Applications,  2021

Resistance distance, Kirchhoff index, and Kemeny’s constant in flower graphs – Kempton, M. C., FAUGHT, NOLAN, KNUDSON, ADAM, published in MATCH Communications in Mathematical and in Computer Chemistry,  2021

Using Survey Data and Mathematical Modeling to Prioritize Water Interventions in Developing Countries – Jarvis, T. J., SAILSBERY, MITCHELL, ROBERTSON, CONNOR, MONCUR, TYLER, COX, JANE, LUND, DARREN, PALMER, KATIE, PETERSEN, KONNOR, CLOUGH, JORDAN, published in Water Resources Management,  2021

The last chapter of Gauss’ Disqusitiones Arithmeticae – Chahal, J. S., ANDERSON, LAURA, Top, J. published in Hardy-Ramanujan J. of Math.,  2021

Four color problem – Chahal, J. S., BASSETT, REBEKAH, CANIZALES, JENNIFER, FACKRELL, THOMAS, RICO, VANESSA, published in Resonance,  2021

Methodological reconstruction of historical seismic events from anecdotal accounts of destructive tsunamis: a case study for the great 1852 Banda arc mega-thrust earthquake and tsunami – Ringer, H., Whitehead, J. P., Krometis, J., Harris, R. A., Glatt-Holtz, N., Giddens, S., Ashcraft, C., CARVER, GARRET, ROBERTSON, ADAM, HARWARD, MCKAY, Fullwood, J., Lightheart, K., HILTON, RYAN, AVERY, ASHLEY, KESLER, CODY, Morrise, M., KLIEN, MICHAEL H., published in Journal of Geophysical Research,  2021

Analysis of the Rigid Motion of a Developable Conical Mechanism – Halverson, D. M., WOODLAND, McKELL, HSUNG, MICHELLE, MATHESON, ERIN, Safsten, C. A., Greenwood, J., Howell, L. L., published in Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference,  2020

Strong Gelfand pairs of Symmetric groups  – ANDERSON, GRADIN, Humphries, S. P., NICHOLSON, NATHAN, published in Journal of Algebra and its Applications,  2020

High order methods for acoustic scattering: Coupling Farfield Expansions ABC with Deferred-Correction methods  – Villamizar Gonzalez, V. R., GRUNDVIG, DANE, Rojas, O., Acosta, S., published in Wave Motion,  2020

High order local absorbing boundary conditions for acoustic and elastic scattering  – Villamizar, V., Khajah, T., Acosta, S., GRUNDVIG, DANE, Badger, J., Rojas, O., published in Journal of the Acoustical Society of America,  2020

Rigorous bounds on the heat transport of rotating convection with Ekman pumping – PACHEV, BENJAMIN., Whitehead, Jared P., Fantuzzi, G., Grooms, I., published in Journal of Mathematical Physics , 2020

High Order Farfield Expansion ABC coupled with IGA and Finite Differences Applied to Acoustic Multiple Scattering – Villamizar Gonzalez, V. R., Badger, J., Khajah, T., ACOSTA, SEBASTIAN, published in 4th International Conference on Mathematical and Numerical Aspects of Wave Propagation,  2019

Transfinitely valued Euclidean domains have arbitrary indecomposable order type  – Conidis, C. J., Nielsen, Pace P., TOMBS, VANDY, published in 2019

How many ways to color America?  – Chahal, Jasbir S., BASSET, REBEKAH, CANIZALES, JENNIFER, FACKRELL, THOMAS, RICO, VANESSA, published in 2019

Zagier duality for level p weakly holomorphic modular forms  – Jenkins, Paul M., MOLNAR, GRANT, published in Ramanujan Journal,  2019

Hidden Symmetries in Real and Theoretical Networks  – Webb, Benjamin Z., SMITH, DALLAS (2019)

Finding Hidden Structures, Hierarchies, and Cores in Networks via Isospectral Reduction  – Webb, Benjamin Z., SMITH, DALLAS, Bunimovich, L., published in Applied Mathematics and Nonlinear Sciences,  2019

General Equitable Decompositions for Graphs with Symmetries  – Webb, Benjamin Z., SMITH, DALLAS, Francis, A., published in Linear Algebra and its Applications,  2019

Difference sets disjoint from a subgroup  – COURTNEY HOAGLAND, Steven Humphries, NATHAN NICHOLSON, SETH POULSEN, published in Graphs and Combinatorics,  2019.

A Reidemeister type theorem for petal diagrams of knots – LESLIE COLTON, CORY GLOVER, Mark Hughes, SAMANTHA SANDBERG, published in Topology and its Applications,  2019.

An experimental investigation of interfacial instability in separated blood  – ALEX HUNTER, DANIEL McCLELLAN Jared Whitehead, published in AIChE Journal,  2019.

Parameterization method for unstable manifolds of standing waves on the line –  Blake Barker, JALEN MORGAN, published in SIAM Journal of Applied Dynamical Systems,  2019.

Generalized regular k-point grid generation of the fly –  JOHN CHRISTENSEN, Rodney Forcade, PARKER HAMILTON, published in Computational Materials Science,  2019.

Normalized coordinate equations and an energy method for predicting natural curved-fold configurations – JACOB BADGER, Denise Halverson, published in ASME Journal of Applied Mechanics,  2019.

Strong Gelfand pairs of symmetric groups – ANDERSON, GRADIN, Humphries, S. P., NICHOLSON, NATHAN, published in Journal of Algebra and its Applications,  2019.

Difference sets disjoint from a subgroup II: order 4p^2 – Steven Humphries, NATHAN NICHOLSON, published in Journal of Combinatorial Theory A,  2019.

A data-driven method for cost-effectiveness analysis to prioritize selection of water interventions in developing countries –  JANE COX, Tyler Jarvis, DERREN LUND, TYLER MONCUR, KATIE PALMER, KONNOR PETERSEN, CONNOR ROBERTSON, MITCHEL SAILSBERY, JORDAN SPENCER, published in Water Resources Management,  2019.

Divisibility properties of coefficients of modular functions in genus zero levels –  VICTORIA IBA, Paul Jenkins, MERRILL WARNICK, published in Integers,  2019.

An exploration of advanced SLW modeling approaches in comprehensive combustion predictions –  JACOB BADGER, Vladimir Soloviev, published in Combustion Science and Technology,  2019.

High order methods for acoustic scattering coupling Farfield expansions ABC with deferred-correction methods –  DANE GRUNDVIG, Vianey Villamizar, published in Wave Motion,  2019.

On zero-sector decreasing operators –  David Cardon, EVAN SORENSON, published in Journal of Mathematical Analysis and its Applications,  2018.

Congruences for coefficients of level 2 modular functions with poles at 0  – Paul Jenkins, RYAN KECK, published in Archiv der Mathematik,  2018.

Fast link prediction on large networks with spectral embedding –  BENJAMIN PAHCEV, Benjamin Webb, published in Journal of Complex Networks,  2017.

Local high order absorbing boundary conditions in terms of Farfield expansions – BLAKE DASTRUP, Vianey Villamizar, published in Journal of Computational Physics,  2017.

Minnesota Journal of Undergraduate Mathematics

ISSN: 2378-5810

The Minnesota Journal of Undergraduate Mathematics focuses on original mathematical research, done primarily by undergraduates, in all areas of mathematics and its applications.  The journal is currently not accepting new articles, while we work to process all of the current submissions.  Authors with submissions should watch for updates via email. We anticipate accepting new submissions later in 2024.  

Sponsors School of Mathematics Math Center for Educational Programs (MathCEP) Institute for Mathematics and its Applications

Current Issue

Vol. 8 No. 1 (2024): 2023-2024 Academic Year

Published: 2024-02-19

The Legendre Approximation and Arithmetic Bias

Megan Paasche, Ghaith Hiary

Expected Value of Statistics on Type-B Permutation Tableaux

Ryan Althoff, Daniel Diethrich, Amanda Lohss, Xin-Dee Low, Emily Wichert

Some Thoughts on the Search for 5 × 5 and 6 × 6 Additive-Multiplicative Magic Squares

Desmond Weisenberg

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The copyright of these individual works published by the University of Minnesota Libraries Publishing remains with the original creator or editorial team. For uses beyond those covered by law or the Creative Commons license, permission to reuse should be sought directly from the copyright owner listed on each article.

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• > The Cambridge Handbook of Undergraduate Research
• > Undergraduate Research in Mathematics

Book contents

• The Cambridge Handbook of Undergraduate Research
• Copyright page
• Contributors
• 1 Introduction
• Part I Theory and Research on Undergraduate Research
• Part II Implementation, Approaches, Methods
• Part III Disciplines
• 17 Introduction
• Part III.1 STEM
• 18 Undergraduate Research in Physics
• 19 Undergraduate Research in Chemistry
• 20 Undergraduate Research in Biology
• 21 Undergraduate Research in Mathematics
• 22 Undergraduate Research in Engineering
• 23 Undergraduate Research in Data Science
• Part III.2 Health
• Part III.3 Social Sciences
• Part III.4 Humanities
• Part III.5 Arts & Design
• Part III.6 Disciplines A–Z
• Part IV International Perspective
• Part V Avenues for Developing Undergraduate Research

21 - Undergraduate Research in Mathematics

from Part III.1 - STEM

Published online by Cambridge University Press:  11 August 2022

Undergraduate research in mathematics is growing and has become a standard practice in some countries. However, for a novice there is much to learn about mentoring students in mathematics research. In this chapter, we discuss the state of undergraduate research in mathematics and detail a set of best practices for successfully mentoring undergraduate students. Also, we explore some needs and future directions that would help improve undergraduate research in mathematics. Throughout the chapter, we include resources for more information on various topics.

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• Undergraduate Research in Mathematics
• By Michael Dorff
• Edited by Harald A. Mieg , Humboldt-Universität zu Berlin , Elizabeth Ambos , Angela Brew , Macquarie University, Sydney , Dominique Galli , Indiana University–Purdue University, Indianapolis , Judith Lehmann , Universidad de Buenos Aires, Argentina
• Book: The Cambridge Handbook of Undergraduate Research
• Online publication: 11 August 2022
• Chapter DOI: https://doi.org/10.1017/9781108869508.029

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Princeton University Math Club

Princeton University

Undergraduate Research

Research in mathematics and its allies takes a variety of forms: from the most abstract algebraic geometry to the most concrete problems in finance and everything in between. Accordingly, there are many ways to get involved in mathematical research. In general, as an underclassman, the best way to do so is to participate in an REU or other research program during the summer. After that, in your junior and senior years, Princeton provides a natural avenue to research: the junior papers (JP), one per semester during your junior year and, of course, the senior thesis, a year-long project undertaken in your final year. Depending on your background and level of interest in research, however, you might want to consider looking for research opportunities during the year, even in your first two years.

