Questions tagged [education]

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

453 questions
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Is there an elementary introduction to higher order functions?

I am teaching a pre-calculus course (using the textbook by Michael Sullivan if it helps), and I realized that higher order functions seem to show up in with some frequency in pre-calculus and calculus....
256 views

This question is intended as public service to mathematics. It is meant to benefit undergrad research students and maybe even researchers wishing to broaden their expertise and learn something away ...
679 views

Comparing the U.S. undergraduate math education to the French “classes préparatoires”

Could anyone comment on how the math track of the "classes préparatoires" compares to the U.S. undergraduate major? I took a look at some of the French entrance exams and was rather intimidated. How ...
138 views

Graphical multiplication tables for $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}$

Inspired by Burkard Polster's beautiful video on Times Tables, Mandelbrot and the Heart of Mathematics I wondered how this graphical approach to visualize the multiplicative structure of finite rings ...
176 views

What examples, exercises, topics, etc should I treat when teaching category theory to non-math people?

A couple friends of mine have become very enthusiastic about learning category theory (which I know at the level of category theory for the working mathematician), so I'm giving them lessons. One is a ...
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Can I write a pdf with exercises taken from other sources, solving them myself and not cite them, or do I have to ask for permission?

I want to create some PDFs that will help future university mathematics students to learn the material. I just started, literally 1 hour ago. I do not want to sell these PDFs but just make them ...
374 views

Alternative introduction to tensor products of vector spaces

One of the main obstacles in understanding the tensor product is that, unlike many other algebraic structures, you cannot really get hold of its element structure. This confuses many beginners. The ...
635 views

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and didn'...
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Our university uses computer software to help automate and expedite the learning process for basic math classes (college algebra, trigonometry, precalculus, etc.). Software such as this provides ...
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I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics ...
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Can it be useful to think of operations on subspaces in terms of operations in elementary set theory?

This question is something that I have been thinking about on and off for a while. The basic premise is that, in Linear Algebra, a lot of the basic operations performed on subspaces have corresponding ...
767 views

Online Video Lectures for Graduate Level Mathematics?

I am wondering if there is a nice compilation of good video lectures in graduate level mathematics? I mean a website, or a forum, or maybe something like course-era (which is mostly undergraduate ...
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Referral of a Textbook or Book that teaches Intuition, focusing on Calculus.

I was wondering if there is a book out there that doesn't teach you how to do calculus, but teaches you how to apply it in the physical or social sciences. I know calculus, integration and ...
209 views

Algorithm for finding “fact families”

My friend's 3rd grader encountered the following question regarding "fact families" on her math homework: I was in 3rd grade sometime in the 1980s, so I don't believe I ever encountered this term ...
263 views

From algebraic master degree to algebraic geomery Phd

I am a foreign master student in algebra at the final year. I'm familar with categorical algebra and have interesting in algebraic geomery and number theory. I have learned some knowledge about scheme ...
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What's the acceptance of rational trigonometry in current mathematics courses?

I've been reading about Wildberger's rational trigonometry and I'm willing to learn it. I'm wondering if it's usage is accepted in undergraduate mathematics courses. It seems there's a redefinition on ...
123 views

Optimal partition for a riemann integral

I am a statistician tasked with teaching an elementary calculus course. I am about to teach Riemann sums. The breakpoints for the rectangles (the partition) that make up the Riemann sum need not be ...
263 views

Bayes analysis as used in a Presidential Election - with calculations shown

Can you show all the steps needed for a Bayesian probability progression as new information is received. As an example, initial estimate for Obama to win (popular vote) is 55%. In state-A, Democrats ...
391 views

Have Changes in Applications Made Linear Algebra More Central/Urgent?

In the days when my father taught civil engineering (some decades ago), mathematical applications seemed to be mainly "scientific." (This was the "space age.) Hence the most important branch of ...
1k views

List of mathematical Summer schools (particulary in Europe)

I would like to apply for a summer school. Particulary it should take place in Europe and center on the topic numerical analysis. Is there something like a comprehensive list of summer schools?
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Math Lessons with Two Parts and a Combination

This is fairly open ended, so I understand if people consider this to be off-topic. I'm interested in creating math lessons where two groups each learn how to use a different simple math skill, and ...
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Arc length of a Polar curve as a Riemann sum

Suppose we have a curve in polar plane satisfying the equation $r=f(\theta)$ with $\theta\in[a,b].$ To find the area enclosed by this curve in this range of $\theta$ using Riemann integrals, we ...
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Books that develop interest in integration skills

Which books develop interest in calculus? By calculus, I mean both the proof based elementary real analysis flavored questions, and also those highly calculation based integration/differential ...
2k views

