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.

457 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
15
votes
1answer
3k views

Where does the “Visual Multiplication” technique originate from?

There is a geometric technique to perform multiplication of numbers. But as the internet goes, it is hard to figure out who deserves the credit. What I've heard is A mayan technique From Vedic ...
12
votes
0answers
928 views

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....
10
votes
0answers
257 views

Undergrad research gateways

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 ...
8
votes
4answers
1k views

Self-study High School Math Textbooks?

I'm new to this website so I apologize in advance if what I'm going to ask isn't meant to be posted here. A bit of background though: I haven't been to school in 6 years and the last level I've ...
8
votes
0answers
689 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 ...
6
votes
0answers
149 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 ...
6
votes
0answers
180 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 ...
6
votes
0answers
96 views

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 ...
6
votes
1answer
675 views

looking for motivation in teaching algebra

I am going to teach some grade 9 students about solving linear and quadratic equations. I am looking for a question from every day life (of a teenager) or a puzzle which is hard to solve without using ...
6
votes
1answer
116 views

Visual questions for 6th graders

I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed ...
6
votes
0answers
381 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 ...
6
votes
0answers
639 views

How important is the “prestige” of your university for undergraduate mathematics?

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'...
6
votes
0answers
156 views

Educational software for graduate mathematics

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 ...
6
votes
0answers
228 views

Advice on learning mathematics

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 ...
5
votes
0answers
80 views

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 ...
5
votes
0answers
840 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 ...
5
votes
0answers
135 views

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 ...
5
votes
0answers
212 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 ...
5
votes
0answers
278 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 ...
5
votes
0answers
309 views

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 ...
5
votes
0answers
124 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 ...
5
votes
0answers
264 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 ...
5
votes
0answers
392 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 ...
5
votes
0answers
2k 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?
4
votes
0answers
31 views

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 ...
4
votes
0answers
98 views

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 ...
4
votes
2answers
58 views

Reformulating the definition of compactness

Consider the following alternative definition of a topological space. Definition: A topological space is an ordered pair $(X, \lessdot)$ consisting of a set $X$ and a binary relation $\lessdot$ ...
4
votes
0answers
104 views

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 ...
4
votes
0answers
82 views

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 ...
4
votes
1answer
79 views

Is the zero considered a leading zero?

According to the formal definition of a leading zero, is the zero itself considered a leading zero?
4
votes
0answers
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 ...
4
votes
0answers
592 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: ...
4
votes
1answer
630 views

Alternative proof that base angles of an isosceles triangle are equal

The "classic textbook proof" of equality of base angles of an isosceles triangles which I studied in my school days is as follows: Let $\Delta ABC$ be a triangle with $AB = AC$ and let $D$ be the mid ...
4
votes
1answer
186 views

What book offers strategies and heuristics for theorem proving in the same spirit as Polya's How to Solve It?

Polya's How to Solve It is all about heuristics and strategies for problem solving, but it's mainly written for problems which require students to find values, not to prove theorems. While Polya's ...
4
votes
0answers
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 ...
4
votes
2answers
208 views

Mathematics or physics at university

I have a strong interest in maths, and I feel that advanced physics is cool too (although I've only studied classical mechanics at high school, which is kind of boring). So I'm not sure about which ...
4
votes
0answers
192 views

distance Pure Math graduate programs?

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 ...
4
votes
1answer
474 views

Where to begin my Math journey

I apologize if this is not the correct forum for this, but I felt it appropriate. I want to start getting into more mathematics and learning all I can to step up my programming career. I know plenty ...
4
votes
0answers
295 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?
4
votes
0answers
229 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 ...
4
votes
0answers
93 views

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? ...
4
votes
0answers
273 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
4
votes
0answers
193 views

$\max_{y} \min_{x} f(x,y)$ 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 ...
4
votes
0answers
320 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 ...
4
votes
0answers
363 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 ...
3
votes
0answers
118 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 ...
3
votes
0answers
112 views

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 -...
3
votes
0answers
131 views

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 ...
3
votes
0answers
71 views

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 ...
3
votes
0answers
55 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 ...