Getting Started [Show] Getting Started [Hide] How do you get started doing research? In general, the answer is to build background through relevant coursework first. Particularly in pure mathematics, it’s very difficult to jump in without having good preparation. Choosing courses that will prepare you for what you want to do, and help you figure out what you want to do for that matter, is important. Necessarily, the details will vary from person to person, but some advice applies across the board. First: choose carefully and plan ahead. Choose your courses thoughtfully. That means thinking about what you want to get out of each course, how your courses in any given semester fit together (in terms of workload, etc.), and what trajectory you’re trying to follow. A lot of this will be uncertain, especially at the start, but thinking about these issues will help remove that uncertainty. Second: consult your peers, advisers, and professors (not necessarily in that order). They have been where you are now, and they can help you get where you are trying to go. You will of course have to choose whom you ask, and have to combine multiple—often conflicting—sources of advice, but the people around you are an invaluable resource in finding your path. That being said, you should take advantage of opportunities to get involved in research early on: it’s often possible to find a good project to work on (at an REU, other research program, or at Princeton) even as a freshman. Early in your undergraduate years, you should be open to the possibilities; research experience, even if it isn’t in the area you ultimately want to pursue, is very useful, notably in helping you find your ultimate interests. As always, consult your academic advisers, professors, and friends (especially older friends) for advice.

Seminars, Lectures, and Colloquia [Show] Seminars, Lectures, and Colloquia [Hide] Attending talks is an important way to find areas of research that interest you. These come in at least three varieties: the Undergraduate Colloquium, which includes faculty, graduate, and undergraduate speakers; the Graduate Student Seminar (GSS), given by graduate students on their research for the benefit of their peers and undergrads; and the various department seminars. If you’re interested in the former two, join the Math Club Listserv and talk to LeeAnn Coleman in the department office to find out how to be added to the GSS mailing list. To get an idea of what goes on in the latter, just look at the seminar listings on the math website at the beginning of every week and see if anything looks interesting. Most seminars provide abstracts, and these will give you an idea about whether you will understand the talk. Look out especially for the department colloquia, because these are usually pitched at a non-specialist level and reasonably accessible—not to mention generally given by very good speakers. The colloquium speaker also sometimes gives a lunchtime talk the day of the colloquium, a practice unique to Princeton; these are also worth attending. As you attend talks, keep in mind that you will sometimes misgauge the difficulty of a talk and at times the speaker will not be very engaging. This will inevitably happen some of the time, but don’t let it discourage you. Try to get at least a little bit out of each talk you go to; an excellent mathematician once remarked to me that he was satisfied if he could come away from a talk with a single sentence of new knowledge: this is a bit extreme, but the general idea is important. In the end, you should attend seminars because you find their subject matter interesting (or intriguing). While they may help you get ideas for research, when you are just starting out, they will more likely point you to areas that are worth looking at. Moreover, attending seminars has long-term benefits for the aspiring researcher.

Junior Seminars [Show] Junior Seminars [Hide] Juniors in the department are required either to write a junior paper or participate in a junior seminar during both semesters. Junior seminars are a learning environment with which you are probably completely unfamiliar. First, it’s largely up to you how much to engage with the lectures and the course overall. For this reason, it’s especially important to pick a seminar whose subject matter interests you. This may be a challenge, as very few seminars are offered, but do your best. Actively following the speaker’s exposition and asking questions where appropriate—never be afraid to ask a question if something is unclear!—are great ways to stay focused on lectures while attending them. To keep up with the course overall, you will want to do the assigned readings, even those that are for talks other than your own. At some point during the semester, you will spend a couple of weeks learning a certain bit of the main topic of the seminar, often contained in a chapter of a textbook or a journal article, and then make a presentation at the seminar. It’s important to give a good talk: it’s your turn to teach your classmates the material. Whether this is your first talk, or you are a veteran lecturer, the best way to ensure a good talk is practice, practice, practice. Practice it at least twice before you give it in the seminar, ideally with another student or even the instructor (feel free to ask). Junior Seminars culminate in a final paper on some topic related to the theme of the seminar. The details vary from seminar to seminar, but, unlike the junior paper and senior thesis, which sometimes include original components, the paper will be purely expository and will generally represent a much more significant effort than a problem set. For advice on finding a topic, consult the section below. Your adviser in this context will be the seminar instructor. Also keep in mind that your paper will not be as elaborate as a senior thesis or junior paper.

What Type of Project is a Senior Thesis (or Junior Paper)? [Show] What Type of Project is a Senior Thesis (or Junior Paper)? [Hide] It’s probably a good idea to start off by saying a bit about what type of “project” a senior thesis and junior paper is. Even if you have participated in an REU or another summer math program for undergraduates, your biggest question might just be, “What type of project does one do with a faculty adviser?” Most theses and JP’s center on a particular important result, research area or program, or major conjecture. The thesis could give an exposition of a proof of a major result (perhaps extending it to slightly more cases), or of major partial results, or of recent results in a research area. It is also possible to undertake original research—though if this is what you want to do, you should ideally prepare yourself thoroughly for it during your first three years (see above). Junior papers are similar, though necessarily less involved, and the project can vary from a specific unsolved problem to an introductory exploration of an area unfamiliar to the student. Ultimately, a thesis or JP is an early step in the career of an aspiring researcher and, accordingly, it is foundational—you will not prove the Riemann hypothesis (probably), you might not end up proving anything, but you will gain valuable experience and learn mathematics that will continue to be useful to you later on. For specific examples, look up old theses in the library and, as always, talk to your older friends! Finally, remember that both a senior thesis and JP require significant writing. Mathematical writing is rather different from the writing you have probably done in other contexts. Various resources on the subject can be found on Terry Tao’s blog, here . In this guide, we’ll just point out that writing clear proofs and definitions makes the relevant concepts much clearer to you and can help you notice subtleties of—and subtle mistakes in—your arguments. One way to help yourself do this, and to find a style to start yourself off with, is to recall a textbook you read that was particularly written and model your writing on its style (not the content, though).

Finding an Adviser [Show] Finding an Adviser [Hide] Starting a thesis or JP requires two major steps: choosing an adviser and choosing a topic. In the overwhelming majority of cases, the former comes first. Choosing your adviser carefully is important. Your adviser’s style and the compatibility between the two of you will deeply influence the quality of your experience. Since you have virtually no time as an upperclassman to experiment with possible advisers—though this will likely happen accidentally anyway—you should consult older students and the faculty academic advisers to figure out which professors might be a good fit for you in terms of research interests and advising style. As always, you will have to be proactive to ensure your experience is all that it can be; ask your peers many questions: about the frequency and content of meetings, the expectations for an undergraduate project (too low? too high?), the level of preparation expected, and so on. Once you have an adviser, you will still need to find an effective way to work together. Sometimes, this will come naturally; that’s especially likely if your adviser often takes undergraduate students. Be that as it may, figure out how often meeting with your adviser is productive; once a week is standard, but some professors prefer biweekly meetings. Even if you have nothing to report, meeting with your adviser helps both of you stay in touch with the project and is an integral part of the research experience. You will also want to prepare for your meetings so as to get the most out of them. While meetings will be your primary interaction with your adviser, e-mails and other day-to-day interactions can be nearly as important. These generally take the form of questions and, here again, you will need to figure out how to make them work best for you. Experience is, for better or for worse, the only real way to learn how to do this. Finally, whoever your adviser is, you will benefit from making friends with their graduate students and postdocs (short for “postdoctoral fellows,” researchers who have recently obtained Ph.D.’s); they can serve as secondary advisers who can help you on a day-to-day basis—and share their experiences with early career research.

Finding a Project [Show] Finding a Project [Hide] Choosing a project is just as important as choosing an adviser. Working on a problem that fascinates and excites you will make your research more enjoyable and rewarding: it is also the best way to ensure you stay motivated throughout the project. Your adviser will likely suggest at least one project at your first meeting, or over e-mail beforehand. Starting the discussion early, whether by e-mail or in person, is helpful; doing so will allow you to go through a few possibilities before committing to one. To decide if an idea is one you want to pursue, you should read about it online, in books, and in the technical literature (for specific places to look, consult your adviser). After you’ve had a chance to look into it, don’t hesitate to voice your doubts about a project if it seems over your head or not interesting to you! All this being said, you should choose a problem early in the term—certainly within the first two or three meetings with your adviser. The easiest way to achieve this is to approach potential advisers well before term starts and to be pro-active about finding a project in advance. While it’s hard to give general advice about choosing a problem, there are a few things to keep in mind. First, choose a project in an area of active research. This will have many benefits, most notably perhaps that you will have access to a wide selection of papers that can help you as you work on your problem. Second, as mentioned above, choosing a project is to a large extent a judgment call: you should choose a topic you find interesting and beautiful if at all possible. Finally, keep in mind that in research, especially early on, things rarely go as planned: balance perseverance with flexibility, and don’t be afraid to change course if necessary, particularly as you figure out what you really want to do with your research.

Advice on the Research Process [Show] Advice on the Research Process [Hide] Read, read, read. And Google. Take time to read about things related to your research. Google—especially Google Scholar—is an excellent way to find material useful to you, often better than arXiv or mathscinet, two popular online technical libraries. Being a Princeton undergraduate means getting access to most journal articles you’ll need, and you should definitely take advantage of the convenience! Google can help answer queries both big and small, from “Find a readable introduction to algebraic K-theory” (huge) to “What does convex cocompact mean?” (tiny). In fact, Googling is almost always the fastest way to resolve any confusion you have as you struggle to understand an idea or term. Ultimately, you may need to read in a more structured way—by focusing on a book or a specific collection of journal articles, for instance—but unstructured reading can help prepare you for that, and help give you a general idea of how the area you’re working in, well, works. Daydreaming (about research) is good for you. If you have a specific problem you need to solve, whether it’s finishing a mostly finished proof, solving a tricky problem, or understand a particularly hard part of a paper you’re reading, it’s frequently useful to daydream about it at random quiet moments during the way: while you walk to class, shower, wait for a friend to meet you for dinner, or whatever. You’ll likely find, as countless mathematicians, scientists, and humanists before you have, that you have more idea during this unstructured time than during scheduled blocks set aside for research (though they have their place—see below). You need structure, too. Regularly setting aside time to work on research is essential. Progress in research is nearly always incremental and non-linear: it takes time and patience. A thesis or a junior paper is a fundamentally long-term project, and to do your best work you will need to treat it that way. To keep yourself productive during structured time, it helps to focus on concrete tasks (e.g., “read this paper”, “work on this part of this proof”, “understand this technique I need”) and to work on answering specific questions.