Orthogonal verus Perpendicular Terminology

This is a pedantic question about the use of the terms 'orthogonal' and 'perpendicular.' I think when people first hear the term 'orthogonal' they learn it to mean perpendicular, but in the linear ...
554 views

E versus e when using scientific notation

When I was calculating pressures in different units, I decided to use Google out of laziness. First I tried: 1.013e-10 mbar and received a result of: ...
164 views

Examples of categories which appear naturally without objects

Regarding the morphisms-only-definition of a category (which is equivalent to the usual one dealing with objects and morphisms), I would like to ask: Which examples of categories in practice appear ...
188 views

I would like to go to a graduate school for pure mathematics, but I do not live where such programs exits. Furthermore, I can not move. Question: Do any Universities have graduate program in pure ...
291 views

What is tensor, really?

How can one understands the definition of tensor from the purely formal point of view? To what abstract structure this concept can be generalized?
223 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
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Teaching Student's distribution

While it is fairly straightforward to show the basics of the normal distribution in a first year undergraduate course, how does a teacher provide good intuition when the Student distribution comes in? ...
272 views

Mind Maps for teaching Mathematics

Has anyone used Mind Maps to teach advanced mathematical topics? If so, how did it work, was it useful or a waste of time? Thanks for any insights. Regards -A
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$\max_{y} \min_{x} f(x,y)$ as motif for exploring mathematics

It's been several years since my undergraduate math days, and I would like to spend a bit of time refreshing and then tackling a few things I never completely mastered. Rather than proceeding topic ...
319 views

How to Create a Lesson Plan with Wolfram Alpha

This will be my first post in this forum. I am so excited to see a lot of interesting posting from the community. From the FAQ, I learned that Mathematics stack exchange discussed about mathematical ...
362 views

“Reverse thinking” exam questions-reference request

I am interested in exam questions that are "backwards" from how they are usually asked. For example: Brian and Megan have the following question on their exam: Find the volume of the solid ...
116 views

Examples of functions that are not Borel measurable that will be accessible to 1st year undergraduates

While teaching statistics, I've grown sick of using terms such as "under (very) weak regulatory conditions..." and would like to be able to provide some solid examples of when these conditions are not ...
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Writing for the purpose of showing that one knows something

Several styles of writing about mathematics are appropriate in different contexts. A mathematician writes something to be read by other mathematicians. A mathematician writes something to be read by ...
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How Beneficial Is It to Read Error-Riddled Textbooks?

I was just reading this math.meta question, and it motivated me to ask about my current situation. I'm an undergraduate student who's reading a textbook (for self-study) that is riddled with errors -...
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Possible Research directions for students interested in Abstract Algebra

This is my first post in MSE: I have completed my Masters in Mathematics.I love to do Abstract Algebra. I have studied Groups,Rings,Fields,Modules and Non-Commutative Rings. But I am weak in Calculus ...
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What does $x2$ mean? Is it $x\cdot 2$ or the variable $x2$?

I'm working on a online mathematical learning environment. There is a mathematical editor where students can give their answers using a graphical interface: However, we have had the problem in the ...
52 views

Find geometric interpretation of differential operators in vector fields.

I'm trying to create some notes on multivariable calculus, but It has been hard to find the geometric point of view of this: Jacobian Matrix (Derivative of a VF) Laplacian Nabla operator Curl ...
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Looking for a collection of calculus problems “from the wild”

I felt I didn't really learn calculus in calculus class, but rather in physics class. In fact I remember distinctly setting up my first differential equation "from scratch" (i.e. from a problem that ...
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How do you prevent being lead astray when you're working on a problem that takes months/years?

Usually, when you're a student, the textbook/teacher has organized the structure of your education such that you are led on the right path. You are basically "taken by hand" to make sure that after a ...
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Is it too late to aim for postgraduate maths?

I don't know where to ask but I decided to give this part of the community a shot. Anyway I am currently studying an IT related degree but lately I have started to found a love on maths. Sadly I ...
413 views

Is group theory and in general pure maths useful in applied mathematics?

I've just finished the first year of Mathematics at University. I've already encountered groups, in a soft mini-course that took around half semester. My idea would be to study applied mathematics, ...
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Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
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Criterion for Improvement

I was recently asked the question "How do you know when you've become a better mathematician/better at mathematics?," and I realized that at that moment I did not have a valid answer, since I have ...
387 views

Intuition behind the link between coding theory and group theory

I am trying to find an easy link between group theory and coding theory. The usual path that most of the texts follow is that they present introductory material on groups, fields, rings, etc., and ...
788 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis -...
My university offers small grants (in the \$100 - \$300 range) for classroom enhancement resources. In the past, I've applied for and received a grant to purchase a Zometools kit used for ...