essay on importance of maths

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Essay on Importance of Mathematics in our Daily Life in 100, 200, and 350 words.

Updated on
Dec 22, 2023

Essay on Importance of Mathematics in our Daily Life

Mathematics is one of the core aspects of education. Without mathematics, several subjects would cease to exist. It’s applied in the science fields of physics, chemistry, and even biology as well. In commerce accountancy, business statistics and analytics all revolve around mathematics. But what we fail to see is that not only in the field of education but our lives also revolve around it. There is a major role that mathematics plays in our lives. Regardless of where we are, or what we are doing, mathematics is forever persistent. Let’s see how maths is there in our lives via our blog essay on importance of mathematics in our daily life.

Table of Contents

1 Essay on Importance of Mathematics in our Daily life in 100 words
2 Essay on Importance of Mathematics in our Daily life in 200 words
3 Essay on Importance of Mathematics in our Daily Life in 350 words

Essay on Importance of Mathematics in our Daily life in 100 words

Mathematics is a powerful aspect even in our day-to-day life. If you are a cook, the measurements of spices have mathematics in them. If you are a doctor, the composition of medicines that make you provide prescription is made by mathematics. Even if you are going out for just some groceries, the scale that is used for weighing them has maths, and the quantity like ‘dozen apples’ has maths in it. No matter the task, one way or another it revolves around mathematics. Everywhere we go, whatever we do, has maths in it. We just don’t realize that. Maybe from now on, we will, as mathematics is an important aspect of our daily life.

Essay on Importance of Mathematics in our Daily life in 200 words

Mathematics, as a subject, is one of the most important subjects in our lives. Irrespective of the field, mathematics is essential in it. Be it physics, chemistry, accounts, etc. mathematics is there. The use of mathematics proceeds in our daily life to a major extent. It will be correct to say that it has become a vital part of us. Imagining our lives without it would be like a boat without a sail. It will be a shock to know that we constantly use mathematics even without realising the same.

From making instalments to dialling basic phone numbers it all revolves around mathematics.

Let’s take an example from our daily life. In the scenario of going out shopping, we take an estimate of hours. Even while buying just simple groceries, we take into account the weight of vegetables for scaling, weighing them on the scale and then counting the cash to give to the cashier. We don’t even realise it and we are already counting numbers and doing calculations.

Without mathematics and numbers, none of this would be possible.

Hence we can say that mathematics helps us make better choices, more calculated ones throughout our day and hence make our lives simpler.

Essay on Importance of Mathematics in our Daily Life in 350 words

Mathematics is what we call a backbone, a backbone of science. Without it, human life would be extremely difficult to imagine. We cannot live even a single day without making use of mathematics in our daily lives. Without mathematics, human progress would come to a halt.

Maths helps us with our finances. It helps us calculate our daily, monthly as well as yearly expenses. It teaches us how to divide and prioritise our expenses. Its knowledge is essential for investing money too. We can only invest money in property, bank schemes, the stock market, mutual funds, etc. only when we calculate the figures. Let’s take an example from the basic routine of a day. Let’s assume we have to make tea for ourselves. Without mathematics, we wouldn’t be able to calculate how many teaspoons of sugar we need, how many cups of milk and water we have to put in, etc. and if these mentioned calculations aren’t made, how would one be able to prepare tea?

In such a way, mathematics is used to decide the portions of food, ingredients, etc. Mathematics teaches us logical reasoning and helps us develop problem-solving skills. It also improves our analytical thinking and reasoning ability. To stay in shape, mathematics helps by calculating the number of calories and keeping the account of the same. It helps us in deciding the portion of our meals. It will be impossible to think of sports without mathematics. For instance, in cricket, run economy, run rate, strike rate, overs bowled, overs left, number of wickets, bowling average, etc. are calculated. It also helps in predicting the result of the match. When we are on the road and driving, mathetics help us keep account of our speeds, the distance we have travelled, the amount of fuel left, when should we refuel our vehicles, etc.

We can go on and on about how mathematics is involved in our daily lives. In conclusion, we can say that the universe revolves around mathematics. It encompasses everything and without it, we cannot imagine our lives.

Deepansh Gautam

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Essay on Importance of Mathematics in Our Daily Life

Students are often asked to write an essay on Importance of Mathematics in Our Daily Life in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

Let’s take a look…

100 Words Essay on Importance of Mathematics in Our Daily Life

Introduction.

Mathematics is a crucial part of everyday life. It helps us make sense of the world around us and solve practical problems.

Mathematics in Daily Tasks

From shopping to cooking, we use math. It helps us calculate costs, quantities, and time.

Mathematics in Professions

In professions like engineering, computer science, and finance, math is indispensable.

Mathematics in Decision Making

Math helps us make informed decisions by analyzing data and predicting outcomes.

250 Words Essay on Importance of Mathematics in Our Daily Life

The pervasive presence of mathematics.

Mathematics, often perceived as a complex and abstract discipline, is in fact an integral part of our everyday lives. It forms the foundation for many of the decisions we make and the actions we perform daily, from managing finances to navigating directions.

A Tool for Logical Reasoning

Mathematics fosters logical reasoning and problem-solving skills. It cultivates an analytical mindset, enabling us to break down complex problems into simpler, manageable parts. This approach is not just confined to mathematical problems but extends to various real-life situations, thereby honing our decision-making abilities.

Mathematics in Technological Advancements

The rapid progress in technology, which has become an inseparable part of our lives, is deeply rooted in mathematical principles. Algorithms, which form the basis of computing, are mathematical models. The internet, smartphones, GPS, and even AI owe their existence to mathematical concepts.

Financial Management and Mathematics

Managing personal finances, a critical life skill, is essentially a mathematical exercise. Budgeting, calculating interest, understanding the implications of loans and mortgages, or even evaluating investment options, all require a good grasp of mathematics.

Mathematics and Scientific Understanding

Mathematics is the language of science. It helps us quantitatively understand and describe the physical world around us, from the trajectory of planets to the behavior of subatomic particles.

500 Words Essay on Importance of Mathematics in Our Daily Life

Mathematics, often perceived as a complex and abstract subject, is in fact deeply intertwined with our daily lives. It is the foundation of numerous activities we engage in, from basic tasks such as shopping and cooking to more complex ones like planning finances or solving problems.

The Ubiquity of Mathematics

Mathematics is everywhere. It is used in our everyday activities, often without our conscious realization. When we shop, we use mathematics to calculate prices, discounts, and taxes. When we cook, we use it to measure ingredients. When we travel, we use it to calculate distances, time, and fuel consumption. Even in our leisure activities such as playing games or music, mathematics plays a crucial role in understanding patterns, probabilities, and rhythms.

Mathematics in the Professional Sphere

Mathematics and problem-solving.

Mathematics also enhances our problem-solving skills. It teaches us to approach problems logically and systematically. It encourages us to break down complex problems into simpler parts, solve them individually, and combine the solutions to solve the original problem. This skill is not just applicable to mathematical problems but to any problem we encounter in life.

Mathematics and Critical Thinking

Furthermore, mathematics fosters critical thinking. It trains us to question assumptions, identify patterns, and draw conclusions based on evidence. It also teaches us to understand the limitations of our solutions and consider alternative approaches. These are valuable skills that can be applied in various aspects of life, from making informed decisions to evaluating the credibility of information.

Mathematics and the Digital Age

In conclusion, mathematics is not just a subject we learn in school. It is a powerful tool that helps us understand and navigate the world around us. It enhances our problem-solving and critical thinking skills, and it opens up a world of opportunities in the professional sphere. Therefore, it is essential that we appreciate the importance of mathematics in our daily lives, and strive to improve our mathematical literacy.

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Recent News

mathematics , the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.

In many cultures—under the stimulus of the needs of practical pursuits, such as commerce and agriculture—mathematics has developed far beyond basic counting. This growth has been greatest in societies complex enough to sustain these activities and to provide leisure for contemplation and the opportunity to build on the achievements of earlier mathematicians.

All mathematical systems (for example, Euclidean geometry ) are combinations of sets of axioms and of theorems that can be logically deduced from the axioms. Inquiries into the logical and philosophical basis of mathematics reduce to questions of whether the axioms of a given system ensure its completeness and its consistency. For full treatment of this aspect, see mathematics, foundations of .

This article offers a history of mathematics from ancient times to the present. As a consequence of the exponential growth of science, most mathematics has developed since the 15th century ce , and it is a historical fact that, from the 15th century to the late 20th century, new developments in mathematics were largely concentrated in Europe and North America . For these reasons, the bulk of this article is devoted to European developments since 1500.

barometer. Antique Barometer with readout. Technology measurement, mathematics, measure atmospheric pressure

This does not mean, however, that developments elsewhere have been unimportant. Indeed, to understand the history of mathematics in Europe, it is necessary to know its history at least in ancient Mesopotamia and Egypt, in ancient Greece, and in Islamic civilization from the 9th to the 15th century. The way in which these civilizations influenced one another and the important direct contributions Greece and Islam made to later developments are discussed in the first parts of this article.

India’s contributions to the development of contemporary mathematics were made through the considerable influence of Indian achievements on Islamic mathematics during its formative years. A separate article, South Asian mathematics , focuses on the early history of mathematics in the Indian subcontinent and the development there of the modern decimal place-value numeral system . The article East Asian mathematics covers the mostly independent development of mathematics in China, Japan, Korea, and Vietnam.