Other Useful Resources

Terence Tao on time management

Ravi Vakil’s advice for graduate students (some of which is applicable to undergraduates)

Acknowledgements

Many thanks to John Pardon ’11 and Max Rabinovich ’13 for contributing this article.

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Undergraduate Research

Where to start:.

A good starting point is the Harvard College Undergraduate Research and Fellowships page. The Office of Undergraduate Research and Fellowships administers research programs for Harvard College undergraduates. Check out the website . Another resource is OCS , the Harvard Office of Career Services. It offers help on preparing a CV or cover letters and gives advice on how to network, interview, etc. Their website is here . Other Sources that can provide additional information on Scholarships, awards, and other grants:

• Committee on General Scholarships: more …
• Office of International Programs: more …
• Student Employment Office: more …

Independent study in Mathematics

Students who would like to do some independent study or a reading class please read the pamphlet page . about Math 91r.

THE ANNUAL OCS SUMMER OPPORTUNITIES FAIR

The Office of Career Services hosts summer programs to help you begin your summer search. Programs are both Harvard affiliated and public or private sector and include internships, public service, funding, travel, and research (URAF staff will be there to answer your questions!). Check out the website.

Harvard-Amgen Scholars program in Biotechnology

Check out the Harvard-Amgen Scholars Program Learn about Harvard’s Amgen 10-week intensive summer research program, one of ten Amgen U.S. programs that support research in biotechnology. The Harvard program includes faculty projects in FAS science departments, SEAS, the Wyss Institute for Biologically-inspired Engineering, and the School of Medicine, open to rising juniors and seniors in biotechnology-related fields.

PRIMO program

The Program for research in Markets and Organizations (PRIMO) is a 10-week program for Harvard undergraduates who wish to work closely with Harvard Business School faculty on research projects.

Harvard Undergraduate Research Events

• Wednesday, October 10, 12:00-1: 20 PM – Fall Undergraduate Research Spotlight. Come and meet Harvard undergraduate peers who will showcase their research projects and share their experiences conducting research at Harvard and abroad, followed by reception and deserts. Event program and list of presentations can be found here: here (pizza and desserts while supplies last). Free for Harvard students. Cabot Library 1st floor Discovery Bar.
• Wednesday, October 17, 12:00-1: 00 PM – Undergraduate Science Research Workshop. Workshop facilitators Dr. Margaret A. Lynch, (Assoc. Director of Science #Education) and Dr. Anna Babakhanyan, (Undergraduate Research Advisor) will help Harvard students learn about science research landscape at Harvard. You will learn about what kind of research (basic science vs. clinical, various research areas) is available at Harvard, where you can conduct research, the types of undergraduate research appointments, how to find a lab that fits, interviewing and more. In addition, the workshop will provide strategies for students to prepare for the Annual HUROS Fair, see below. No registration is required for this event (pizza while supplies last). Free for all Harvard students. Cabot Library first floor Discover Bar. More.

Outside Programs

Caltech always announces two summer research opportunities available to continuing undergraduate students. Examples: WAVE Student-Faculty Programs The WAVE Fellows program provides support for talented undergraduates intent on pursuing a Ph.D. to conduct a 10-week summer research project at Caltech. And then there is the AMGEN Scholars program. See the website for more details.

Johns Hopkins Summer 2018 Opportunities

The Johns Hopkins University Center for Talented Youth (CTY) is seeking instructors and teaching assistants for our summer programs. CTY offers challenging academic programs for highly talented elementary, middle, and high school students from across the country and around the world. Positions are available at residential and day sites at colleges, universities, and schools on the East and West coasts, as well as internationally in Hong Kong. Website

Math REU list from AMS

Mellon Mays opportunities awareness

The Mellon Mays Undergraduate Fellowship Program ( MMUF ) selects ten students in their sophomore year to join a tightly-knit research community during junior and senior years to conduct independent research in close collaboration with a faculty mentor. Join us at this information session to find out more about the program. MMUF exists to counter the under-representation of minority groups on college and university faculties nationwide through activities designed to encourage the pursuit of the Ph.D. in the humanities and core sciences.

MIT Amgen and UROP

You may be familiar with the Amgen Scholars Program, a summer research program in science and biotechnology. The Massachusetts Institute of Technology is a participant in the Amgen-UROP Scholars Program for a ninth year. UROP is MIT’s Undergraduate Research Opportunities Program. The mission of the Amgen-UROP Scholars Program is to provide students with a strong science research experience that may be pivotal in their undergraduate career, cultivate a passion for science, encourage the pursuit of graduate studies in the sciences, and stimulate interest in research and scientific careers. MIT is delighted to invite undergraduate students from other colleges and universities to join our research enterprise. We value the knowledge, experience, and enthusiasm these young scholars will bring to our campus and appreciate this opportunity to build a relationship with your faculty and campus.

More REU's, not only math

The National Science Foundation Research Experiences for Undergraduates (REU) NSF funds a large number of research opportunities for undergraduate students through its REU Sites program. An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific research project, where he/she works closely with the faculty and other researchers. Students are granted stipends and, in many cases, assistance with housing and travel. Undergraduate students supported with NSF funds must be citizens or permanent residents of the United States or its possessions. An REU Site may be at either the US or foreign location. By using the web page , search for an REU Site, you may examine opportunities in the subject areas supported by various NSF units. Also, you may search by keywords to identify sites in particular research areas or with certain features, such as a particular location. Students must contact the individual sites for information and application materials. NSF does not have application materials and does not select student participants. A contact person and contact information are listed for each site.

Here is a link with more information about summer programs for undergraduates at NSA: NSA The most math-related one is DSP, but those students who are more interested in computer science could also look at, say, CES SP. They are all paid with benefits and housing is covered. Note that application deadlines are pretty early (usually mid-October). The application process will involve usually a few interviews and a trip down to DC.

NSF Graduate Research Fellowships

US citizens and permanent residents who are planning to enter graduate school in the fall of 2019 are eligible (as are those in the first two years of such a graduate program, or who are returning to graduate school after being out for two or more years). The program solicitation contains full details. Information about the NSF Graduate Research Fellowship Program (GRFP) is here . The GRFP supports outstanding graduate students in NSF-supported science, technology, engineering, and mathematics disciplines who are pursuing research-based Masters and doctoral degrees at accredited United States institutions. The program provides up to three years of graduate education support, including an annual, 000 stipend. Applications for Mathematical Sciences topics are due October 26, 2018.

Pathway to Science

summer research listings from pathways to science.

Perimeter Institute

Applications are now being accepted for Perimeter Institute’s Undergraduate Theoretical Physics Summer Program. The program consists of two parts:

• Fully-Funded Two Week Summer School (May 27 to June 7, 2019) Students are immersed in Perimeter’s dynamic research environment — attending courses on cutting-edge topics in physics, learning new techniques to solve interesting problems, working on group research projects, and potentially even publishing their work. All meals, accommodation, and transportation provided
• Paid Research Internship (May 1 to August 30, 2019, negotiable) Students will work on projects alongside Perimeter researchers. Students will have the opportunity to develop their research skills and absorb the rich variety of talks, conferences, and events at the Perimeter Institute. Applicants can apply for the two-week summer school or for both the summer school and the research internship. Summer school and internship positions will be awarded by February 28, 2019. Selected interns will be contacted with the research projects topics. All research interns must complete the two-week summer school.

Apply online at perimeterinstitute.ca/undergrad

Stanford resident counselors

Stanford Pre-Collegiate Institutes is hiring Residential Counselors for the summer to work with the following courses:

• Cryptography (grades 9-10)
• Knot Theory (grades 10-11)
• Logic and Problem Solving (grades 8-9)
• Number Theory (grades 9-11)
• Excursions in Probability (grades 8-9)
• Discrete Mathematics (grades 9-10)
• The Mathematics of Symmetry (grades 10-11)
• Mathematical Puzzles and Games (grades 8-9)

Stanford Pre-Collegiate Institutes offers three-week sessions for academically talented high school students during June and July. Interested candidates can learn more about our positions and apply by visiting our employment website .

Summer Research 2019 at Nebraska

We are now accepting applications for the University of Nebraska’s 2019 Summer Research Program, and we’d like to encourage your students to apply. Details.

