Questions related to the teaching and learning of mathematics.

learn more… | top users | synonyms (1)

12
votes
3answers
786 views

What should a math graduate know? [closed]

There are a lot of undergraduate courses out there and most of them agree on certain things, with regard to the subjects covered. Courses that include mathematics (engineering, physics, etc) are ...
12
votes
2answers
3k views

Best software to take math notes?

I have read some old discussions about this topic and would like to get some up-to-date advice, if possible. How can I take math notes, write formulas and draw graphs on my pc (win 7), the easiest ...
12
votes
4answers
454 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 ...
12
votes
4answers
265 views

Should the domain of a function be inferred?

It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ...
12
votes
2answers
231 views

How to do math and help people

I am currently an junior math and statistics student at the University of Florida. For my whole life I have really enjoyed math and really do find a calling in mathematics. Math classes are the only ...
12
votes
2answers
602 views

Is Mathematics graduation important for a Computer Scientist?

I know this might be a personal problem, but I often find some friends in the same problem as me so I think this might be helpful to them after all. I am going to graduate in Computer Science in ...
12
votes
2answers
683 views

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 ...
12
votes
1answer
294 views

Developing research experience in mathematics

I am not sure whether this is the right forum for this question, so it might be migrated somewhere else; but, it is, I think, certainly germane to the wider idea of pursuing interesting questions and ...
11
votes
5answers
2k views

Why teach linear algebra before abstract algebra?

Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra? I'm asking this because personally it seems to be much easier to understand the architecture behind ...
11
votes
7answers
906 views

When is something “obvious”?

I try to be a good student but I often find it hard to know when something is "obvious" and when it isn't. Obviously (excuse the pun) I understand that it is specific to the level at which the writer ...
11
votes
2answers
2k views

Path to Basics in Algebraic Geometry from HS Algebra and Calculus?

In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it ...
11
votes
9answers
739 views

Sources of problems for teaching/tutoring young mathematicians

I am tutoring several talented students, middle school level and early high school level, in mathematics. I am always looking for new sources from which to draw questions. Can anyone recommend books, ...
11
votes
3answers
997 views

I want to learn math!

Let me introduce myself. My name is Filip and I am going to 10th grade now. My school deals with electrotechnics and computers (programming, hardware etc.) I was always good at math but not quite ...
11
votes
1answer
588 views

What is the expected mathematical repertoire of a Ph.D. program applicant?

I am an undergraduate (currently a sophomore) studying to prepare for applying to a Ph.D. program in mathematics. I have thus far structured my course selection upon the advice of a friend I met ...
11
votes
1answer
170 views

How can I raise my intuition in solving mathematical problem?

I am an undergraduate student studying some elementary calculus and statistics. In my honor calculus class, my professor gave one of final exam problem: $$\lim_{n \to \infty} \int_{[0,1]^{n}} ...
11
votes
1answer
158 views

Studies on lack of mathematical education

I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that ...
11
votes
0answers
227 views

Anecdote about mathematicians leaping to tops of problems and then building a staircase down?

I've run across this cute little story before, and now for the life of me I can't find it anywhere. It goes something like: Two people are looking out onto a mathematical landscape, and there are ...
10
votes
5answers
2k views

Advice for Self-Study

I am a senior in high school who has taught myself through Calculus BC and I got a 5 on the exam. However, I have taken all the math I can at my school. I have also taught myself multi-variable ...
10
votes
4answers
569 views

Best way of introducing determinants in a linear algebra course

What is the best way of introducing determinants in a linear algebra course? I want to give real life examples of where the determinant is applied. It should have a real impact.
10
votes
4answers
745 views

Is there a more efficient method of trig mastery than rote memorization?

I would like to get alot better at trig than I am. What is the best/most efficient method? Thanks much in advance Joe
10
votes
4answers
3k views

Is “locally linear” an appropriate description of a differentiable function?

In this answer on meta, Pete L. Clark said: I think the question concerns the idea that a differentiable curve becomes more and more like a straight line segment the closer one zooms in on its ...
10
votes
4answers
452 views

Why would you expand a square wave in a Fourier series?

The periodic square wave $$ f(x) = \cases{ 1 \text{ if } 0 \le x \le \pi \\ 0 \text { if } -\pi \le x < 0} $$ seems easy enough to work with. Why transform it into a series of sines and cosines? ...
10
votes
3answers
660 views

Is the golden ratio overrated?

While reading many sources and watching many video's about nature and physics I wonder if the golden ratio is really that often occurring in nature and physics ? If I look on the Wikipedia pages I see ...
10
votes
5answers
2k views

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
10
votes
5answers
481 views

Areas of math that can be “gamified”?

My old high school math teacher has started up a math club recently. It's become quite popular (to my pleasant surprise), and I've been looking for ways to contribute. To that end I've been looking to ...
10
votes
2answers
373 views

Elementary Geometry Nomenclature: why so bad?