The substantive branches of mathematics are treated in several articles. See algebra ; analysis ; arithmetic ; combinatorics ; game theory ; geometry ; number theory ; numerical analysis ; optimization ; probability theory ; set theory ; statistics ; trigonometry .

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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

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What is the importance of mathematics in our daily lives?

Mathematics is a powerful tool for global understanding and communication that organizes our lives and prevents chaos. Mathematics helps us understand the world and provides an effective way of building mental discipline.

Math encourages logical reasoning, critical thinking, creative thinking, abstract or spatial thinking, problem-solving ability, and even effective communication skills. Let's understand the importance of mathematics in our daily life.

Importance of mathematics

The Importance of Mathematics in Our Daily Lives

Mathematics : introduction.

Mathematics helps to develop the ability to think.
It helps explain how things work.
It helps to develop wisdom.
It increases the speed of intuition.
It helps to make the child smarter.
Money can be collected in mathematics when used as a profession.
It is important in a constantly evolving world.
It provides the child with an opportunity to get to the world.

Mathematics in Our Everyday Life

Although the importance of Mathematics can never be denied, a general fear of dealing with math exists in students across the world.

Having said that, most people, nowadays grapple with the calculations, as they find them too tough to handle.

To ease their life, there exists a comprehensive platform like Khanacademy and mathisfun. Moving from specific to general, it has a host of calculators dealing with physics, chemistry, general arithmetic’s, and many more.

So, students of various disciplines can use this website to solve their math’s-related problems without any hassle.

The Most Important Uses of Mathematics

Practical uses of mathematics in everyday life, the importance of mathematics to individuals, the importance of mathematics to society, نموذج الاتصال.

Why Is Math Important? 9 Reasons Why Math Skills Improve Quality of Life

Written by Ashley Crowe

Parent Resources

Why is math so important in life?
9 Benefits of a great math education
Why students struggle to master certain math concepts
Set your child’s math skills up for life with Prodigy Math

Math isn't just an important subject in school — it’s essential for many of your daily tasks. You likely use it every day to perform real-life skills, like grocery shopping, cooking and tracking your finances.

What makes math special is that it’s a universal language — a powerful tool with the same meaning across the globe. Though languages divide our world, numbers unite us. Math allows us to work together towards new innovations and ideas.

In this post, learn why math is important for kids and adults. Plus, find out why learning even the most basic math can significantly improve your family’s quality of life.

You simply can’t make it through a day without using some sort of basic math. Here’s why.

A person needs an understanding of math, measurements and fractions to cook and bake. Many people may also use math to count calories or nutrients as part of their diet or exercise routine.

You also need math to calculate when you should leave your house to arrive on time, or how much paint you need to redo your bedroom walls.

And then the big one, money. Financial literacy is an incredibly important skill for adults to master. It can help you budget, save and even help you make big decisions like changing careers or buying a home.

Mathematical knowledge may even be connected to many other not-so-obvious benefits. A strong foundation in math can translate into increased understanding and regulation of your emotions, improved memory and better problem-solving skills.

The importance of math: 9 benefits of a great math education

Math offers more opportunities beyond grade school, middle school and high school. Its applications to real-life scenarios are vast.

Though many students sit in math class wondering when they’ll ever use these things they’re learning, we know there are many times their math skills will be needed in adulthood.

The importance of mathematics to your child’s success can’t be overstated. Basic math is a necessity, but even abstract math can help hone critical thinking skills — even if your child chooses not to pursue a STEM-style career. Math can help them succeed professionally, emotionally and cognitively. Here’s why.

1. Math promotes healthy brain function

“Use it or lose it.” We hear this said about many skills, and math is no exception.

Solving math problems and improving our math skills gives our brain a good workout. And it improves our cognitive skills over time. Many studies have shown that routinely practicing math keeps our brain healthy and functioning well.

2. Math improves problem-solving skills

At first, classic math problems like Johnny bringing home 42 watermelons and returning 13 of them can just seem a silly exercise. But all those math word problems our children solve really do improve their problem solving skills. Word problems teach kids how to pull out the important information and then manipulate it to find a solution.

Later on, complex life problems take the place of workbooks, but problem-solving still happens the same way. When students understand algorithms and problems more deeply, they can decode the facts and more easily solve the issue. Real-life solutions are found with math and logic.

3. Math supports logical reasoning and analytical thinking

A strong understanding of math concepts means more than just number sense. It helps us see the pathways to a solution. Equations and word problems need to be examined before determining the best method for solving them. And in many cases, there’s more than one way to get to the right answer.

It’s no surprise that logical reasoning and analytical thinking improve alongside math skills. Logic skills are necessary at all levels of mathematical education.

4. Math develops flexible thinking and creativity

Practicing math has been shown to improve investigative skills, resourcefulness and creativity.

This is because math problems often require us to bend our thinking and approach problems in more than one way. The first process we try might not work. We need flexibility and creativity to think of new pathways to the solution. And just like anything else, this way of thinking is strengthened with practice.

5. Math opens up many different career paths

There are many careers that use a large number of math concepts. These include architects, accountants, and scientists.

But many other professionals use math skills every day to complete their jobs. CEOs use math to analyze financials. Mailmen use it to calculate how long it will take them to walk their new route. Graphic designers use math to figure out the appropriate scale and proportions in their designs.

No matter what career path your child chooses, math skills will be beneficial.

Math skills might become even more important for today's kids!

Math can certainly open up a lot of opportunities for many of us. But did you know that careers which heavily use math are going to be among the fastest-growing jobs by the time kids today start their careers? These jobs include:

Statisticians
Data scientists
Software developers
Cybersecurity analysts

It's not just STEM jobs that will require math either. Other popular, high-growth careers like nursing and teaching now ask for a minimum knowledge of college-level math.

6. Math may boost emotional health

While this research is still in its early days, what we have seen is promising.

The parts of the brain used to solve math problems seem to work together with the parts of the brain that regulate emotions. This suggests that math practice can actually help us cope with difficult situations. In these studies, the better someone was with numerical calculations, the better they were at regulating fear and anger. Strong math skills may even be able to help treat anxiety and depression.

7. Math improves financial literacy

Though kids may not be managing their finances now, there's going to be plenty of times where math skills are going to make a massive difference in their life as an adult.

Budgeting and saving is a big one. Where can they cut back on their spending? How will budgeting help them reach their financial goals? Can they afford this new purchase now?

As they age into adulthood, It will benefit your child to understand how loans and interest work before purchasing a house or car. They should fully grasp profits and losses before investing in the stock market. And they will likely need to evaluate job salaries and benefits before choosing their first job.

Child putting money in piggy bank with mom.

8. Math sharpens your memory

Learning mental math starts in elementary school. Students learn addition tables, then subtraction, multiplication and division tables. As they master those skills, they’ll begin to memorize more tips and tricks, like adding a zero to the end when multiplying by 10. Students will memorize algorithms and processes throughout their education.

Using your memory often keeps it sharp. As your child grows and continues to use math skills in adulthood, their memory will remain in tip top shape.

9. Math teaches perseverance

“I can do it!’

These are words heard often from our toddlers. This phrase is a marker of growth, and a point of pride. But as your child moves into elementary school, you may not hear these words as often or with as much confidence as before.

Learning math is great for teaching perseverance. With the right math instruction, your child can see their progress and once again feel that “I can do it” attitude. The rush of excitement a child experiences when they master a new concept sticks in their memory. And they can reflect back on it when they’re struggling with a new, harder skill.

Even when things get tough, they’ll know they can keep trying and eventually overcome it — because they’ve done it before.

Tip: Set goals to inspire and motivate your child to learn math

If your child has a Prodigy Math Membership , you can use your parent account to set learning goals for them to achieve as they play our online math game.

The best bit? Every time they complete a goal, they'll also get a special in-game reward!

Many students experience roadblocks and hurdles throughout their math education. You might recognize some of these math struggles below in your child. But don’t worry! Any struggle is manageable with the right support and help. Together, you and your child can tackle anything.

Here are some of the most common math struggles.

Increasing complexity

Sometimes the pace of class moves a bit faster than your child can keep up with. Or the concepts are just too abstract and difficult for them to wrap their mind around in one lesson. Some math ideas simply take more time to learn.

Wrong teaching style

A good teaching style with plenty of practice is essential to a high-quality math education. If the teacher’s style doesn’t mesh well with how your child learns, math class can be challenging.

Fear of failure

Even as adults, we can feel scared to fail. It’s no surprise that our children experience this same same fear, especially with the many other pressures school can bring.

Lack of practice

Sometimes, all your child needs is a little more practice. But this can be easier said than done. You can help by providing them with plenty of support and encouragement to help them get that practice time in.

Math anxiety

Algorithms and complex problems can strike anxiety in the heart of any child (and many adults). Math anxiety is a common phenomenon. But with the right coping strategies it can be managed.

Set your child’s math skills up for success with Prodigy Math

Now we've discovered just how important math is in both our everyday and life decisions, let's set the next generation up for success with the right tools that'll help them learn math.