Undergraduate Research Journals

• Biology, Chemistry, and General Science
• Math and Physics
• Technology and Engineering
• Business and Economics
• Humanities and Social Sciences
• Interdisciplinary

Undergraduate Research Journals for Math and Physics

• Involve: A Journal of Mathematics " Involve showcases and encourages high-quality mathematical research involving students from all academic levels. Submissions in all mathematical areas are encouraged. Submissions should include substantial faculty input; faculty co-authorship is strongly encouraged. Involve , bridging the gap between the extremes of purely undergraduate-research journals and mainstream research journals, provides a venue to mathematicians wishing to encourage the creative involvement of students." Published 5 times per year.
• Journal of Young Investigators "The Journal of Young Investigators is dedicated to representing undergraduate research in biological/biomedical sciences, physical sciences, mathematics and engineering, psychology and social sciences. We accept submissions of original research articles and literature review articles from undergraduate students." Published monthly.
• Missouri Journal of Mathematical Sciences "The Missouri Journal of Mathematical Sciences (MJMS) publishes well-motivated original research articles as well as expository and survey articles of exceptional quality in mathematical sciences. A section of the MJMS is also devoted to interesting mathematical problems and solutions."
• Pentagon The Pentagon is the official journal of Kappa Mu Epsilon. "It is published semiannually in December and May of each year. Articles of interest to undergraduate mathematics students are included, assisting the Society in achieving its objectives. Most of the papers are written by student KME members and many have previously been presented at national or regional conventions."
• Pi Mu Epsilon Journal The Pi Mu Epsilon Journal is interested in considering mathematical papers. Papers written by undergraduates are preferred. Submissions are accepted from any undergraduate student, and membership in Pi Mu Epsilon is not a requirement.
• PUMP Journal of Undergraduate Research "The PUMP Journal of Undergraduate Research publishes articles written by undergraduate students that want to pursue doctoral studies in the Mathematical Sciences." The journal is published at California State University and welcomes submissions of research papers, papers containing new proofs of known results, and expository papers which propose original points of view.
• Rose-Hulman Undergraduate Mathematics Journal "Devoted entirely to papers written by undergraduates on topics related to mathematics. Although the authors need not be undergraduates at the time of submission or publication, the work must have been completed before graduation. Each paper must be sponsored by a mathematician familiar with the student's work and each paper will be refereed. Many departments of mathematics require senior projects or papers. Presentations at undergraduate mathematics conferences could be expanded and made suitable for publication. Work from summer internships requiring mathematical tools also might be appropriate for publication. Although the paper need not contain original research in mathematics, it must be interesting, well written, and at a level that is clearly beyond a typical homework assignment. Readers of the journal should expect to see new results, new and interesting proofs of old results, historical developments of a theorem or area of mathematics, or interesting applications of mathematics." Submission deadlines are February 1 for the spring issue and September 15 for the fall issue.
• SIAM Undergraduate Research Online " SIAM Undergraduate Research Online (SIURO) is a web-based publication devoted to undergraduate research in applied and computational mathematics. The publication represents a wide range of applied topics, including but not limited to, analysis, discrete mathematics, statistics, operations research, optimization, dynamical systems, modeling, and computation. Typical areas of application include but are not limited to, physical, life, financial, and management sciences and engineering. Each paper must be submitted with a letter from a sponsor. Papers will be posted online as they are accepted."

Subject Guide

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• Last Updated: Jul 12, 2023 2:29 PM
• URL: https://libguides.citytech.cuny.edu/undergradjournals

Quick Links +

Undergraduate research.

Undergraduate Research is an great opportunity to get more involved in the Math Department while working directly with faculty to expand the bounds of existing knowledge. There are many benefits to conducting undergraduate research, including the opportunity to:

• Explore an area of interest more deeply
• Learn first-hand about research to determine if you would like to pursue advanced study after your bachelor's degree
• Gain experience that is often highly valued by graduate school admissions committees
• Present your findings at the UC Davis Undergraduate Research Conference or other symposia, and possibly co-author a published paper
• Build relationships with faculty, which can lead to personalized letters of recommendation

MAT 099/199: Research Credit

Students completing undergraduate research (MAT 99/199) will receive lower/upper division credit toward graduation requirements (180 unit requirement) but will not receive credit toward their major. Every 1 unit of credit corresponds to 3 hours of work a week, or 30 hours of work per quarter.

MAT 099 : Undergraduates students who have 83 units or less completed (lower division credit)

MAT 199 : Undergraduate students who have 84 units or more completed (upper division credit)

Academic Year Research Projects

Each quarter, a list of advertised research projects (along with a link to apply to these projects) can be found on the Quarterly Research Projects webpage .

Undergrad Research Conference 2021

The following are presentations held during the annual conference: 

Research in Ramsey Theory and Automatic Theorem Proving

One-Dimensional range restrcited C^2 Interpolation Algorithm

Approximating K-Means using an ADMM Approach

Recovering Individual Based Model Outcomes on Spatiotemporally Coarsened Data

Summer Research Projects

We have research projects happening each summer. For a list of summer projects (and to apply, if they are taking new students), see the Summer Research webpage .

Undergraduate Research Advisor

The undergraduate research advisor is a faculty member who has agreed to help students with all details related to a Research Experience for Undergraduates (REU). Primary responsibilities include helping students on finding a mentor, selecting students for available fellowships, and advertising other REU programs and fellowships outside of UC Davis.

Contact Professor Babson for help! [email protected]

Undergraduate Senior Thesis in Mathematics

The Department of Mathematics at UC Davis offers undergraduate students the opportunity to participate in original mathematical research that will culminate in a senior undergraduate thesis. A student taking advantage of this opportunity would work under the guidance of a faculty mentor, pursuing original research.

Eligibility

To be eligible to write a senior thesis, advanced undergraduate students must

• Have a GPA of 3.5 or above in upper level courses in Mathematics OR be in the Honors Program .
• Find an appropriate research mentor willing to supervise their research project. Research supervisors can be faculty from the Mathematics Department or faculty from the Graduate Group in Applied Mathematics (GGAM) .
• Students that do not meet the GPA requirement may also be permitted to write a senior thesis. However, they must be nominated by a faculty member who is willing and able to supervise them in a research project, and the nomination must be approved by Undergraduate Research Committee.

Requirements for completion of an undergraduate thesis

• Students must complete two full quarters of research prior to graduation.
• While pursuing their research, students must complete MAT 199 (Special Studies for Advanced Undergraduates) and/or MAT 194 (Undergraduate Thesis) for a total of at least 6 units of credit over two quarters.
• Students must complete a thesis of sufficient quality and substance. Both the research supervisor and the Undergraduate Program Committee Chair (UPC) will evaluate a student's thesis.
• The UPC must receive a draft of the thesis no later than the beginning of the eighth week of the quarter in which the student plans to graduate. The UPC must also receive the supervisor's evaluation of the thesis at this time. The final copy of the thesis must be submitted to the department by the end of finals week.

Students who have a cumulative GPA that exceeds a College of Letters & Science requirement, complete at least 6 units of credits of MAT 199 and/or 194 over two quarters, and complete theses may be considered for graduation with High Honors or Highest Honors. All students completing theses will be recognized at the June Graduation Reception and in the Fall Department Newsletter.

Undergraduate Senior Thesis - Archived Submissions

Research programs at uc davis.

UC LEADS is a comprehensive two-year program designed to prepare economically or educationally disadvantaged students for success in doctoral degree programs in science, engineering, technology, or mathematics. Students are assigned individual faculty mentors, who guide them in academic year and summer research experiences. Scholars receive stipends and housing for their summer research and participate in extensive academic enrichment activities, including presenting their research at the annual UC LEADS Symposium.

MURPPS is a UC Davis undergraduate mentoring program designed to increase the number of disadvantaged students who pursue graduate studies in the physical and mathematical sciences by offering students the chance to work with professors on research projects relevant to their major. The goal of MURPPS is to help create a diverse post-graduate population in the Physical and Mathematical Sciences. Students are paid a quarterly stipend. MURPPS also runs seminars which introduce students to faculty and research projects, offers academic guidance, and access to the tutoring at the Academic Assistance and Tutoring Centers .

The Mentorships for Undergraduate Research in Agriculture, Letters, and Science (MURALS) is a two-quarter program that encourages students to further their education beyond the baccalaureate degree by providing opportunities to participate in academic research with a faculty mentor. MURALS welcomes students from all academic disciplines. For application information, please go to their "How to Apply" webpage.

Online Research Search Engines

The following are just a few suggested links that may prove helpful when you begin your research endeavors at UC Davis. Each site — or search engine — offers a wide variety of research aides including published articles and reviews, mathematical documents for specific phrases, or membership listings.

• Undergraduate Research Opportunities at UC Davis A comprehensive site relative to undergraduate research related to UC Davis, both on and off campus. Includes a link to the Undergraduate Research Center.
• eScholarship The publication listings for the entire University of California. This includes all research topics, but also mathematics.
• Front for the Mathematics ArXiv A front end to assist in searching the mathematics articles archive maintained by Cornell University.
• MathSciNet American Mathematical Society's listing of math reviews on the web.
• American Mathematical Society
• Society for Industrial and Applied Mathematics
• Combined Membership List A searchable database of the combined membership listings of the American Mathematical Society (AMS), Mathematical Association of America (MAA), Society for Industrial and Applied Mathematics (SIAM), American Mathematical Association of Two-Year Colleges (AMATYC), and the Association for Women in Mathematics (AWM).

Undergraduate Research

The following are research opportunities for Stanford undergraduates.  The department does not offer any research opportunities for undergraduates who are not Stanford students.

SURIM, the Stanford Undergraduate Research Institute in Mathematics, is a ten-week program that provides Stanford undergraduates the opportunity to work on mathematical problems in an extra-curricular context. Most students will work on interesting mathematical problems in a collaborative environment. A number will work one-on-one with faculty member. Summer funding will be provided to all participants, thanks to VPUE.

See the  SURIM page for more information.

Honors Thesis

Honors Math majors research and write a senior honors thesis under the direction and guidance of one of our faculty.  Honors majors enroll in Math 197: Senior Honors Thesis with their advisor.  See our Honors in the Major page, including our Math 197 Guidelines.

International Journal of Research in Undergraduate Mathematics Education

• Offers comprehensive coverage of research in the teaching and learning of mathematics at post-secondary level.
• Presents new ideas and major developments in post-secondary mathematics education.
• Publishes empirical, theoretical, and methodological reports about the teaching and learning of mathematics at post-secondary level.
• Reflects the variety of research concerns within the field and the range of methods used to study them.
• All articles undergo a rigorous, double-blind peer review process.
• Alejandro González-Martín,
• Elise Lockwood,
• Elena Nardi

Latest issue

Volume 10, Issue 1

Latest articles

Students' self-work during lectures in calculus courses – cognitive and affective effects of a small intervention.

• Arielle Leitner

When Learner-Centered Teaching and Learning Goes Online: Zooming into Linear Algebra Tutorials During the Pandemic

• Miriam N. Wallach
• Igor’ Kontorovich

Student Interpretations of Eigenequations in Linear Algebra and Quantum Mechanics

• Megan Wawro
• Kevin Watson

Critical, Intersectional, Quantitative Analyses of Instructional Practices and Changes in Undergraduate Students’ Math Affect

• Naneh Apkarian
• Matthew Voigt
• Jason Guglielmo

Graduate Teaching Assistants’ Perception of Student Difficulties and Use in Teaching

• Jungeun Park
• Douglas Rizzolo

Journal information

• Emerging Sources Citation Index
• Google Scholar
• OCLC WorldCat Discovery Service
• TD Net Discovery Service

Rights and permissions

Editorial policies

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• Find a journal
• Publish with us
• Track your research

An Undergraduate's Guide to Funding and Publishing Research

• URECA and other SBU Research Programs and Opportunities
• Funding Your Research
• Publishing Your Research: Why and How?
• Publishing Your Research: List of Undergraduate Journals

SBU's own publications

Note that among the journals listed here are SBU's own publications such as  SBU Brooklogue ,  Young Investigator's Review  and the Stony Brook Undergraduate History Journal . 

