For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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Fun math outreach/social activities

What are some great math social activities for students? I'm looking for things that bring people together with a "light" mathematical touch. The goal is to create a stronger mathematical community in ...
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1answer
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Strange old multiplication table found in Oklahoma school

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
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Grasping mathematics

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...
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High school algebra textbooks for gifted students

Cross-posted to Math Educators Stack Exchange. (link) I am looking for high school algebra/mathematics textbooks targeted at talented students, as preparation for fully rigorous calculus à la Spivak. ...
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Proving a certain map on the closed unit disc must be the identity

Bounty expired. Will gladly re-create one if a satisfactory answer is posted in the future. Prove: Let $f$ be a continuous function on the closed unit disc with two properties: 1. $f$ is the ...
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1answer
671 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
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How does advancing through the math major work? [closed]

I am an undergrad math major that just completed Calculus 3 last semester. This semester I signed up for Discrete Mathematics, and will be taking Intro to Advanced/Abstract Math next. Of course-- I ...
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Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
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Motivating infinite series

What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, ...
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Alternative set theories

This is a (soft!) question for students of set theory and their teachers. OK: ZFC is the canonical set theory we all know and love. But what other, alternative set theories, should a serious student ...
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800 views

Exciting games and material to motivate children to math

We are a group of people trying to motivate children, especially living in the countryside, to science and math. We have different activities with children such as doing scientific experiments and ...
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4answers
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Common student mistakes/misconceptions in a first year calculus course

What are the common mistakes and misconceptions students make in a first year calculus course? More importantly: What can I do to prevent/rectify them? Context: Soon I will be doing ...
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2answers
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Relearning from the basics to Calculus and beyond.

Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus ...
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Best intuitive metaphors for math concepts (of any level)

Frequently, we introduce a new concept with a formal definition, then immediately say "Intuitively, what this means is..." What are the absolute best metaphors you've seen (for concepts of any level)? ...
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2answers
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Learning Mathematics using only audio.

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...
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13answers
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How to explain the perpendicularity of two lines to a High School student?

Today I was teaching my friend from High School about linear functions. One of the exercises we had to do was finding equations of perpendicular and parallel lines. Explaining parallel equations was ...
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5answers
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When I was teaching absolute function properties, I suddenly made this question …

I was teaching absolute function properties in a K-12 class. I made this question in my mind. Suppose $f(x)$ is a one-to-one function, and its definition is $f(x)=max\left \{ x,3x\right ...
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Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
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8answers
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Why are epsilon-delta proofs difficult?

What conceptual difficulties do students learning epsilon-delta proofs have, or, why are the proofs difficult? Motivation I have to teach people and never found the epsilonistics particularly ...
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4answers
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Why study Hopf Algebras?

I'm looking for reasons that motivate the study of Hopf Algebra, like its applications in other branches of mathematics or maybe with physics. The first I've got is that they're interesting by ...
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Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...
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5answers
814 views

Math department space design ideas

I'm looking for resources on design space for academic departments, particularly, We've been asked to provide ideas on designing a "dream math department". I'd like to gather some ideas for doing ...
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7answers
499 views

Common inadequate definitions

I had the good fortune of assigning the following problem on the first day of my freshman honors calculus course: Is $a$ contained in the interval $[a,a)$? Explain. The majority of my students ...
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5answers
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Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
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Fun math for young, bored kids?

For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay ...
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8answers
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How to explain brackets to young students

It's amazing how simple questions from young students can often uncover unexpected gaps in (at least my) knowledge, or at least the ability to explain. Today, a student asked me why she can "forget ...
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2answers
107 views

why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem? [duplicate]

In standard multivariable analysis texts, the change of variables for multivariable integration in Euclidean space is almost always stated for a $C^1$ diffeomorphism $\phi$, giving the familiar ...
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1answer
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Research in differential geometry

I am an 3rd year undergrad interested in mathematics and theoretical physics. I have been reading some classical differential geometry books and I want to pursue this subject further. I have three ...
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8answers
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Elementary Papers at ArXiv

Inspired by this question, at MO i am asking this question. Can anyone list some elementary articles at ArXiv which can be understood by High-School/Undergrad Students. I am asking this because, i ...
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3answers
458 views

which exact integration techniques belong in a first year calculus/analysis course?