Prodigy Math is a game-based, online learning platform that makes learning math fun for kids. As kids play and explore a safe, virtual world filled with fun characters and pets to collect, they'll answer math questions. These questions are curriculum-aligned and powered by an adaptive algorithm that can help them master math skills more quickly.

Plus, with a free parent account , you'll also get to be a big part of their math education without needing to be a math genius. You'll get to:

Easily keep up with their math learning with a monthly Report Card
See how they're doing in math class when their teacher uses Prodigy Math
Send them motivational messages to encourage their perseverance in math

Want to play an even bigger role in helping your child master math? Try our optional Math Memberships for extra in-game content for your child to enjoy and get amazing parent tools like the ability to set in-game goals and rewards for them to achieve.

See why Prodigy can make math fun below!

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Table of Contents

September 2, 2017

Why Is It Important to Study Math?

What’s the point of learning math? Why is it so important that kids are exposed to mathematical thinking? And what do parents and teachers need to know about learning real math? Keep on reading to find out.

By Math Dude Jason Marshall

PeopleImages Getty Images

Today is a very special episode of the Math Dude. To begin with, it’s episode 300. And because we humans have 10 fingers, we love to give special meaning to multiples of 10. But while that’s fun, it’s not the big news of the day or what makes this episode special to me. The big news is that this 300th episode is my last. Between my day job as a physics and astronomy professor and my day-and-night job of being “Dad” to an awesome and bustling 3-year-old, my free time for Math Dude duties has dwindled. And although I will surely miss all of you math fans, after seven years on the job, it's time to say goodbye.

But before I go, I have one more thing to say—and I think it’s the most important thing I’ve ever said on the show. It’s not something that I would (or even could) have said when I wrote the first episode seven years ago, because I wasn’t yet a father and so I wasn’t yet watching somebody discover the world for the first time. So please take a few minutes and listen, because I think this is something that everybody who has kids or might have kids or works with kids or might work with kids should know.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

Here it is: Math is a playground … so play! Allow me to explain.

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10 Reasons Why Math is Important to Life

From www.piday.org -- This is a great article to discuss with your kids. What do you use math for? Why do you need math? Imagine a world without math.. .How would you survive without math? Could you? We think the answer is no. Look at all the wonderful things math is used for an why math is important. Seriously, try one day without math and see if you catch yourself using it anyway. Math is a natural way to organize and to think. For example, when you're using the microwave, aren't you deciding how long to set the timer? TIME? Did you say TIME? Can you tell someone when to meet you if you couldn't tell time? How do you know when it's lunchtime?

How about your child's locker? These are often numbered. Could you tell one locker from the next without an identifying number? And then there's the matter of the combination. Yes.. some are letters but numbers are more common.

How about cooking and baking? You need to be able to measure ingredients and proportion ingredients if you need more or less servings.

Add your own reasons and then see what the kids come up with.

https://www.piday.org/2018/10-reasons-why-math-is-important-in-life/

Q1. Jenny has six apples. If she gives away four apples, how many apples does she have remaining? Q2. Two trains are traveling nonstop to Kansas City, one leaving from Boston (1450 miles away) at 50 miles per hour and one leaving from San Francisco (1850 miles away) at 40 miles per hour. Both trains leave their origins at the exact same time early in the morning. Which train will arrive first, and what will be the time difference of the two trains’ arrival in their final destination in Kansas City? Q3. What is the radius of a circle with circumference 2π?

(Check the bottom of this blog post for the answers to the math problems posted above!)

While it may seem like math problems like the above have no real use in life, this couldn’t be farther from the truth! Math is incredibly important in our lives and, without realizing it, we use mathematical concepts, as well as the skills we learn from doing math problems, every day. The laws of mathematics govern everything around us, and without a good understanding of them, one can encounter significant problems in life.

Read on to learn a few reasons that math is a powerful and incredibly useful tool.

Learning math is good for your brain. Research conducted by Dr. Tanya Evans of Stanford University indicates that children who know math are able to recruit certain brain regions more reliably, and have greater gray matter volume in those regions, than those who perform more poorly in math. The brain regions involved in higher math skills in high-performing children were associated with various cognitive tasks involving visual attention and decision-making. While correlation may not imply causation, this study indicates that the same brain regions that help you do math are recruited in decision-making and attentional processes.
Math helps you tell time. “I’m late, I’m late for a very important date.” – White Rabbit from the movie Alice in Wonderland . Don’t let your ignorance of math make you like the White Rabbit! A recent study indicated that 4 out of 5 children living in Oklahoma City cannot read the hands on an analog clock to tell time. Knowing math, and particularly, fractions , can help you better tell time. While analog clocks may eventually become obsolete, don’t let your ability to tell time become outdated! Use your knowledge of fractions to help you tell time on analog clocks that have an hour, minute, and (sometimes) second hand.
Math helps you with your finances. Math can be helpful for balancing your budget because you will have a good understanding of how to make sure that your costs are less than the money you have. Balancing one’s bank account, for example, is an important life skill that requires math in order to subtract balances. People who know math are therefore less likely to go into debt because they did not know how much money they had versus how much money they spent.
Math makes you a better cook (or baker). With a knowledge of math, for example, you can quickly deduce that a half-cup of flour is the same thing as eight tablespoons of flour. This can prove handy if you find that your half-cup measure is missing. Likewise, if you are cooking from a recipe that serves 4 people, but you need to feed 8 people, your math skills tell you that you can simply double all of the necessary ingredients. Without math, you may not have enough food (or have too much food) to feed your guests…
Math helps us have better problem-solving skills. Math helps us think analytically and have better reasoning abilities. Analytical thinking refers to the ability to think critically about the world around us. Reasoning is our ability to think logically about a situation. Analytical and reasoning skills are important because they help us solve problems and look for solutions. While it may seem farfetched to think that solving the train problem above can help you solve a problem in your life, the skills that you use in framing the problem, identifying the knowns and unknowns, and taking steps to solve the problem can be a very important strategy that can be applied to other problems in life.
Math is used in practically every career in some way. Obviously, mathematicians and scientists rely on mathematical principles to do the most basic aspects of their work such as test hypotheses. While scientific careers famously involve math, they are not the only careers to do so. Even operating a cash register requires that one understands basic arithmetic. People working in a factory must be able to do mental arithmetic to keep track of the parts on the assembly line and must, in some cases, manipulate fabrication software utilizing geometric properties (such as the dimensions of a part) in order to build their products. Really, any job requires math because you must know how to interpret your paycheck and balance your budget.
Math is all around us and helps us understand the world better. To live in a mathematically-driven world and not know math is like walking through an art museum with your eyes closed. Learning and appreciating math can help you appreciate things that you would not otherwise notice about the world. In reality, math is everywhere ! Don’t believe me? Read on for some examples of math in nature.

Bees, masters of geometry, use hexagons to build their honeycombs. The Fibonacci sequence , a famous sequence of numbers in mathematics, is found throughout nature: in pinecones, seashells, trees, flowers, and leaves.

The number pi can also be observed all around us. Pi is a cool number with many unique properties. Pi is approximately 3.14, but in reality it is greater than 3.14, with an infinite string of numbers after the decimal point. Because pi is, in reality, an infinitely long number, it is expressed as the Greek letter pi (π). It cannot be expressed as a fraction; numbers that cannot be expressed as fractions are said to be irrational . Pi is also transcendental , which means that it is non-algebraic; this means that pi cannot be the solution of single-variable polynomial equation whose coefficients are all integers. (By definition, all transcendental numbers are also irrational.)

The number pi can be observed in the shapes of rivers. The ratio of a river’s length to the distance from the source to its mouth is called the “meandering ratio.” The average meandering ratio of rivers approaches the number pi. It makes sense that the average meandering ratio of rivers approaches pi, because rivers tend to bend into loops, which are circular in nature. The ratio of a circle’s circumference to its diameter is also equal to pi.

Now that you know more about pi and about how math governs nature, don’t you feel that you have a greater command over the mathematical laws of the universe? It can be empowering to learn about mathematical principles because it can help make sense of a world that, oftentimes, does not make much sense.

Math can make you more popular. Before you start to disagree with me, think about how great it is to go to dinner with a friend who can quickly divide a check in their mind to determine how much each person needs to pay to split the bill. Your knowledge of fractions can also help you divide a pizza among a few people. While math is popularly the realm of nerds, your ability to avoid awkward confusion and silence as you and your friends try to divide a pizza or a dinner bill is truly a valuable skill. Be known as the cool (yes, I said cool ) person that knows how to do mental math quickly!
Math can help you shop a good sale. Not only will your quick mental arithmetic skills help you become known as the smart person who everyone appreciates when the waiter brings the check to your table, your math skills can also help you shop. Knowledge of percentages and how to calculate them quickly can help you save time when shopping at a sale at the mall – for example, to quickly calculate a discounted price, or to determine whether you’ve been correctly charged when paying for a shirt at the store. You don’t need a Ph.D. in math to develop some quick mental arithmetic skills; they can help you in these and other areas of your life in the long run.