How do I know whether my discipline is considered a Humanities or Social Science field?

Humanities includes fields such as Art History, Classics, English, Comparative Literature, History, Musicology, and Philosophy. Sometimes History can be considered broadly as either a Humanities or Social Science discipline, but for the sake of this list, most history journals are listed in the Arts & Humanities category. Likewise, Women's, Gender, and Sexuality Studies and related fields often use methods from both Humanities and Social Science research, so you might find related topics on either the Humanities or Social Science list. Psychology is another borderline discipline that might be classified as either a social science or STEM field. For the sake of this list, Psychology is listed with the Social Sciences. STEM fields are those affiliated with science, technology, engineering, or math.

Journals that publish undergraduate research

There are many journals that focus specifically on publishing undergraduate research. The Council on Undergraduate Research (CUR) keeps an ever growing list of journals that feature undergraduate work . However, many of those listed by CUR are hosted by a specific institution and might only publish the work of their own students, and others might not be peer-reviewed or have publishing fees, so read the descriptions carefully. And, as always, carefully review each journal's website, published articles, and the author submission guidelines before submitting your work.

Below is a list of selected journals that SBU undergraduates are eligible to submit to, organized into the following categories:

• Broad Scope: Journals that publish research in any disciplinary area.
• Arts and Humanities : Fields such as Art History, Classics, English, Comparative Literature, Cultural Studies, History, Musicology, Philosophy, Theology, and Writing & Rhetoric. Sometimes History-related fields are also classified as a Social Science, but on this page, most history journals are in the Arts & Humanities category.
• Social Sciences: Fields such as Sociology, Psychology, Economics, International Affairs, Geography, Sustainability, Political Science, and Human Rights are included here.
• STEM : Fields in the hard sciences, technology, engineering and mathematics.

Broad Scope: Journals that publish research in any discipline

• Aletheia: The Alpha Chi Journal of Undergraduate Scholarship Peer-reviewed journal for undergraduate scholarship run by the Alpha Chi National College Honor Society.
• American Journal of Undergraduate Research (AJUR) AJUR is a national, independent, faculty peer-reviewed, open-source, quarterly, multidisciplinary student research journal.
• Butler Journal of Undergraduate Research (BJUR) Submission of original, scholarly research articles is open to undergraduates from any accredited college or university. BJUR publishes scholarship across the humanities, social sciences, and natural sciences.
• Discussions: The Undergraduate Research Journal of Case Western Reserve University The journal accepts research papers written by current undergraduate students from accredited colleges and universities around the globe. The research can be on any topic.
• Inquiries: Social Sciences, Arts, & Humanities An open access academic journal focusing on publishing high quality original work across a range of disciplines, especially on work in the social sciences, arts, and humanities.
• International Journal of Undergraduate Research & Creative Activities (IJURCA) Peer-reviewed, open-access journal dedicated to the publication of outstanding scholarship by undergraduates and their mentors. Accepts submissions from all academic disciplines, including original research in the the form of articles and literature reviews, as well as creative work in a variety of media.
• Journal of Student Research Multidisciplinary and faculty-reviewed journal devoted to the rapid dissemination of current research done by high school, undergraduate, and graduate students.
• Midwest Journal of Undergraduate Research Multidisciplinary scholarly journal produced by a team of Monmouth College student editors and faculty members with peer and faculty reviewers for each article.
• SBU Brooklogue SBU's exclusively undergraduate, peer-reviewed journal for humanities and social sciences.
• Undergraduate Research Journal Double-blind, educator-reviewed print and electronic journal published annually. A forum for multidisciplinary undergraduate research and creative endeavors including case studies, conceptual pieces, creative writing, journalism writings, literature reviews, original art, photography, and scientific studies. Highlights mentored undergraduate scholarly products across all disciplines from all types of higher education institutions.
• UReCA: The NCHC Journal of Undergraduate Research & Creative Activity The official undergraduate journal of the National Collegiate Honors Council. Submissions are accepted from undergraduates in the following categories: STEM, Social Science, Humanities, Fine Art, and Creative Writing.

Arts and Humanities

• Animus: The Undergraduate Classical Journal of the University of Chicago Supports undergraduate scholarship in the Classics and related fields.
• Apollon Undergraduate Journal A peer-reviewed journal run by faculty and students at Fairfield University. Any undergraduate student whose research was produced through coursework in the humanities may submit.
• Archive: An Undergraduate Journal of History Accepts submissions of History scholarship, including scholarly papers, articles, book reviews, and historical essays from undergraduate students of all majors from colleges and universities in the U.S. or abroad.
• Berkeley Undergraduate Journal of Classics Original manuscripts on any topic related to Classics from undergraduate students in any major at an institution which confers a bachelor's degree are eligible to submit.
• Clio's Scroll: The Berkeley Undergraduate History Journal The journal publishes articles by undergraduates and recent graduates of any university on historical topics.
• Dies Ligibiles: An Undergraduate Journal of Medieval Studies The journal accepts research papers, book reviews, translations, and art in English, French, and Spanish from any undergraduate student at any college or university. The work must pertain to the time period 400 - 1600 CE.
• Epistemai: An Undergraduate Philosophy Journal A student-run philosophy journal at the University of Minnesota Twin Cities. The journal publishes short, original philosophical work done by undergraduates from universities across the country, and internationally.
• Falsafa: Undergraduate Journal of Philosophy Run by the Philosophy Club at the University of California, Irvine, this journal highlights philosophical ideas and research by undergraduates.
• Forbes & Fifth This undergraduate journal of the Dietrich School of Arts and Sciences at the University of Pittsburgh considers both scholarly and creative work from students at any accredited university in the world.
• The Gettysburg College Journal of the Civil War Era Open access peer-reviewed undergraduate journal that publishes academic essays, public history essays, and book reviews on the Civil War Era.
• History Matters: An Undergraduate Journal of Historical Research An undergraduate history journal published annually by the Department of History at Appalachian State University. The journal is indexed by EBSCOhost's America: History and Life.
• Journal of Art History and Museum Studies (JAHMS) An undergraduate peer-reviewed journal that publishes undergraduate scholarship by a diverse coalition of student artists and historians.
• The Kennesaw Tower: Undergraduate Foreign Language Research Journal Annual undergraduate double blind and peer-reviewed journal publishes scholarly work of advanced undergraduates students in Chinese, FLED, French, German, Italian, Portuguese, and Spanish.
• Mysterion: The Theology Journal of Boston College Publishes undergraduate research from around the world on topics related to theology.
• Nota Bene: Canadian Undergraduate Journal of Musicology Publishes essays written by undergraduate students from universities around the world. Topics include historical musicology, ethnomusicology, popular music studies, music theory, music education, and interdisciplinary subjects. Double blind review by professors across Canada.
• The Oswald Review: An International Journal of Undergraduate Research and Criticism in the Discipline of English Published annually, and requiring a faculty member's endorsement, the refereed journal in indexed in EBSCO and accepts undergraduate criticism and research in the field of English from students throughout the U.S. and abroad.
• Queen City Writers: a journal of undergraduate writing & composing Refereed journal that publishes essays and multimedia work by undergraduate students affiliated with any post-secondary institution. Topics covered include writing, rhetoric, reading, pedagogy, literacy broadly conceived, popular culture and media, community discourses and multimodal and digital composing.
• Rock Creek Review An undergraduate journal edited, produced and published at Heidelberg University in partnership with the English Department. The journal publishes literary research from schools around the world for an annual publication. Check the website for the "call for papers," which will explain the theme of the next issue.
• RhetTech Undergraduate Journal Run by students at James Madison University, this journal showcases exemplary work being done in undergraduate writing, rhetoric, and technical communication courses around the country.
• Simpliciter: Brandies Philosophy Journal Run by students at Brandeis University, this journal aims to recognize excellent works of philosophy produced by undergraduates from universities anywhere in the world.
• sprinkle: an undergraduate journal of feminist and queer studies A peer-reviewed journal devoted to the diverse voices of emerging scholar-activists, authors, and artists in Women's Gender & Queer Studies and related fields. First established at McGill University, sprinkle is now published at Cal Poly San Luis Obispo and welcomes submissions from around the world.
• Stance: An International Undergraduate Philosophy Journal Peer-reviewed journal publishes original work by undergraduates from around the world.
• Stony Brook Undergraduate History Journal Peer-reviewed publication that showcases the research of SBU students writing about history at the local, national and international levels.
• UC Berkeley Comparative Literature Undergraduate Journal Publishes undergraduate research in comparative texts and media, treating a broad range of topics including theoretical literary discourse, international trends in literature, and comparisons for national literature. Showcases the best work across the U.S. and also highlight more contemplative writing by students regarding multicultural issues, culture shock, or transnational experiences such as studying abroad.
• UC Santa Barbara Undergraduate Journal of History A space for undergraduates to share original research other scholarly works of history. Reviewed by graduate students with faculty mentorship.
• Xchanges: An Interdisciplinary Journal of Technical Communication, Rhetoric, and Writing Across the Curriculum The fall issues publishes these and research projects of upper-level undergraduate students. Submissions may be traditional articles or multimodal "webtexts." Based in the English Department at the University of New Mexico.
• Yale Historical Review Welcomes works from undergraduates at any institution on any historically relevant topic.
• Young Scholars in Writing (YSW) An international peer-reviewed journal. Publishes original research and theoretical articles by undergraduates of all majors and years on the subjects of rhetoric, writing, writers, discourse, language, and related topics.