A long-ish wall of text, and I apologize. Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A ...
10
votes
3answers
399 views

Popular general-interest math courses

I'm hoping the userbase here doesn't mind if I do a little crowd-sourcing. I'm curious to find out about popular general-interest mathematics or statistics classes that are offered universities that ...
10
votes
2answers
346 views

Is “problem solving” a subject to be taught?

Note: This question has been cross-posted to MathOverflow: see here. I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all ...
10
votes
0answers
612 views

What are some strong PhD programs in (algebraic) number theory?

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
10
votes
0answers
2k views

Self-study Real analysis Tao or Rudin?

The reference requests for analysis books have become so numerous as to blot out any usefulness they could conceivably have had. So here come another one. Recently I've began to learn real analysis ...
10
votes
0answers
277 views

How to be a bird

Freeman Dyson has famously characterized two styles of mathematics, that of the bird and that of the frog. I was asked recently the following question, which I don't know how to answer: If, in ...
9
votes
11answers
2k views

False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)

Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...
9
votes
7answers
6k views

practical uses of matrix multiplication

The use of matrix multiplication is usually given with graphics initially (scalings, translations, rotations, etc). Then there are more in-depth examples such as counting the number of walks between ...
9
votes
4answers
371 views

Middle school number theory

Find at least three numbers that satisfy all three conditions: (1) there is a remainder of $1$ when the number is divided by $2$; (2) there is a remainder of $2$ when the number is divided by $3$; ...
9
votes
7answers
2k views

What should the high school math curriculum consist of?

"Life is open book." With the advent of widely accessible, inexpensive (or even free) computational tools and Computer Algebra Systems (TI-89, Wolfram|Alpha, etc.), much of what traditionally ...
9
votes
2answers
454 views

Is there any way to read articles without subscription?

This is not mathematician question but I think it's related. How I can get access to some of "Software: Practice and Experience" articles without subscription? Any advice is welcome. Sorry if I'm ...
9
votes
2answers
342 views

How to explain the commutativity of multiplication to middle school students?

It's easy for natural numbers: $3\times 5=5\times 3$ ***** ***** ***** but how do you explain that $x.y=y.x$ for any real numbers $x$ and $y$. Moreover, in $\Bbb{N}$, do you prefer to define ...
9
votes
3answers
741 views

how to explain prime numbers to children

My little cousin (12year) asked me about how emails are encrypted and I want to answers her in such a way she understands it. This is diffuct, but I am happy with teaching the definition of a prime ...
9
votes
4answers
286 views

Recommended survey of mathematics [closed]

What do you see as the most explanatory and beautiful survey of mathematics book...For short is there a book like Feynman lectures but for math?I've looked at Elementary Mathematics from an Advanced ...
9
votes
4answers
251 views

Communicating mathematics

As a TA, my ratings have been fairly mediocre. There's nothing to suggest I'm a problem, but I have room to improve. What's more disturbing to me is that I even struggle to communicate math with ...
9
votes
3answers
218 views

Links to Online Videos of Good-Quality Lectures by Mathematicians

I am not trying to do anything new here, but I would like to start an activity that has been going on at Math Overflow. Hopefully, people here at the Math StackExchange can also enjoy the good stuff. ...
9
votes
4answers
227 views

Is studying mathematics chronologically a good idea or not and why?

In high school nowadays most mathematics you learn is fairly 'old'. You have your geometry, all of which (taught in high school) was known to the Greeks more than 2 thousand years ago. You have ...
9
votes
1answer
333 views

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 ...
9
votes
1answer
469 views

Undergrad Student Trying to Figure Out What to Study

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
9
votes
1answer
126 views

How and what to teach on a first year elementary number theory course?

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. ...
9
votes
1answer
219 views

General question: What one can do to help students one is grading?

Due to unknown reason I was assigned as a grader this semester for a certain proof writing class in my universtiy. The class size is 65 and students took it usually comes from a computer science ...
9
votes
1answer
215 views

Where can I find the 1960s New Math syllabus?

I've been looking everywhere for even a short summary of the content of the 1960s New Mathematics Math education reform in the US but I cannot ;-; Does anyone know?
9
votes
1answer
185 views

Journals or Magazines on Study Skills or How to Study Math

I am trying to find only journals or trustworthy magazines which can help math students to study math more efficiently and productively. I am not asking about books in this thread. In particular, I am ...
9
votes
5answers
168 views

The use for solving quadradic equations for high school students

I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials. He asked me what why we learn this and how this could apply to a ...
8
votes
5answers
274 views

Why does $n^0 = 1$?

Why is it that $n^0 = 1$? I understand how $n^2 = n*n$ and how $n^1 = n$ but I can't understand why $n^0 = 1$.