Tip: use the 10 rule while sale-shopping. If you want to brush up on your math skills to be a better bargain-hunter, remember this rule: to subtract 10 from a price, you can just move the decimal place to the left by one digit. Take, for example, a shirt that has a price of $25.00 and is on sale for an additional 20 off. You can move the decimal over to the left by one digit to calculate 10 off – $2.50. Since 20 off is 2 x 10 off, you can quickly multiply $2.50 x 2 to get the discount amount – $5.00. Subtract the discount amount from the original price of the shirt: $25.00 – $5.00 = $20.00. You can use the 10 rule to quickly calculate 10 of the price and multiply it by a factor that can help you estimate price discounts quickly.

Math skills can be pretty helpful!

Math is the universal language. Sure, it’s mostly equations, numbers, and some Greek letters, but math is understood the same virtually all over the world (and who knows, maybe all over the universe)! A math equation doesn’t need to be translated to another language to be understood by someone on the other side of the planet. A mathematical law doesn’t change because someone has a different religion than you or speaks a different language from you. 2 + 2 = 4 in every single place on planet Earth. Pretty cool! The universality of math is one of the many things that makes it such a powerful tool and, indeed, essential life skill.

In summary, math is not only important for success in life; it is all around us. The laws of mathematics are evident throughout the world, including in nature, and the problem-solving skills obtained from completing math homework can help us tackle problems in other areas of life. While many may complain that math is boring or complicated, the truth is that a life devoid of math means that we go around experiencing the world on a much less interesting level than we could.

Math problem answers: A1. Two apples A2. To solve this problem, simply divide the distance travelled for each train by its speed to obtain the time that the journey will take. Assuming that the trains travel a uniform velocity and make no stops, The Boston train will arrive in Kansas City in (1450 / 50) = 29 hours. The San Francisco train will arrive in (1850/40) = 46.25 hours. To calculate the time difference, simply subtract 46.25 from 29 = 17.25. Therefore, the Boston train will arrive first – and the San Francisco train will arrive 17.25 hours later. A3. The circumference of a circle is equal to the diameter of the circle times pi. Therefore, dividing the circumference (2π) by π gives us the diameter, which is 2. The radius is half the diameter, so in this case, 2/2 = 1. Therefore, the radius of a circle with circumference 2π is equal to 1.

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Math Essay Ideas for Students: Exploring Mathematical Concepts

Are you a student who's been tasked with writing a math essay? Don't fret! While math may seem like an abstract and daunting subject, it's actually full of fascinating concepts waiting to be explored. In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!

The Beauty of Fibonacci Sequence

Have you ever wondered why sunflowers, pinecones, and even galaxies exhibit a mesmerizing spiral pattern? It's all thanks to the Fibonacci sequence! Explore the origin, properties, and real-world applications of this remarkable mathematical sequence. Discuss how it manifests in nature, art, and even financial markets. Unveil the hidden beauty behind these numbers and show how they shape the world around us.

The Mathematics of Music

Did you know that music and mathematics go hand in hand? Dive into the relationship between these two seemingly unrelated fields and develop your writing skills . Explore the connection between harmonics, frequencies, and mathematical ratios. Analyze how musical scales are constructed and why certain combinations of notes create pleasant melodies while others may sound dissonant. Explore the fascinating world where numbers and melodies intertwine.

The Geometry of Architecture

Architects have been using mathematical principles for centuries to create awe-inspiring structures. Explore the geometric concepts that underpin iconic architectural designs. From the symmetry of the Parthenon to the intricate tessellations in Islamic art, mathematics plays a crucial role in creating visually stunning buildings. Discuss the mathematical principles architects employ and how they enhance the functionality and aesthetics of their designs.

Fractals: Nature's Infinite Complexity

Step into the mesmerizing world of fractals, where infinite complexity arises from simple patterns. Did you know that the famous Mandelbrot set , a classic example of a fractal, has been studied extensively and generated using computers? In fact, it is estimated that the Mandelbrot set requires billions of calculations to generate just a single image! This showcases the computational power and mathematical precision involved in exploring the beauty of fractal geometry.

Explore the beauty and intricacy of fractal geometry, from the famous Mandelbrot set to the Sierpinski triangle. Discuss the self-similarity and infinite iteration that define fractals and how they can be found in natural phenomena such as coastlines, clouds, and even in the structure of our lungs. Examine how fractal mathematics is applied in computer graphics, art, and the study of chaotic systems. Let the captivating world of fractals unfold before your eyes.

The Game Theory Revolution

Game theory isn't just about playing games; it's a powerful tool used in various fields, from economics to biology. Dive into the world of strategic decision-making and explore how game theory helps us understand human behavior and predict outcomes. Discuss in your essay classic games like The Prisoner's Dilemma and examine how mathematical models can shed light on complex social interactions. Explore the cutting-edge applications of game theory in diverse fields, such as cybersecurity and evolutionary biology. If you still have difficulties choosing an idea for a math essay, find a reliable expert online. Ask them to write me an essay or provide any other academic assistance with your math assignments.

Chaos Theory and the Butterfly Effect

While writing an essay, explore the fascinating world of chaos theory and how small changes can lead to big consequences. Discuss the famous Butterfly Effect and how it exemplifies the sensitive dependence on initial conditions. Delve into the mathematical principles behind chaotic systems and their applications in weather forecasting, population dynamics, and cryptography. Unravel the hidden order within apparent randomness and showcase the far-reaching implications of chaos theory.

The Mathematics Behind Cryptography

In an increasingly digital world, cryptography plays a vital role in ensuring secure communication and data protection. Did you know that the global cybersecurity market is projected to reach a staggering $248.26 billion by 2023? This statistic emphasizes the growing importance of cryptography in safeguarding sensitive information.

Explore the mathematical foundations of cryptography and how it allows for the creation of unbreakable codes and encryption algorithms. Discuss the concepts of prime numbers, modular arithmetic, and public-key cryptography. Delve into the fascinating history of cryptography, from ancient times to modern-day encryption methods. In your essay, highlight the importance of mathematics in safeguarding sensitive information and the ongoing challenges faced by cryptographers.

Writing a math essay doesn't have to be a daunting task. By choosing a captivating topic and exploring the various mathematical concepts, you can turn your essay into a fascinating journey of discovery. Whether you're uncovering the beauty of the Fibonacci sequence, exploring the mathematical underpinnings of music, or delving into the game theory revolution, there's a world of possibilities waiting to be explored. So embrace the power of mathematics and let your creativity shine through your words!

Remember, these are just a few math essay ideas to get you started. Feel free to explore other mathematical concepts that ignite your curiosity. The world of mathematics is vast, and each concept has its own unique story to tell. So go ahead, unleash your inner mathematician, and embark on an exciting journey through the captivating realm of mathematical ideas!

Tobi Columb, a math expert, is a dedicated educator and explorer. He is deeply fascinated by the infinite possibilities of mathematics. Tobi's mission is to equip his students with the tools needed to excel in the realm of numbers. He also advocates for the benefits of a gluten-free lifestyle for students and people of all ages. Join Tobi on his transformative journey of mathematical mastery and holistic well-being.

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Home — Essay Samples — Science — Mathematics in Everyday Life — Mathematics In Everyday Life: Most Vital Discipline

Mathematics in Everyday Life: Most Vital Discipline

Categories: Mathematics in Everyday Life

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Words: 795 |

Published: Mar 14, 2019

Words: 795 | Pages: 2 | 4 min read

Works Cited

Benacerraf, P. (1991). Mathematics as an object of knowledge. In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics: Selected readings (pp. 1-13). Cambridge University Press.
EdReady. (n.d.). Home. Retrieved from https://www.edready.org/
Puttaswamy, T. K. (2012). Engineering mathematics. Dorling Kindersley (India) Pvt. Ltd.
Steen, L. A. (Ed.). (2001). Mathematics today: Twelve informal essays. Springer Science & Business Media.
Suter, B. W. (2012). Mathematics education: A critical introduction. Bloomsbury Academic.
Tucker, A. W. (2006). Applied combinatorics. John Wiley & Sons.
Vakil, R. (2017). A mathematical mosaic: Patterns & problem solving. Princeton University Press.
Wolfram MathWorld. (n.d.). MathWorld--The web's most extensive mathematics resource. Retrieved from http://mathworld.wolfram.com/
Wu, H. H. (2011). The mis-education of mathematics teachers. Educational Studies in Mathematics, 77(1), 1-20.
Ziegler, G. M., & Aigner, M. (2012). Proofs from THE BOOK. Springer Science & Business Media.

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Math Matters in Everyday Life

Dear Parents,

Math is very useful in everyday life. Math can help us do many things that are important in our everyday lives. Here are some daily tasks for which math is important:

Managing money $$$
Balancing the checkbook
Shopping for the best price
Preparing food
Figuring out distance, time and cost for travel
Understanding loans for cars, trucks, homes, schooling or other purposes
Understanding sports (being a player and team statistics)
Playing music
Home decorating
Gardening and landscaping

Parents can help teens connect math they learn in school and their everyday lives. As a parent, you could talk to your teen about how you use math in your daily life. You could also ask family members and friends how they use math in their daily lives. Please talk to your teens about these math connections to real world. Share with your child the examples of everyday math applications, which are listed below. When your teens hear how math can be used every day, they will be more likely to view math as important and valuable. They may also become more interested in mathematics. Remember that you as a parent can greatly influence how your child thinks about mathematics.