Social Sciences

• Afkar: The Undergraduate Journal of Middle East Studies International peer-reviewed journal that accepts research articles, essays, and book reviews that focus on the politics, history, culture, and society of the Middle East and North Africa.
• Al Noor Boston College's Middle Eastern Studies journal. It is run by undergraduates and publishes work from students around the world.
• Cambridge Journal of Political Affairs A student-run academic journal supported by the Department of Politics and International Studies at the University of Cambridge. The journal publishes undergraduate scholarly work on topics such as political philosophy, political history, comparative politics, international relations, political anthropology, and political sociology.
• Chicago Journal of Foreign Policy: University of Chicago's Premiere Undergraduate Journal of International Affairs Accepts submissions from undergraduates from around the world on articles related to foreign policy, international relations, and related topics, preferably pertaining to the period since 1945..
• Compass: An Undergraduate Journal of American Political Ideas A joint project of Northern Illinois University and Arizona State University, Compass publishes work related to American democracy understood in the broad contexts of political philosophy, history, literature, economics, and culture.
• Consilience: The Journal of Sustainable Development To encourage an international community to think more broadly, deeply, and analytically about sustainable development, the journal publishes work by students, researchers, professors, and practitioners from a variety of academic fields and geographic regions.
• Critique: a worldwide student journal of politics Peer-reviewed journal that publishes scholarship by students of political science. The journal is recognized by the American Political Science Association and indexed by EBSCO.
• The Developing Economist Student-run undergraduate economics research journal, published with support from the Longhorn Chapter of the Omicron Delta Epsilon Economics Honor Society and the Department of Economics at the University of Texas at Austin.
• Issues in Political Economy Co-edited by undergraduates at Elon University and the University of Mary Washington, the journal publishes undergraduate research in the field of economics and is indexed in Cabell's Directory of Publishing Opportunities in Economics and Finance.
• Journal of Integrated Social Sciences A web-based, peer-reviewed journal committed to the scholarly investigation of social phenomena. We especially encourage students and their faculty advisors to submit the results of their investigations in Psychology, Sociology, and Gender Studies.
• Journal of Interpersonal Relations, Intergroup Relations, and Identity (JIRIRI) Affiliated with the Universite de Montreal, the international peer-reviewed journal publishes the work of undergraduates on new theoretical ideas in the fields of psychology, identity, interpersonal and intergroup relations. It publishes both theoretical and empirical articles.
• The Journal of Undergraduate Ethnic Minority Psychology (JUEMP) Open access, double blind, peer-reviewed journal devoted to publishing research authored or co-authored by undergraduates. The journal is especially interested in submissions that are from ethnic minorities perspectives, that focus on the thoughts and behaviors of ethnic minority populations, or both.
• New Errands: The Undergraduate Journal of American Studies Sponsored by The Eastern American Studies Association and the American Studies Program at Penn State Harrisburg, this journal publishes undergraduate research in the field of American Studies.
• The Philosophy, Politics, and Economics Review International undergraduate journal housed in the Kellogg Center for Philosophy, Politics, and Economics at Virginia Tech. Through a double blind review process, the journal publishes original research in the humanities and social sciences from undergraduates worldwide.
• Process: Journal of Multidisciplinary Undergraduate Scholarship Published quarterly, the journal publishes undergraduate writings that rigorously engage with issues of social justice, transformative education, politics, identity, and cultural production. Publishes both critical essays and non-traditional or multimodal compositions.
• Righting Wrongs: A Journal of Human Rights Based at Webster University's Institute for Human Rights and Humanitarian Studies, this peer-reviewed academic journal publishes undergraduate research papers, book reviews, opinion pieces, and photo essays that explore human rights issues.
• Social Moments: A Student Journal of Social Relations Interdisciplinary peer-reviewed journal examining the social and cultural world through a social science lens. All undergraduate and graduate students are invited to submit work in any social science discipline.
• Sociology between the Gaps: Forgotten and Neglected Topics Undergraduates, graduates, and professionals in sociology and related fields may submit their articles, books and film reviews, and point of view essays. Double blind peer review.
• Undergraduate Journal of Global Citizenship Based at Fairfield University, the journal publishes undergraduate research on topics related to International Studies such as global awareness, interdependence, environmental responsibility, social justice, humanitarianism, and other themes that promote the understanding of global citizenship.
• Undergraduate Journal of Service Learning & Community-Based Research Refereed, multidisciplinary, open access undergraduate journal that publishes articles from students all around the world. Accepted articles contribute to the literature on service learning and community-based research through reflection, research, or analysis. Based at University of North Carolina Wilmington.
• The Undergraduate Research Journal of Psychology at UCLA (URJP) Based at UCLA, but accepting submissions of undergraduate research from institutions all over the world, this peer-reviewed journal aims to empower undergraduate students to engage in and with research and facilitate scientific conversation and inquiry in the field of psychology.

STEM Fields

• Columbia Undergraduate Science Journal (CUSJ) Open access science journal that publishes manuscripts resulting from significant scientific research or analysis. Each paper undergoes a double-blind peer review process and a faculty review by the CUSJ Faculty Advisory Board.
• EvoS: The Evolutional Studies Consortium A peer-reviewed open access journal, EvoS welcomes work from all academic disciplines and interdisciplinary scholarship that incorporates evolutionary theory.
• Illumin Magazine: A Review of Engineering in Everyday Life An online magazine dedicated to exploring the science and technology behind the things we encounter every day. Features the work of University of Southern California undergraduate engineers, as well as submissions from universities across the U.S.
• Impulse: The Premier Undergraduate Neuroscience Journal International online neuroscience journal for undergraduate publications.
• International Journal of Exercise Science This journal engages undergraduate and graduate students in scholarly activity as both authors and reviewers. Articles on exercise science undergo peer review.
• Intersect: The Stanford Journal of Science, Technology, and Society An open access international science, technology, and society research journal that accepts undergraduate, graduate, and PhD submissions at the intersection of history, culture, sociology, art, literature, business, law, health, and design with science and technology. Students from around the world are invited to submit.
• Involve: A Journal of Mathematics High quality mathematical research involving students from all academic levels. Submissions should include substantial faculty input; faculty co-authorship is required and the submission should come from a faculty member.
• Journal of Undergraduate Chemistry Research Peer-reviewed journal that publishes undergraduate students' work in chemistry, including analytical, organic, inorganic, physical, polymers, and biochemistry.
• Journal of Undergraduate Kinesiology Research Published by the Kinesiology Department at the University of Wisconsin Eau Claire, the peer-reviewed, journal is dedicated to original undergraduate research in Kinesiology. Currently, the research originates from students at the University of Wisconsin, but undergraduates from all institutions are invited to submit.
• Journal of Undergraduate Research in Physics and Astronomy (JURPA) Peer-reviewed publication of the Society of Physics Students comprised of undergraduate research, outreach, and scholarly reporting.
• Journal of Young Investigators (JYI) JYI publishes original work in the sciences written by undergraduates mentored by a faculty member. The mission of the journal is to improve undergraduate science training by providing innovative, high quality educational experiences in science writing, publication, and the peer-review process.
• Psi Chi Journal Undergraduate, graduate, and faculty submissions welcome year round to this peer-reviewed psychology journal.
• Rose-Hulman Undergraduate Mathematics Journal Devoted entirely to papers written by undergraduates on topics in the mathematical sciences. Sponsored by the Mathematics Department at Rose-Hulman Institute of Technology, the journal accepts submissions from undergraduates around the world and faculty co-authors are not permitted.
• RURALS: Review of Undergraduate Research in Agricultural and Life Sciences Faculty-refereed international journal devoted to the publication of high quality research by undergraduates in all agricultural research problem areas.
• SIAM Undergraduate Research Online (SIURO) Run by the Society for Industrial and Applied Mathematics (SIAM), SIURO publishes articles written by undergraduates from all over the world in the field of computational mathematics. Each paper must be submitted with a letter from a faculty advisor.
• Spectrum Published by the University of Alberta, this multidisciplinary journal publishes research completed by undergraduates in a variety of formats including research articles, review articles, music, video, visual arts, and creative writing.
• Spora: A Journal of Biomathematics Published by Illinois State, this is an open access refereed research journal dedicated to publishing high quality manuscripts by undergraduate or graduate students that describe mathematical and statistical techniques to solve problems in biological settings, as well as in experimental biology. Requires an article processing charge.
• PUMP Journal of Undergraduate Research PUMP stands for Preparing Undergraduate Mathematicians for Ph.D.s, and the journal publishes articles by undergraduates students who want to pursue doctoral studies in the Mathematical Sciences. The journal especially encourages submissions by students from underrepresented groups. Topics include pure and applied mathematics and statistics and authors may submit research papers, papers containing new proofs of known results, and expository papers which propose original points of view.
• Undergraduate Journal of Experimental Microbiology and Immunology (UJEMI+) Based at the University of British Columbia, the journal has two versions -- one that publishes only UBC students (UJEMI) and the other that is open to external submissions (UJEMI+). Dedicated to the publication of undergraduate articles in fields related to microbiology and immunology, the journal requires a formal endorsement from a course instructor or researcher who mentored the student authors.
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181 Mathematics Research Topics From PhD Experts

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

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Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

• Roll two dice and calculate a probability
• Discuss ancient Greek mathematics
• Is math really important in school?
• Discuss the binomial theorem
• The math behind encryption
• Game theory and its real-life applications
• Analyze the Bernoulli scheme
• What are holomorphic functions and how do they work?
• Describe big numbers
• Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

• Methods to count discrete objects
• The origins of Greek symbols in mathematics
• Methods to solve simultaneous equations
• Real-world applications of the theorem of Pythagoras
• Discuss the limits of diffusion
• Use math to analyze the abortion data in the UK over the last 100 years
• Discuss the Knot theory
• Analyze predictive models (take meteorology as an example)
• In-depth analysis of the Monte Carlo methods for inverse problems
• Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

• Discuss the greatest common divisor
• Explain the extended Euclidean algorithm
• What are RSA numbers?
• Discuss Bézout’s lemma
• In-depth analysis of the square-free polynomial
• Discuss the Stern-Brocot tree
• Analyze Fermat’s little theorem
• What is a discrete logarithm?
• Gauss’s lemma in number theory
• Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

• Discuss Brun’s constant
• An in-depth look at the Brahmagupta–Fibonacci identity
• What is derivative algebra?
• Describe the Symmetric Boolean function
• Discuss orders of approximation in limits
• Solving Regiomontanus’ angle maximization problem
• What is a Quadratic integral?
• Define and describe complementary angles
• Analyze the incircle and excircles of a triangle
• Analyze the Bolyai–Gerwien theorem in geometry
• Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

• Mathematics and its appliance in Artificial Intelligence
• Try to solve an unsolved problem in math
• Discuss Kolmogorov’s zero-one law
• What is a discrete random variable?
• Analyze the Hewitt–Savage zero-one law
• What is a transferable belief model?
• Discuss 3 major mathematical theorems
• Describe and analyze the Dempster-Shafer theory
• An in-depth analysis of a continuous stochastic process
• Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