At our university we are now discussing changes to the course contents and there is some heated discussion regarding integration in the first year calculus courses. Currently, the techniques of exact ...
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5answers
898 views

Reflections on math education

Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary ...
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4answers
503 views

Mathematical Habit

Whenever I have to do proofs or understand a concept, I start with examples and generalize. As an aspiring mathematician, I have fears that it might hurt me, especially when we have so many ...
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1answer
235 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
16
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1answer
707 views

Alternative construction of the tensor product (or: pass this secret)

The paper Tensor products and bimorphisms by B. Banachewski and E. Nelson studies tensor products (defined by classifying bimorphisms) in concrete categories. It is quite interesting that their main ...
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6answers
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No radical in the denominator — why? [duplicate]

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...
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6answers
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What is the best way to develop Mathematical intuition? [closed]

I want to develop my pure mathematics knowledge and would like to know what is the best way to develop mathematical intuition? I am going through exercises that ask for proofs and I don't have the ...
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12answers
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Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
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7answers
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Films about math: a question about math education and motivation for learning math [closed]

I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
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5answers
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Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor?

Talking to students in different areas and taking different classes in math, physics, electrical engineering I have been struck by the differing amounts of rigor in use. I know little about economics ...
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3answers
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What makes a good mathematician?

A soft question but I believe important to help get maturity in maths. Not until I got admitted to a graduate applied math program that I started to learn math. Before that, I was a life science ...
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1answer
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How do you remember theorems?

I am currently a Master's student in math. I do very well in my classes, understand the material, can do the proofs w/o having to read the text, etc, but as time passes, I find that I will forget ...
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2answers
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How to deal with exercises with no solutions given?

Probably most people will acknowledge the importance of doing exercises when reading a mathematical textbook. Here I am talking about a textbook of similar level as those ones listed in GTM. However, ...
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1answer
336 views

Do lay persons really believe that all of mathematics is known?

I once found a professor of medicine to be under the impression that everything in mathematics is already known. It's probably commonplace to hear that the masses labor under that misconception. In ...
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10answers
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Are there 3 trig functions or are there 6 trig functions?

In my algebra class we are being taught that there are only the 3 basic trig functions (cosine, sine, and tangent). But my friend who is 2 math grade levels ahead of me is saying that there is 6 trig ...
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8answers
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What math should a programmer know?

I am an application programmer focussing on Line Of Business (LOB) applications. I am from non-mathematics and non-CS background. What mathematics should I learn which help me improve my programming ...
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5answers
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Is $ 5 $ nearer to $ 0 $ or $ 10 $?

My 6-year-old’s homework was “to find the nearest $ 10 $.” For example, $$ 42 \to 40 \quad \text{and} \quad 28 \to 30. $$ For $ 55 $, she answered “$ 50 $” and was marked wrong. How is this wrong? ...
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4answers
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Motivation behind the definition of GCD and LCM

According to me, I can find the GCD of two integers (say $a$ and $b$) by finding all the common factors of them, and then finding the maximum of all these common factors. This also justifies the ...
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5answers
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Is the skill to learn new math by reading textbook alone (no lectures) required when one becomes a PhD student?

I've taken a few math classes in college. I'm wondering as one graduates college and applies to become a PhD student in math, is he/she going to be required to learn math related materials alone ...
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Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...
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5answers
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Inspiring a new generation

Tomorrow is a very special day for both my students and I: we will be starting a calculus course. I'm looking for some nice quotes to read to them to convey just what a complete game changer calculus ...