The testimonials included on this website give brief examples of how people use math in their daily lives. Please watch these. You can share information from these videos with your teen.

Examples of Math Connections to Daily life

Managing money.

Your teen will learn skills in algebra class that will help them with money. One important skill they will learn is how to calculate interest and compound interest. Your teen can use this skill to manage their money now and when they grow up. This skill also will help them pick the best bank account. It will also help them decide which credit card is best to have. People who take out loans need to understand interest. It will also help them figure out the best ways to save and invest money.

Recreational Sports

Geometry and trigonometry can help your teens who want to improve their skill in sports. It can help them find the best way to hit a ball, make a basket or run around the track. Basic knowledge of math also helps keep track of sports scores.

Home Decorating and Remodeling

Calculating areas is an important skill. It will be useful for your teen in remodeling future homes and apartments. It will help your teen find how much paint they need to buy when repainting a room. It is also an important skill for anyone who wants to install new tiles in a bathroom or a kitchen. Knowing how to calculate perimeters can help your child when deciding how much lumber to buy for floor or ceiling trim.

People use math knowledge when cooking. For example, it is very common to use a half or double of a recipe. In this case, people use proportions and ratios to make correct calculations for each ingredient. If a recipe calls for 2/3 of a cup of flour, the cook has to calculate how much is half or double of 2/3 of a cup. Then the cook has to represent the amount using standard measures used in baking, such as ¼ cup, 1/3 cup, ½ cup or 1 cup.

Your teen will use math when buying different items. When buying a new computer, your child will need to figure out which store offers the best price or best financing. Math is useful in finding the best deal for food items. For example, your teen will need to decide which pack of soda to buy when given a choice of 20 oz., 2-liter, 12 pack, or 24-pack. Stores often have sales that give a percentage off an original price. It is helpful for people to know how to figure out the savings. This math skill is very useful because it helps us calculate discounts so we can buy an item for the best price offered.

Note. Partial content of this web page is adapted from Making Connections: Helping Your Teen With the Choices Ahead brochure (Harackiewicz, Hyde & Hulleman, n.d.) and Making Connections: Helping Your Teen Find Value in School brochure (Hulleman, Harackiewicz & Hyde, 2007). Please refer to the links to the brochures under the useful links for parents tab if you would like access to the full brochures.

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Essay: Why Is Math Important And How To Pass It?

Essay: Why Is Math Important…

Why is math important? By now, it is obvious to see that computers are taking our jobs. In a few years, robots will take more than 15% of our current jobs. It teaches us about the importance of math. So why is math important? It’s not too complicated. We use math everyday. For example, we use math when crossing the road, cooking, telling the time, and many more.

It’s possible to live our lives with basic addition, subtraction, and multiplication. Moreover, computers can do more than simple arithmetic. Engineers created the technologies that are taking our jobs. Math is important because if we can’t do what computers can’t do, then we can kiss our jobs goodbye. We can fix it by learning higher math. Students must come together, and we must decide why math is important for our lives.

As college students, we’re expected to have mastered high school math standards. Moreover, some of us had mathematical difficulties in high school.

That’s not a problem because we’re teachable. Brain scan has shown us that the brain can be regrown. It can be regrown through games, food, reading etc. Some of us enrolled in degrees such as nursing, art, math, etc.

All of us in this degree are expected to take math. We all have different reasons for enrolling in math requirement courses, so there’s no need to drop our degrees. It is necessary to understand that everyone has trouble in math, and our teachers had problems in math.

Therefore, we can improve our weaknesses in math by knowing our technological aid, our educational background, and our classroom environments.

Firstly, technological aid are technologies that assist students to learn and help teachers to teach easier. This includes calculators, math multimedia programs, and electronic boards, etc. Mymathlab is a popular technological aid at our school. It’s excellent because it educates students both in class and at home.

It is a sufficient condition because it takes us through the hard problems and provides answers with suitable explanations. According to Abbas Johari, “inductive multimedia programs help students understand math better”. Mr. Johari expanded on a study of multimedia programs using graph and word problems to educate 98 undergraduate students of a large southwest college who were enrolled in a computer literacy course. The research was successful. Because by the end of the research, students showed high improvement in their grades.

The problem is that MyMathLab prevails in spatial learning than in kinesthetic (hands-on learning), auditory (Listening learning), and linguistic(language learning). However, some of us learn differently, and some of us abuse the program because we copy and paste answers. Some researchers believe that students’ performance in math depends on the mathematics curriculum.

According to John K Alsup and Mark J. Sprigler, the ” traditional method(Houghton-Mifflin) showed positive results than the reform method (Cord Applied). The traditional method is based on non-reality problems, but the reform method is based on real problems. It depends on the teachers who teach it. There were about 335 eighth-graders in western United State from different areas that participated in this research. They did it by comparing SAT results of students from both curriculums.

It makes sense because schools such as Harvard University, M.I.T, and UMUC use different math curriculums. Because if schools used the same math curriculum, it wouldn’t make sense to pay high tuition for Harvard. Instead, we can pay less for UMUC and achieve equivalent knowledge.

Mymathlab is part of our curriculum that is given to us by our schools. If we know the program isn’t sufficient, then we should tell the school board. We need to take responsibility for our failures and do better.

Secondly, Educational background refers to our family’s educational values, our learning styles, and our understanding of math. If we know our educational background, then it prepares us for our careers. It is not late to prepare our mindset. Because it reveals our strengths and our weaknesses in math, it gives us the opportunity to grow our weaknesses.

It is a necessary condition that helps us keep track of the lesson. If our parents have a high educational value, then they can help us in math. It helps us know our learning styles. It facilitates learning to the best of our understanding, and it will lead us to do better in math. Knowing all of this can exponentially increase our understanding and performance in mathematics.

Moreover, some of us are doing well without the knowledge of our educational background. So why does it matter? Some of us have tried it so many times and gave up on it. It is not surprising, math is hard. Some of us have math learning disabilities. The ability of low understanding in math. According to Emmanuel Manalo, Julie K. Bunnell, and Jennifer A. Stillman, “Students with math learning disabilities can improve highly through process mnemonics”.

They conducted a study with 13-14-year old’s, and they were distributed to various groups. Two Experiments were conducted to test Process mnemonics, no instruction, and demonstration imitation. They used different variables. Process mnemonics are using techniques such as rhymes to remember things. Demonstration imitation is the modeling of what you see.

We all know it’s a challenging subject. Some of us have come far without any knowledge of our educational background; If we attain it, then we’re guaranteed to improve our current educational values in math by 5%. Some of us with learning disabilities can improve. According to John Woodward, ” Strategies of teaching facts and extensive practice drills can help develop automaticity in math”.

This study was conducted on 58 fourth graders. Some with learning disabilities, and some with no disabilities. It proves that practice drills and strategies that teachers use to teach us can improve our math understanding.

For example, the speech teacher asked Brandon and his classmates if they knew their learning styles. Since Brandon knew his learning style because his DVR-0061 teacher taught him. He was among the students who knew what she was talking about. It shows how important learning styles are.

Thirdly, the classroom environment is an important aspect of the understanding. The classroom environment includes climate, teachers, and classmates. Climate is an important fact in understanding math. Because if students are not comfortable in their environment, then they will have a hard time perceiving and processing mathematical information.

For instance, if it is hot outside and a student goes to class. He/she will expect the classroom to be cold. If the temperature in the classroom is the same as the temperature outside, then the student will have a hard time learning. Sometimes, we fail to ask our teachers questions when we don’t understand. It’s important to have a teacher that cares about math.

If teachers don’t care, then students won’t care. We don’t take into consideration that our classmates can tutor us. At times, we understand better from classmates than from our teachers.

According to Karen J. Graham and Francis Fennell, ” Successful teaching depends on teachers’ ability to make decisions based on their knowledge of mathematics, the curriculum expectations, the classroom/ school environment, and the needs of the students”. Our teachers are part of our misunderstanding. If so, why are our teachers allowed to teach us?

Because teachers are meant to teach us depending on our understanding, they are supposed to boost our self-esteem and self-concept in math. Furthermore, teachers are also responsible for everything in the classroom. It implies that teachers need to fix the temperature if it doesn’t correlate with the students in the class.

Is it right to blame our teachers for our failures and misunderstanding? If we think about it as college students, it’s our responsibility to fix our classroom environmental issues. First, we must suggest our opinions with our teachers on class environmental changes. If our teachers can’t help, then we can dress depending on the classroom temperature.

If we don’t understand, then it’s our responsibility to go and find a tutor. For instance, our schools provide us with free tutoring for every subject available. It s up to us to carry ourselves there to learn.

Improvement in mathematical skills is possible through our technological aid, educational background, and classroom environments. Mathematics is important in many ways. First, it is the foundation of the world. Because currently, robots are already taking our jobs, no one will want to employ a person if a computer is faster and better than them. Plus, they don’t need to pay for a computer. Many majors we take today require math, and we need math in our daily lives.

Computers are structured using math, but their math skills are limited. Math is a hard subject, but we can understand it by managing our tech-aides, learning background, and environments. We need to take advantage of the resources around us. Especially us in community colleges because the world does not care about who does the job.

They only want people who can get the job done and fast. We must keep practicing until we understand. Therefore, we must not give up on math under any circumstances because we have dreams to conquer.