• Define the hyperbola
• Do we need to use a calculator during math class?
• The binomial theorem and its real-world applications
• What is a parabola in geometry?
• How do you calculate the slope of a curve?
• Define the Jacobian matrix
• Solving matrix problems effectively
• Why do we need differential equations?
• Should math be mandatory in all schools?
• What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

• Discuss the reductio ad absurdum approach
• Discuss Boolean algebra
• What is consistency proof?
• Analyze Trakhtenbrot’s theorem (the finite model theory)
• Discuss the Gödel completeness theorem
• An in-depth analysis of Morley’s categoricity theorem
• How does the Back-and-forth method work?
• Discuss the Ehrenfeucht–Fraïssé game technique
• Discuss Aleph numbers (Aleph-null and Aleph-one)
• Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

• Discuss the differential equation
• Analyze the Jacobson density theorem
• The 4 properties of a binary operation in algebra
• Analyze the unary operator in depth
• Analyze the Abel–Ruffini theorem
• Epimorphisms vs. monomorphisms: compare and contrast
• Discuss the Morita duality in algebraic structures
• Idempotent vs. nilpotent in Ring theory
• Discuss the Artin-Wedderburn theorem
• What is a commutative ring in algebra?
• Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

• What are the goals a mathematics professor should have?
• What is math anxiety in the classroom?
• Teaching math in UK schools: the difficulties
• Computer programming or math in high school?
• Is math education in Europe at a high enough level?
• Common Core Standards and their effects on math education
• Culture and math education in Africa
• What is dyscalculia and how does it manifest itself?
• When was algebra first thought in schools?
• Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

• What is a multiplication table?
• Analyze the Scholz conjecture
• Explain exponentiating by squaring
• Analyze the Myhill-Nerode theorem
• What is a tree automaton?
• Compare and contrast the Pushdown automaton and the Büchi automaton
• Discuss the Markov algorithm
• What is a Turing machine?
• Analyze the post correspondence problem
• Discuss the linear speedup theorem
• Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

• What is two-element Boolean algebra?
• The life of Gauss
• The life of Isaac Newton
• What is an orthodiagonal quadrilateral?
• Tessellation in Euclidean plane geometry
• Describe a hyperboloid in 3D geometry
• What is a sphericon?
• Discuss the peculiarities of Borel’s paradox
• Analyze the De Finetti theorem in statistics
• What are Martingales?
• The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

• Discuss Newton’s laws of motion
• Analyze the perpendicular axes rule
• How is a Galilean transformation done?
• The conservation of energy and its applications
• Discuss Liouville’s theorem in Hamiltonian mechanics
• Analyze the quantum field theory
• Discuss the main components of the Lorentz symmetry
• An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

• Most useful trigonometry functions in math
• The life of Archimedes and his achievements
• Trigonometry in computer graphics
• Using Vincenty’s formulae in geodesy
• Define and describe the Heronian tetrahedron
• The math behind the parabolic microphone
• Discuss the Japanese theorem for concyclic polygons
• Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

• Finding critical points in a graph
• The basics of calculus
• What makes a graph ultrahomogeneous?
• How do you calculate the area of different shapes?
• What contributions did Euclid have to the field of mathematics?
• What is Diophantine geometry?
• What makes a graph regular?
• Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

• What are extremal problems and how do you solve them?
• Discuss an unsolvable math problem
• How can supercomputers solve complex mathematical problems?
• An in-depth analysis of fractals
• Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
• An in-depth look at Einstein’s field equation
• The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

• When do we need to apply the L’Hôpital rule?
• Discuss the Leibniz integral rule
• Calculus in ancient Egypt
• Discuss and analyze linear approximations
• The applications of calculus in real life
• The many uses of Stokes’ theorem
• Discuss the Borel regular measure
• An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

• The life and work of the famous Pierre de Fermat
• What are limits and why are they useful in calculus?
• Explain the concept of congruency
• The life and work of the famous Jakob Bernoulli
• Analyze the rhombicosidodecahedron and its applications
• Calculus and the Egyptian pyramids
• The life and work of the famous Jean d’Alembert
• Discuss the hyperplane arrangement in combinatorial computational geometry
• The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

• Is paying a loan with another loan a good approach?
• Discuss the major causes of a stock market crash
• Best debt amortization methods in the US
• How do bank loans work in the UK?
• Calculating interest rates the easy way
• Discuss the pros and cons of annuities
• Basic business math skills everyone should possess
• Business math in United States schools
• Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

• What is the autoregressive conditional duration?
• Applying the ANOVA method to ranks
• Discuss the practical applications of the Bates distribution
• Explain the principle of maximum entropy
• Discuss Skorokhod’s representation theorem in random variables
• What is the Factorial moment in the Theory of Probability?
• Compare and contrast Cochran’s C test and his Q test
• Analyze the De Moivre-Laplace theorem
• What is a negative probability?

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Research Papers readable by undergraduates

From here and there, I sometimes encounter mathematical papers that are readable by me, an undergraduate student in Mathematics, which don't go into much specializations in specific fields, which I usually find quite interesting. Some examples are: D.I.E paper , DwD paper and this one . I would be glad if someone could provide me with a list of such papers to read or point to a source which does.

• reference-request
• soft-question
• recreational-mathematics

• 4 $\begingroup$ Many papers in the MAA journals (The Monthly, Mathematics Magazine, College Math Journal) would qualify. $\endgroup$ –  Gerry Myerson Commented Dec 6, 2016 at 8:14
• 1 $\begingroup$ @GerryMyerson It would be better any of these were available for free reading. $\endgroup$ –  IamThat Commented Dec 6, 2016 at 8:20
• $\begingroup$ They are, if your university library has a subscription. $\endgroup$ –  Gerry Myerson Commented Dec 6, 2016 at 11:10
• 2 $\begingroup$ Here's a link to scads of papers written by undergraduates as part of the University of Chicago REU program: math.uchicago.edu/~may/REU2016 I found this by just typing $$\rm{ reu\ papers\ math}$$ into Google, there's probably lots more out there. $\endgroup$ –  Gerry Myerson Commented Dec 7, 2016 at 0:26
• 2 $\begingroup$ REU papers aren't always well-written enough to be "readable by undergraduates"; you'd have to sift the chaff from the wheat just as much as with research papers (in my experience). That said, May's page is a great resource, if you are willing to do that sifting. $\endgroup$ –  darij grinberg Commented Dec 14, 2016 at 10:38

8 Answers 8

See the following link: MAA awards

You will find a long list of awarded expository articles published by MAA journals (like the College Mathematics Journal, the Mathematics Magazine, and the American Mathematical Monthly). Among these awards I recommend the Paul R. Halmos - Lester R. Ford Awards and the Carl B. Allendoerfer Awards .

For most of them, pdfs are available for FREE .

From my experience :

I hear Mathematical Intelligencer is good but I have never read it.

I have heard that reading things that you don't completely understand is good for mathematicians so I also recommend the Notices of the AMS.

Plus is a math themed magazine. I feel doubtful it would prepare you for graduate school in any way.

College Mathematics Journal

Mathematics Magazine

American Mathematical Monthly. Also the Pi Mu Epsilon Journal would make a very good read. I would also recommend reading Mathematical Spectrum.

It's quite likely that the function $f:[1707, 2016] \cap \mathbb{N} \to [0,1] \cap \mathbb{Q}$ given by

$$f(t) = \frac{\text{# of published research papers written in year} \ t \ \text{readable by current undergraduate students}}{\text{# of published research papers written in year} \ t}$$

is decreasing. Therefore, it would perhaps be in your interest to look for older research papers. Moreover, reading older papers helps provide some historical context as to how mathematics got to where it is today. I feel that this is indispensable for an undergraduate to know.

(Fun fact: Euler was born in $1707$)

I would suggest

Manjul Bhargava , The factorial function and generalizations . Amer. Math. Monthly 107 (2000), no. 9, 783--799

This article is an exciting paper based on elementary ideas, and an invitation to read more, written by a (future at that time) Fields medalist.

Thomas J. Osler (yes, THAT Osler for those who are into long distance running) has a lot of papers freely available that would be suitable. By looking up the homepages of the authors listed in the bibliographies of these papers, you should find a few other people who have similar freely available lists of papers. Keep repeating this, and very soon you'll get a large number of papers.

(To address concern raised in comment) My intent is to show you "how to fish" rather than "giving you a fish". The idea is to search for people and not just for papers. Look at the authors of papers (in whatever areas of math you're interested in) that are published in the journals in which Osler's papers appear (these are journals that tend to publish the kinds of papers you are interested in), and visit these people's homepages. For most journals, you don't need to have university library access or get past paywalls to look at the table of contents (to see the titles and the authors of the papers in the journal).

• $\begingroup$ Most of the papers from the site are related to applied analysis and some of them are from perhaps algebra-precalculus. What I intended to ask was papers from every field, such as number-theory, linear and abstract algebra, combinatorics, graph-theory, etc. which don't use terms and results studied explicitly by graduate students. Examples can be found above. $\endgroup$ –  IamThat Commented Dec 6, 2016 at 16:35
• $\begingroup$ (After edit)Well, what I meant to say in this analogy that the fish-pond is kind of trivial, and just manipulates things learnt in high-school. I do have mathematics professors in my college too and if I were to look at any papers I could start from there too. But, as I said most of them require specializations. In the link provided by you, most of them are (nearly) elementary. $\endgroup$ –  IamThat Commented Dec 15, 2016 at 5:22
• $\begingroup$ What about Alexander Abian's papers ? Quite a few of them are accessible without a lot of background knowledge, and they're not focused on manipulation like Thomas J. Osler's papers are. Indeed, I've cited many of Abian's papers since 1999 (mostly in sci.math, before 2010 or so) for their detailed and elementary treatment of various topics. Here's one I cited in stachexchange: Methods to prove axiom independence $\endgroup$ –  Dave L. Renfro Commented Dec 15, 2016 at 15:03
• $\begingroup$ I just noticed that Osler's web page link no longer works. This internet.archive version shows his papers (up to 17 February 2016), although the links to the .pdf files of his papers don't work. However, this google scholar list of his papers has feely available links to many of his papers. $\endgroup$ –  Dave L. Renfro Commented Jan 4, 2022 at 10:47

If you're interested in applied mathematics, the SIAM Review publishes annual articles on current and significant research, which are often written by preeminent scholars in the field (and accompanied by a great number of references). Although it is not free, most institutions have subscriptions to it. In addition, if you are an undergraduate, you may be able to get a free student membership to SIAM , which grants access to the Review.