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“What is Mathematics?” and why we should ask, where one should experience and learn that, and how to teach it

Conference paper
Open Access
First Online: 02 November 2017
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Günter M. Ziegler 3 &
Andreas Loos 4

Part of the book series: ICME-13 Monographs ((ICME13Mo))

112k Accesses

9 Citations

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“What is Mathematics?” [with a question mark!] is the title of a famous book by Courant and Robbins, first published in 1941, which does not answer the question. The question is, however, essential: The public image of the subject (of the science, and of the profession) is not only relevant for the support and funding it can get, but it is also crucial for the talent it manages to attract—and thus ultimately determines what mathematics can achieve, as a science, as a part of human culture, but also as a substantial component of economy and technology. In this lecture we thus

discuss the image of mathematics (where “image” might be taken literally!),

sketch a multi-facetted answer to the question “What is Mathematics?,”

stress the importance of learning “What is Mathematics” in view of Klein’s “double discontinuity” in mathematics teacher education,

present the “Panorama project” as our response to this challenge,

stress the importance of telling stories in addition to teaching mathematics, and finally,

suggest that the mathematics curricula at schools and at universities should correspondingly have space and time for at least three different subjects called Mathematics.

This paper is a slightly updated reprint of: Günter M. Ziegler and Andreas Loos, Learning and Teaching “ What is Mathematics ”, Proc. International Congress of Mathematicians, Seoul 2014, pp. 1201–1215; reprinted with kind permission by Prof. Hyungju Park, the chairman of ICM 2014 Organizing Committee.

You have full access to this open access chapter, Download conference paper PDF

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What is mathematics.

Defining mathematics. According to Wikipedia in English, in the March 2014 version, the answer to “What is Mathematics?” is

Mathematics is the abstract study of topics such as quantity (numbers), [2] structure, [3] space, [2] and change. [4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. [7][8] Mathematicians seek out patterns (Highland & Highland, 1961 , 1963 ) and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

None of this is entirely wrong, but it is also not satisfactory. Let us just point out that the fact that there is no agreement about the definition of mathematics, given as part of a definition of mathematics, puts us into logical difficulties that might have made Gödel smile. Footnote 1

The answer given by Wikipedia in the current German version, reads (in our translation):

Mathematics […] is a science that developed from the investigation of geometric figures and the computing with numbers. For mathematics , there is no commonly accepted definition; today it is usually described as a science that investigates abstract structures that it created itself by logical definitions using logic for their properties and patterns.

This is much worse, as it portrays mathematics as a subject without any contact to, or interest from, a real world.

The borders of mathematics. Is mathematics “stand-alone”? Could it be defined without reference to “neighboring” subjects, such as physics (which does appear in the English Wikipedia description)? Indeed, one possibility to characterize mathematics describes the borders/boundaries that separate it from its neighbors. Even humorous versions of such “distinguishing statements” such as

“Mathematics is the part of physics where the experiments are cheap.”

“Mathematics is the part of philosophy where (some) statements are true—without debate or discussion.”

“Mathematics is computer science without electricity.” (So “Computer science is mathematics with electricity.”)

contain a lot of truth and possibly tell us a lot of “characteristics” of our subject. None of these is, of course, completely true or completely false, but they present opportunities for discussion.

What we do in mathematics . We could also try to define mathematics by “what we do in mathematics”: This is much more diverse and much more interesting than the Wikipedia descriptions! Could/should we describe mathematics not only as a research discipline and as a subject taught and learned at school, but also as a playground for pupils, amateurs, and professionals, as a subject that presents challenges (not only for pupils, but also for professionals as well as for amateurs), as an arena for competitions, as a source of problems, small and large, including some of the hardest problems that science has to offer, at all levels from elementary school to the millennium problems (Csicsery, 2008 ; Ziegler, 2011 )?

What we teach in mathematics classes . Education bureaucrats might (and probably should) believe that the question “What is Mathematics?” is answered by high school curricula. But what answers do these give?

This takes us back to the nineteenth century controversies about what mathematics should be taught at school and at the Universities. In the German version this was a fierce debate. On the one side it saw the classical educational ideal as formulated by Wilhelm von Humboldt (who was involved in the concept for and the foundation 1806 of the Berlin University, now named Humboldt Universität, and to a certain amount shaped the modern concept of a university); here mathematics had a central role, but this was the classical “Greek” mathematics, starting from Euclid’s axiomatic development of geometry, the theory of conics, and the algebra of solving polynomial equations, not only as cultural heritage, but also as a training arena for logical thinking and problem solving. On the other side of the fight were the proponents of “Realbildung”: Realgymnasien and the technical universities that were started at that time tried to teach what was needed in commerce and industry: calculation and accounting, as well as the mathematics that could be useful for mechanical and electrical engineering—second rate education in the view of the classical German Gymnasium.

This nineteenth century debate rests on an unnatural separation into the classical, pure mathematics, and the useful, applied mathematics; a division that should have been overcome a long time ago (perhaps since the times of Archimedes), as it is unnatural as a classification tool and it is also a major obstacle to progress both in theory and in practice. Nevertheless the division into “classical” and “current” material might be useful in discussing curriculum contents—and the question for what purpose it should be taught; see our discussion in the Section “ Three Times Mathematics at School? ”.

The Courant–Robbins answer . The title of the present paper is, of course, borrowed from the famous and very successful book by Richard Courant and Herbert Robbins. However, this title is a question—what is Courant and Robbins’ answer? Indeed, the book does not give an explicit definition of “What is Mathematics,” but the reader is supposed to get an idea from the presentation of a diverse collection of mathematical investigations. Mathematics is much bigger and much more diverse than the picture given by the Courant–Robbins exposition. The presentation in this section was also meant to demonstrate that we need a multi-facetted picture of mathematics: One answer is not enough, we need many.

Why Should We Care?

The question “What is Mathematics?” probably does not need to be answered to motivate why mathematics should be taught, as long as we agree that mathematics is important.

However, a one-sided answer to the question leads to one-sided concepts of what mathematics should be taught.

At the same time a one-dimensional picture of “What is Mathematics” will fail to motivate kids at school to do mathematics, it will fail to motivate enough pupils to study mathematics, or even to think about mathematics studies as a possible career choice, and it will fail to motivate the right students to go into mathematics studies, or into mathematics teaching. If the answer to the question “What is Mathematics”, or the implicit answer given by the public/prevailing image of the subject, is not attractive, then it will be very difficult to motivate why mathematics should be learned—and it will lead to the wrong offers and the wrong choices as to what mathematics should be learned.

Indeed, would anyone consider a science that studies “abstract” structures that it created itself (see the German Wikipedia definition quoted above) interesting? Could it be relevant? If this is what mathematics is, why would or should anyone want to study this, get into this for a career? Could it be interesting and meaningful and satisfying to teach this?

Also in view of the diversity of the students’ expectations and talents, we believe that one answer is plainly not enough. Some students might be motivated to learn mathematics because it is beautiful, because it is so logical, because it is sometimes surprising. Or because it is part of our cultural heritage. Others might be motivated, and not deterred, by the fact that mathematics is difficult. Others might be motivated by the fact that mathematics is useful, it is needed—in everyday life, for technology and commerce, etc. But indeed, it is not true that “the same” mathematics is needed in everyday life, for university studies, or in commerce and industry. To other students, the motivation that “it is useful” or “it is needed” will not be sufficient. All these motivations are valid, and good—and it is also totally valid and acceptable that no single one of these possible types of arguments will reach and motivate all these students.

Why do so many pupils and students fail in mathematics, both at school and at universities? There are certainly many reasons, but we believe that motivation is a key factor. Mathematics is hard. It is abstract (that is, most of it is not directly connected to everyday-life experiences). It is not considered worth-while. But a lot of the insufficient motivation comes from the fact that students and their teachers do not know “What is Mathematics.”

Thus a multi-facetted image of mathematics as a coherent subject, all of whose many aspects are well connected, is important for a successful teaching of mathematics to students with diverse (possible) motivations.

This leads, in turn, to two crucial aspects, to be discussed here next: What image do students have of mathematics? And then, what should teachers answer when asked “What is Mathematics”? And where and how and when could they learn that?

The Image of Mathematics

A 2008 study by Mendick, Epstein, and Moreau ( 2008 ), which was based on an extensive survey among British students, was summarized as follows:

Many students and undergraduates seem to think of mathematicians as old, white, middle-class men who are obsessed with their subject, lack social skills and have no personal life outside maths. The student’s views of maths itself included narrow and inaccurate images that are often limited to numbers and basic arithmetic.

The students’ image of what mathematicians are like is very relevant and turns out to be a massive problem, as it defines possible (anti-)role models, which are crucial for any decision in the direction of “I want to be a mathematician.” If the typical mathematician is viewed as an “old, white, male, middle-class nerd,” then why should a gifted 16-year old girl come to think “that’s what I want to be when I grow up”? Mathematics as a science, and as a profession, looses (or fails to attract) a lot of talent this way! However, this is not the topic of this presentation.

On the other hand the first and the second diagnosis of the quote from Mendick et al. ( 2008 ) belong together: The mathematicians are part of “What is Mathematics”!

And indeed, looking at the second diagnosis, if for the key word “mathematics” the images that spring to mind don’t go beyond a per se meaningless “ $ a^{2} + b^{2} = c^{2} $ ” scribbled in chalk on a blackboard—then again, why should mathematics be attractive, as a subject, as a science, or as a profession?

We think that we have to look for, and work on, multi-facetted and attractive representations of mathematics by images. This could be many different, separate images, but this could also be images for “mathematics as a whole.”

Four Images for “What Is Mathematics?”

Striking pictorial representations of mathematics as a whole (as well as of other sciences!) and of their change over time can be seen on the covers of the German “Was ist was” books. The history of these books starts with the series of “How and why” Wonder books published by Grosset and Dunlop, New York, since 1961, which was to present interesting subjects (starting with “Dinosaurs,” “Weather,” and “Electricity”) to children and younger teenagers. The series was published in the US and in Great Britain in the 1960s and 1970s, but it was and is much more successful in Germany, where it was published (first in translation, then in volumes written in German) by Ragnar Tessloff since 1961. Volume 18 in the US/UK version and Volume 12 in the German version treats “Mathematics”, first published in 1963 (Highland & Highland, 1963 ), but then republished with the same title but a new author and contents in 2001 (Blum, 2001 ). While it is worthwhile to study the contents and presentation of mathematics in these volumes, we here focus on the cover illustrations (see Fig. 1 ), which for the German edition exist in four entirely different versions, the first one being an adaption of the original US cover of (Highland & Highland, 1961 ).

The four covers of “Was ist was. Band 12: Mathematik” (Highland & Highland, 1963 ; Blum, 2001 )

All four covers represent a view of “What is Mathematics” in a collage mode, where the first one represents mathematics as a mostly historical discipline (starting with the ancient Egyptians), while the others all contain a historical allusion (such as pyramids, Gauß, etc.) alongside with objects of mathematics (such as prime numbers or $ \pi $ , dices to illustrate probability, geometric shapes). One notable object is the oddly “two-colored” Möbius band on the 1983 cover, which was changed to an entirely green version in a later reprint.

One can discuss these covers with respect to their contents and their styles, and in particular in terms of attractiveness to the intended buyers/readers. What is over-emphasized? What is missing? It seems more important to us to

think of our own images/representations for “What is Mathematics”,

think about how to present a multi-facetted image of “What is Mathematics” when we teach.

Indeed, the topics on the covers of the “Was ist was” volumes of course represent interesting (?) topics and items discussed in the books. But what do they add up to? We should compare this to the image of mathematics as represented by school curricula, or by the university curricula for teacher students.

In the context of mathematics images, let us mention two substantial initiatives to collect and provide images from current mathematics research, and make them available on internet platforms, thus providing fascinating, multi-facetted images of mathematics as a whole discipline:

Guy Métivier et al.: “Image des Maths. La recherche mathématique en mots et en images” [“Images of Maths. Mathematical research in words and images”], CNRS, France, at images.math.cnrs.fr (texts in French)

Andreas D. Matt, Gert-Martin Greuel et al.: “IMAGINARY. open mathematics,” Mathematisches Forschungsinstitut Oberwolfach, at imaginary.org (texts in German, English, and Spanish).

The latter has developed from a very successful travelling exhibition of mathematics images, “IMAGINARY—through the eyes of mathematics,” originally created on occasion of and for the German national science year 2008 “Jahr der Mathematik. Alles was zählt” [“Year of Mathematics 2008. Everything that counts”], see www.jahr-der-mathematik.de , which was highly successful in communicating a current, attractive image of mathematics to the German public—where initiatives such as the IMAGINARY exhibition had a great part in the success.

Teaching “What Is Mathematics” to Teachers

More than 100 years ago, in 1908, Felix Klein analyzed the education of teachers. In the introduction to the first volume of his “Elementary Mathematics from a Higher Standpoint” he wrote (our translation):

At the beginning of his university studies, the young student is confronted with problems that do not remind him at all of what he has dealt with up to then, and of course, he forgets all these things immediately and thoroughly. When after graduation he becomes a teacher, he has to teach exactly this traditional elementary mathematics, and since he can hardly link it with his university mathematics, he soon readopts the former teaching tradition and his studies at the university become a more or less pleasant reminiscence which has no influence on his teaching (Klein, 1908 ).

This phenomenon—which Klein calls the double discontinuity —can still be observed. In effect, the teacher students “tunnel” through university: They study at university in order to get a degree, but nevertheless they afterwards teach the mathematics that they had learned in school, and possibly with the didactics they remember from their own school education. This problem observed and characterized by Klein gets even worse in a situation (which we currently observe in Germany) where there is a grave shortage of Mathematics teachers, so university students are invited to teach at high school long before graduating from university, so they have much less university education to tunnel at the time when they start to teach in school. It may also strengthen their conviction that University Mathematics is not needed in order to teach.

How to avoid the double discontinuity is, of course, a major challenge for the design of university curricula for mathematics teachers. One important aspect however, is tied to the question of “What is Mathematics?”: A very common highschool image/concept of mathematics, as represented by curricula, is that mathematics consists of the subjects presented by highschool curricula, that is, (elementary) geometry, algebra (in the form of arithmetic, and perhaps polynomials), plus perhaps elementary probability, calculus (differentiation and integration) in one variable—that’s the mathematics highschool students get to see, so they might think that this is all of it! Could their teachers present them a broader picture? The teachers after their highschool experience studied at university, where they probably took courses in calculus/analysis, linear algebra, classical algebra, plus some discrete mathematics, stochastics/probability, and/or numerical analysis/differential equations, perhaps a programming or “computer-oriented mathematics” course. Altogether they have seen a scope of university mathematics where no current research becomes visible, and where most of the contents is from the nineteenth century, at best. The ideal is, of course, that every teacher student at university has at least once experienced how “doing research on your own” feels like, but realistically this rarely happens. Indeed, teacher students would have to work and study and struggle a lot to see the fascination of mathematics on their own by doing mathematics; in reality they often do not even seriously start the tour and certainly most of them never see the “glimpse of heaven.” So even if the teacher student seriously immerges into all the mathematics on the university curriculum, he/she will not get any broader image of “What is Mathematics?”. Thus, even if he/she does not tunnel his university studies due to the double discontinuity, he/she will not come back to school with a concept that is much broader than that he/she originally gained from his/her highschool times.

Our experience is that many students (teacher students as well as classical mathematics majors) cannot name a single open problem in mathematics when graduating the university. They have no idea of what “doing mathematics” means—for example, that part of this is a struggle to find and shape the “right” concepts/definitions and in posing/developing the “right” questions and problems.

And, moreover, also the impressions and experiences from university times will get old and outdated some day: a teacher might be active at a school for several decades—while mathematics changes! Whatever is proved in mathematics does stay true, of course, and indeed standards of rigor don’t change any more as much as they did in the nineteenth century, say. However, styles of proof do change (see: computer-assisted proofs, computer-checkable proofs, etc.). Also, it would be good if a teacher could name “current research focus topics”: These do change over ten or twenty years. Moreover, the relevance of mathematics in “real life” has changed dramatically over the last thirty years.

The Panorama Project

For several years, the present authors have been working on developing a course [and eventually a book (Loos & Ziegler, 2017 )] called “Panorama der Mathematik” [“Panorama of Mathematics”]. It primarily addresses mathematics teacher students, and is trying to give them a panoramic view on mathematics: We try to teach an overview of the subject, how mathematics is done, who has been and is doing it, including a sketch of main developments over the last few centuries up to the present—altogether this is supposed to amount to a comprehensive (but not very detailed) outline of “What is Mathematics.” This, of course, turns out to be not an easy task, since it often tends to feel like reading/teaching poetry without mastering the language. However, the approach of Panorama is complementing mathematics education in an orthogonal direction to the classic university courses, as we do not teach mathematics but present (and encourage to explore ); according to the response we get from students they seem to feel themselves that this is valuable.

Our course has many different components and facets, which we here cast into questions about mathematics. All these questions (even the ones that “sound funny”) should and can be taken seriously, and answered as well as possible. For each of them, let us here just provide at most one line with key words for answers:

When did mathematics start?

Numbers and geometric figures start in stone age; the science starts with Euclid?

How large is mathematics? How many Mathematicians are there?

The Mathematics Genealogy Project had 178854 records as of 12 April 2014.

How is mathematics done, what is doing research like?

Collect (auto)biographical evidence! Recent examples: Frenkel ( 2013 ) , Villani ( 2012 ).

What does mathematics research do today? What are the Grand Challenges?

The Clay Millennium problems might serve as a starting point.

What and how many subjects and subdisciplines are there in mathematics?

See the Mathematics Subject Classification for an overview!

Why is there no “Mathematical Industry”, as there is e.g. Chemical Industry?

There is! See e.g. Telecommunications, Financial Industry, etc.

What are the “key concepts” in mathematics? Do they still “drive research”?

Numbers, shapes, dimensions, infinity, change, abstraction, …; they do.

What is mathematics “good for”?

It is a basis for understanding the world, but also for technological progress.

Where do we do mathematics in everyday life?

Not only where we compute, but also where we read maps, plan trips, etc.

Where do we see mathematics in everyday life?