Although some articles are not written at an undergraduate level, I find that the Survey and Review papers often are. Here are some recent, well-written reviews and surveys likely to be of interest:

• Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures
• Computational Methods for Linear Matrix Equations
• Pairwise Compatibility Graphs: A Survey
• Border-Collision Bifurcations in $\mathbb{R}^N$

You can take a look at this: The Mathematics Student

• $\begingroup$ Beautiful. Thanks for sharing! $\endgroup$ –  IamThat Commented Dec 3, 2021 at 13:40

My two tips would sound more-less like this: 1) Try to read some articles concerning metrics, or functional equations, basic number theory, as they do not require deep, intensive research to understand the very idea behind the given reasoning. 2) Don't divulge into some fuzzy logic, pde or stuff which generally requires a lot of theoretical basis.

You can use http://www.ams.org/mrlookup to find something which would catch your interest.

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Department of Mathematics

Undergraduate research, summer undergraduate research at yale (sumry).

The SUMRY program is a ten-­week undergraduate research program run by the mathematics department at Yale University, usually between early June and early August. In a recent year , there were 15-20 funded positions for undergraduates to investigate open research problems in the mathematical sciences. Students work either individually or in small groups, directed by faculty members, post­doctoral fellows, and graduate students. The work pursued in this program will give participants an idea of what research in mathematics is like.

Directed Reading Program

The Directed Reading Program pairs undergraduate students with graduate student mentors to read and work through a mathematics text over the course of one semester. The pairs meet once each week for one hour, with the undergraduates expected to do about 4 hours of independent reading per week. At the end of the semester, undergraduates either give a talk to their peers or prepare a short exposition of some of the material from the semester. Undergraduates are expected to have a high level of mathematical maturity and eagerness to learn the topic.

Math 470 is an individual studies course, it can be taken for graduation credit (but not applied toward undergraduate math major requirements). By default, it can be taken only once, though under exceptional circumstances, the DUS may permit it to be taken twice. Interested students must submit a proposal to math.dus@yale.edu at least three days before the end of add / drop period, with the name of their adviser, and details about the proposed study (both its content and the structure of the course). Typically, the class will require weekly meetings with the adviser, it will have some assignments along the way (that are to be written up or presented to the adviser), and it will terminate with a final paper or project. Please note that university rules do not allow independent study on topics that are taught in existing courses (there can be a bit of overlap, but you cannot do independent study to learn Math 370, for example). 

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Mathematics Undergraduate Research Awards (MURA)

The Mathematics Undergraduate Research Award (MURA) Program is an undergraduate research award program sponsored by the Faculty of Mathematics . This award provides experience that nurtures an interest in research careers and mathematics experience for undergraduate students with financial support during a full-time, on-campus or remote position for 16 weeks.​

Application deadlines

The MURA is awarded three times a year. Applications are typically due 4 months before the start of the research term. A secondary deadline will be announced if there are remaining awards to allocate.

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Compensation

Eligibility, how to apply.

Interested students with questions should first refer to the  Undergraduate research FAQ  for more information. 

If you have difficulties regarding the applications forms or any parts of the MURA process not listed here or on the FAQ, please contact  Daniel Huab .

Clara worked with Professor Xi He , where she investigated and designed novel techniques to support differentially private analysis of graph data during the Winter 2022 term.

" One thing I appreciated a lot about my research assistantship under Dr. He was the amount of independence and ownership I had over my project. This autonomy and level of trust between my supervisor and I was unlike anything I had never experienced before in my previous co-ops. "

I would absolutely recommend other undergraduate students to pursue a research assistantship if they're curious about research or graduate school at all. It's hard to know what research is really like until you do it! Clara Xi, BCS candidate

Length of Project

Full-time (35 hours per week) for 16 consecutive weeks (80 working days).

• Can be counted as a co-op work term but you do not need to be a co-op student to be eligible for this award.

A student is not allowed to be taking courses full-time or working on another project/job while holding the MURA as it is considered a full-time job.

Commencing Fall 2024, MURA recipients will receive a minimum of $10,018 / term:

The value of the NSERC USRA: $6,000

• The supervisor’s contribution: $4018 (minimum)

Additional Funding Sources

Students/supervisors may supplement their MURA with the Undergraduate Research Fellowship (URF) valued at $7,500.

Students admitted with the President’s Scholarship of Distinction can claim the President’s Research Award ($1,500) to supplement the supervisor's contribution.

Student eligibility

To be considered eligible for the MURA, students must

• be registered in at least one of the two terms immediately before holding the award in a bachelor’s degree program in the Faculty of Mathematics at the University of Waterloo,
• have completed all the course requirements of at least the first year of university study (i.e. must be in their 2A term or higher), 
• have a cumulative average (CAV) of at least 80%, and
• be a Canadian citizen, a permanent resident of Canada, or an International Student with a valid study/work permit, as of the application deadline.

Further, students

• cannot have started a program of graduate studies in a field of mathematics at any time,
• cannot hold more than one MURA per fiscal year (May 1 to April 30),
• cannot hold more than three MURAs during their undergraduate degree, and
• cannot hold both USRA and MURA in the same term.

Supervisor eligibility

To be considered eligible for the MURA, supervisors must

• hold a faculty appointment in the Faculty of Mathematics, preferably with an appointment in the School of Computer Science,
• be authorized to independently supervise students,
• be eligible to administer NSERC funds, and
• propose a research project that falls under NSERC’s mandate .

After finding an eligible supervisor that has agreed to work with you and deciding on a research project that clearly defines your role and responsibilities with the supervisor, the following steps must be completed.

• Complete the online form  using your WATIAM sign-in information.
• Your supervisor will have to  complete the following online form . 
• A recent copy of your unofficial transcript.
• The date you expect to complete your degree (month/year).

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This subreddit is for discussion of mathematics. All posts and comments should be directly related to mathematics, including topics related to the practice, profession and community of mathematics.

Advice for Publishing Research in Undergraduate

I am a junior, undergraduate math major in the US. Since the summer of 2021 I have been working continuously on a research project with a professor at my university acting as an advisor. I have produced original results which I and my advisor feel to be substantial. The paper I am working on builds upon a 2019 paper which was published in a professional journal.

My advisor has told me that she feels my work is of sufficient quality that it could be published in a professional journal, but has also said that she feels it may be a better choice career wise to publish in an undergraduate journal. Her reasoning is that if I were to submit to a professional journal, the refereeing process may take a long time, and my submission may not be accepted by the time I will be applying to grad schools.

While I see her point, I am a little bit skeptical of undergraduate journals in general. I would love some advice on how to think about this decision, as well as any sources for me to read some more about the difference between undergraduate and professional journals.

Some specific questions I have are as follows.

How would grad schools view a paper accepted to an undergraduate journal, vs a paper that has only been submitted (but not accepted) to a professional journal?

Is it unreasonable of me to think that undergraduate journals are less "serious" than professional journals?

Am I being too optimistic about my chances of acceptance to a professional journal? I would like to reiterate that my results are completely original, and both I and my advisor feel that they are substantial and of high quality.

Any tips for writing up my results in a professional manner?

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Building a mathematical model for a simple harmonic oscillator that uses educational methods found in both physics education research and in the language disciplines that make it accessible to undergraduate students in an introductory musical acoustics course

• Linz, Jill A.

At the basis of any course in acoustics is the fundamental idea of the simple harmonic oscillator. The term alone is confusing to students with little to no background in physics or math. For courses in musical acoustics at the undergraduate level, this topic is often minimized due to the lack of preparation. This, in turn, results in a more superficial approach to the advanced topics. While deriving the mathematical treatment from first principles is out of reach to these students, approaching the math itself as a language where they are building a description of a simple mass and spring system in their new, yet somewhat familiar, language can be accomplished through pictures, graphs and hands on activities. Students begin to build a vocabulary of "words" that can be strung together in "sentences" that tell the story of how the motion of a mass on a spring is produced. Emphasis is placed on the analogous comparison of physical properties by relating variables such as amplitude and frequency to that of volume and pitch. This model can then be used as a building block to the understanding of how sound is produced, propagated and perceived.

Mathematics success in getting Undergraduate LMS Research Bursaries

Congratulations to Michael Morris, Abby Saynor and Matthew Yeung for getting Undergraduate LMS Research Bursaries to conduct research over the summer months.

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By Siobhan Roberts

At the headquarters of Google DeepMind, an artificial intelligence laboratory in London, researchers have a longstanding ritual for announcing momentous results: They bang a big ceremonial gong.

In 2016, the gong sounded for AlphaGo, an A.I. system that excelled at the game Go. In 2017, the gong reverberated when AlphaZero conquered chess. On each occasion the algorithm had beaten human world champions.

Last week the DeepMind researchers got out the gong again to celebrate what Alex Davies, a lead of Google DeepMind’s mathematics initiative, described as a “massive breakthrough” in mathematical reasoning by an A.I. system. A pair of Google DeepMind models tried their luck with the problem set in the 2024 International Mathematical Olympiad, or I.M.O., held from July 11 to July 22 about 100 miles west of London at the University of Bath. The event is said to be the premier math competition for the world’s “brightest mathletes,” according to a promotional post on social media.

The human problem-solvers — 609 high school students from 108 countries — won 58 gold medals, 123 silver and 145 bronze. The A.I. performed at the level of a silver medalist, solving four out of six problems for a total of 28 points. It was the first time that A.I. has achieved a medal-worthy performance on an Olympiad’s problems.

“It’s not perfect, we didn’t solve everything,” Pushmeet Kohli, Google DeepMind’s vice president of research, said in an interview. “We want to be perfect.”

Nonetheless, Dr. Kohli described the result as a “phase transition” — a transformative change — “in the use of A.I. in mathematics and the ability of A.I. systems to do mathematics.”

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Undergraduate

Mathematics provides a language and tools for understanding the physical world around us and the abstract world within us. MIT's Mathematics Department is one of the strongest in the world, representing a broad spectrum of fields ranging from the traditional areas of pure mathematics such as analysis, algebra, geometry, and topology, to applied mathematics areas such as combinatorics, computational biology, fluid dynamics, theoretical computer science, and mathematics of data.

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