There is more maths in every smart phone than anyone learns in school.

What are the greatest achievements of mathematics through history?

Make your own list!

An additional question is how to make university mathematics more “sticky” for the tunneling teacher students, how to encourage or how to force them to really connect to the subject as a science. Certainly there is no single, simple, answer for this!

Telling Stories About Mathematics

How can mathematics be made more concrete? How can we help students to connect to the subject? How can mathematics be connected to the so-called real world?

Showing applications of mathematics is a good way (and a quite beaten path). Real applications can be very difficult to teach since in most advanced, realistic situation a lot of different mathematical disciplines, theories and types of expertise have to come together. Nevertheless, applications give the opportunity to demonstrate the relevance and importance of mathematics. Here we want to emphasize the difference between teaching a topic and telling about it. To name a few concrete topics, the mathematics behind weather reports and climate modelling is extremely difficult and complex and advanced, but the “basic ideas” and simplified models can profitably be demonstrated in highschool, and made plausible in highschool level mathematical terms. Also success stories like the formula for the Google patent for PageRank (Page, 2001 ), see Langville and Meyer ( 2006 ), the race for the solution of larger and larger instances of the Travelling Salesman Problem (Cook, 2011 ), or the mathematics of chip design lend themselves to “telling the story” and “showing some of the maths” at a highschool level; these are among the topics presented in the first author’s recent book (Ziegler, 2013b ), where he takes 24 images as the starting points for telling stories—and thus developing a broader multi-facetted picture of mathematics.

Another way to bring maths in contact with non-mathematicians is the human level. Telling stories about how maths is done and by whom is a tricky way, as can be seen from the sometimes harsh reactions on www.mathoverflow.net to postings that try to excavate the truth behind anecdotes and legends. Most mathematicians see mathematics as completely independent from the persons who explored it. History of mathematics has the tendency to become gossip , as Gian-Carlo Rota once put it (Rota, 1996 ). The idea seems to be: As mathematics stands for itself, it has also to be taught that way.

This may be true for higher mathematics. However, for pupils (and therefore, also for teachers), transforming mathematicians into humans can make science more tangible, it can make research interesting as a process (and a job?), and it can be a starting/entry point for real mathematics. Therefore, stories can make mathematics more sticky. Stories cannot replace the classical approaches to teaching mathematics. But they can enhance it.

Stories are the way by which knowledge has been transferred between humans for thousands of years. (Even mathematical work can be seen as a very abstract form of storytelling from a structuralist point of view.) Why don’t we try to tell more stories about mathematics, both at university and in school—not legends, not fairy tales, but meta-information on mathematics—in order to transport mathematics itself? See (Ziegler, 2013a ) for an attempt by the first author in this direction.

By stories, we do not only mean something like biographies, but also the way of how mathematics is created or discovered: Jack Edmonds’ account (Edmonds, 1991 ) of how he found the blossom shrink algorithm is a great story about how mathematics is actually done . Think of Thomas Harriot’s problem about stacking cannon balls into a storage space and what Kepler made out of it: the genesis of a mathematical problem. Sometimes scientists even wrap their work into stories by their own: see e.g. Leslie Lamport’s Byzantine Generals (Lamport, Shostak, & Pease, 1982 ).

Telling how research is done opens another issue. At school, mathematics is traditionally taught as a closed science. Even touching open questions from research is out of question, for many good and mainly pedagogical reasons. However, this fosters the image of a perfect science where all results are available and all problems are solved—which is of course completely wrong (and moreover also a source for a faulty image of mathematics among undergraduates).

Of course, working with open questions in school is a difficult task. None of the big open questions can be solved with an elementary mathematical toolbox; many of them are not even accessible as questions. So the big fear of discouraging pupils is well justified. On the other hand, why not explore mathematics by showing how questions often pop up on the way? Posing questions in and about mathematics could lead to interesting answers—in particular to the question of “What is Mathematics, Really?”

Three Times Mathematics at School?

So, what is mathematics? With school education in mind, the first author has argued in Ziegler ( 2012 ) that we are trying cover three aspects the same time, which one should consider separately and to a certain extent also teach separately:

A collection of basic tools, part of everyone’s survival kit for modern-day life—this includes everything, but actually not much more than, what was covered by Adam Ries’ “Rechenbüchlein” [“Little Book on Computing”] first published in 1522, nearly 500 years ago;

A field of knowledge with a long history, which is a part of our culture and an art, but also a very productive basis (indeed a production factor) for all modern key technologies. This is a “story-telling” subject.

An introduction to mathematics as a science—an important, highly developed, active, huge research field.

Looking at current highschool instruction, there is still a huge emphasis on Mathematics I, with a rather mechanical instruction on arithmetic, “how to compute correctly,” and basic problem solving, plus a rather formal way of teaching Mathematics III as a preparation for possible university studies in mathematics, sciences or engineering. Mathematics II, which should provide a major component of teaching “What is Mathematics,” is largely missing. However, this part also could and must provide motivation for studying Mathematics I or III!

What Is Mathematics, Really?

There are many, and many different, valid answers to the Courant-Robbins question “What is Mathematics?”

A more philosophical one is given by Reuben Hersh’s book “What is Mathematics, Really?” Hersh ( 1997 ), and there are more psychological ones, on the working level. Classics include Jacques Hadamard’s “Essay on the Psychology of Invention in the Mathematical Field” and Henri Poincaré’s essays on methodology; a more recent approach is Devlin’s “Introduction to Mathematical Thinking” Devlin ( 2012 ), or Villani’s book ( 2012 ).

And there have been many attempts to describe mathematics in encyclopedic form over the last few centuries. Probably the most recent one is the gargantuan “Princeton Companion to Mathematics”, edited by Gowers et al. ( 2008 ), which indeed is a “Princeton Companion to Pure Mathematics.”

However, at a time where ZBMath counts more than 100,000 papers and books per year, and 29,953 submissions to the math and math-ph sections of arXiv.org in 2016, it is hopeless to give a compact and simple description of what mathematics really is, even if we had only the “current research discipline” in mind. The discussions about the classification of mathematics show how difficult it is to cut the science into slices, and it is even debatable whether there is any meaningful way to separate applied research from pure mathematics.

Probably the most diplomatic way is to acknowledge that there are “many mathematics.” Some years ago Tao ( 2007 ) gave an open list of mathematics that is/are good for different purposes—from “problem-solving mathematics” and “useful mathematics” to “definitive mathematics”, and wrote:

As the above list demonstrates, the concept of mathematical quality is a high-dimensional one, and lacks an obvious canonical total ordering. I believe this is because mathematics is itself complex and high-dimensional, and evolves in unexpected and adaptive ways; each of the above qualities represents a different way in which we as a community improve our understanding and usage of the subject.

In this sense, many answers to “What is Mathematics?” probably show as much about the persons who give the answers as they manage to characterize the subject.

According to Wikipedia , the same version, the answer to “Who is Mathematics” should be:

Mathematics , also known as Allah Mathematics , (born: Ronald Maurice Bean [1] ) is a hip hop producer and DJ for the Wu-Tang Clan and its solo and affiliate projects. This is not the mathematics we deal with here.

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Acknowledgment

The authors’ work has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 247029, the DFG Research Center Matheon, and the the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”.

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Ziegler, G.M., Loos, A. (2017). “What is Mathematics?” and why we should ask, where one should experience and learn that, and how to teach it. In: Kaiser, G. (eds) Proceedings of the 13th International Congress on Mathematical Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-62597-3_5

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samplius.com uses cookies to offer you the best service possible.By continuing we’ll assume you board with our cookie policy .--> --> Z. I. Ali, M. Sango, Probabilistic weak solutions for nonlinear stochastic evolution problems involving pseudomonotone operators, , (2022), 997–1020. https://doi.org/10.1007/s11253-022-02117-y doi: [2] , (2012), 788–815. https://doi.org/10.1093/imamat/hxs049 --> G. Allaire, H. Hutridurga, Homogenization of reactive flows in porous media and competition between bulk and surface diffusion, , (2012), 788–815. https://doi.org/10.1093/imamat/hxs049 doi: [3] , (1992), 37–53. --> A. Bensoussan, Some existence results for stochastic partial differential equations, , (1992), 37–53. [4] , (2021), 2718–2745. https://doi.org/10.1137/19M130277 --> H. Bessaih, Y. Efendiev, R. F. Maris, Stochastic homogenization of a convection-diffusion equation, , (2021), 2718–2745. https://doi.org/10.1137/19M130277 doi: [5] , John Wiley & Sons, 2013. --> P. 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Figure 1. Sketch of domain $ D $ and its related notations
Figure 2. Mesh of perforated media $D$ used in the simulations
Figure 3. Solution computed with nonconforming finite element for spatial mesh $h = 2^{-6}$ and time mesh $\Delta t = 10^{-6}$. The deterministic solute concentration (left), and stochastic solute concentration (right) along the axes $X$ and $Y$
Figure 4. Solution computed with non-conforming finite element for spatial mesh $h = 2^{-6}$ and time mesh $\Delta t = 10^{-6}$. The deterministic solute concentration (left), and stochastic solute concentration (right) along the axes $X$ and $Y$

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“What is Mathematics?” and why we should ask, where one should experience and learn that, and how to teach it