Questions tagged [mathematics-education]

For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/

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17 votes
7 answers
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Uppercase Point Labels in High-School Diagrams: from Euclid?

I wonder if the convention of labeling points in geometric diagrams with uppercase symbols ultimately derives from Greek mathematics, which was originally written in "majuscule" (uppercase) Greek ...
Joseph O'Rourke's user avatar
63 votes
20 answers
13k views

What should we teach to liberal arts students who will take only one math course?

Even professors in academic departments other than mathematics---never mind other educated people---do not know that such a field as mathematics exists. Once a professor of medicine asked me whether ...
8 votes
4 answers
2k views

What would be good to know before starting my undergraduate studies to become a good mathematician?

First of all, I'm sorry if this isn't the kind of question that should be made in MathOverflow. I read the FAQ and I didn't consider this (that) inappropriate. I couldn't resist! People here are ...
12 votes
10 answers
16k views

Learning Algebra & Group Theory on my own [closed]

I'm learning Algebra & Group Theory, casually, on my own. Professionally, I'm a computer consultant, with a growing interest in the mathematical and theoretical aspects. I've been amazed with ...
20 votes
9 answers
5k views

Mathematics and autodidactism

Mathematics is not typically considered (by mathematicians) to be a solo sport; on the contrary, some amount of mathematical interaction with others is often deemed crucial. Courses are the student's ...
151 votes
18 answers
22k views

Why do we care about $L^p$ spaces besides $p = 1$, $p = 2$, and $p = \infty$?

I was helping a student study for a functional analysis exam and the question came up as to when, in practice, one needs to consider the Banach space $L^p$ for some value of $p$ other than the obvious ...
23 votes
16 answers
6k views

What are your experiences of handouts in mathematics lectures?

There are many different styles of lecturing, and many different aspects that are blended together to give a whole "lecturing style". That said, I'm particularly interested in hearing people's ...
42 votes
7 answers
11k views

On starting graduate school and common pitfalls...

Hi, I'll be starting graduate school soon, and when I look back at my college career, there are certain things I wish I could have done differently. In hindsight, I wished I wasn't in such a rush to ...
4 votes
4 answers
1k views

Less-known conjectures of significant influence and the contrary

In mathematics, it is common that theorems/results and problems appearing dull in one generation get revitalized and become the center of research in another one. Sometimes conjectures that are ...
14 votes
11 answers
34k views

Why does undergraduate discrete math require calculus?

Often undergraduate discrete math classes in the US have a calculus prerequisite. Here is the description of the discrete math course from my undergrad: A general introduction to basic ...
2 votes
1 answer
7k views

Websites hosting free math ebooks. [duplicate]

Possible Duplicates: Free, high quality mathematical writing online? Most helpful math resources on the web A lot has been said about different kinds of math resources here in MO. To mention a ...
29 votes
15 answers
4k views

Making sure that you have comprehended a concept

I have a question that I've been thinking about for a long time. How can you assure yourself that you've fully comprehended a concept or the true meaning of a theorem in mathematics? I mean how can ...
8 votes
3 answers
9k views

Applications of Group Theory Which Motivate Theoretical Questions?

I'm going to be a teaching assistant for an undergraduate class in abstract algebra next semester, for students who have not taken abstract algebra before. It will deal with group theory and linear ...
4 votes
3 answers
2k views

How do undergrad students write papers by themselves?

Can a student write a paper and send it to a professor review?
45 votes
14 answers
12k views

Examples of undergraduate mathematics separation from what mathematicians should know

I'm looking for examples of four kinds of things: Material that is usually covered in standard undergraduate mathematics courses and/or in first-year graduate work (or tested in qualifying ...
13 votes
10 answers
2k views

A place to find original papers

I currently use scholar.google.com to find papers in cases like Sophus Lie's original papers on "Transformation Groups". Does anyone know of other places that collect original works like this, i.e. ...
5 votes
2 answers
748 views

Does A "Connections" Blog/Podcast exist for Math?

What I mean is this: Does there exist a mathematics podcast where a mathematician of some sort looks at undergraduate/graduate mathematical topics and look into the history (how those objects came ...
6 votes
6 answers
2k views

Resources for learning domain theory?

I'm a computer programmer who's caught on to denotational semantics. I mostly work with Ruby, JavaScript and C, but I know a little Haskell and ML. I've taken my first steps towards reasoning about ...
jvoorhis's user avatar
35 votes
14 answers
4k views

Where have you used computer programming in your career as an (applied/pure) mathematician?

For background: I'm working on a book to help mathematicians learn how to program. However, I need to see some examples from people in the field that have done different kinds of things than I have. ...
14 votes
11 answers
4k views

Math History books

I'm teaching a course over the summer (it's a sort of make-your-own course for non-majors) and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and ...
Charles Siegel's user avatar
1051 votes
292 answers
341k views

Examples of common false beliefs in mathematics

The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent people have while ...
22 votes
3 answers
1k views

Do rational numbers admit a categorification which respects the following "duality"?

I need to give a lot of quite basic background to this question because I think (at least from conversing with fellow graduate students) that most mathematicians have not really thought about ...
Steven Gubkin's user avatar
7 votes
0 answers
3k views

Good textbooks on probability and/or stochastic processes, emphasizing simulation

Any recommendations for textbooks on probability and/or stochastic processes that emphasize simulation? I'll be teaching this course in the Fall.
James Propp's user avatar
74 votes
21 answers
24k views

How should one present curl and divergence in an undergraduate multivariable calculus class?

I am a TA for a multivariable calculus class this semester. I have also TA'd this course a few times in the past. Every time I teach this course, I am never quite sure how I should present curl and ...
Kevin H. Lin's user avatar
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0 votes
7 answers
3k views

Good/Economical textbook for undergraduate intro to diff.eq. for engineers?

In the fall I will be teaching an intro to diff.eq.s course for undergrad engineers. The usual textbook is $150 with solution manual and it's not that great. There must be a cheaper alternative that's ...
32 votes
5 answers
7k views

The interrelationship problem of modern mathematics – How to deal with it in first year graduate courses?

I was reading recently online Peter May's complaints (I'm a fan, you can tell, I'm sure) about teaching the third quarter of the graduate algebra sequence at the University of Chicago. This course ...
15 votes
5 answers
17k views

Reference letters for graduate school after a couple years in the industry

How does one return to graduate school after spending a couple years in the industry? In particular, what are ways of getting good recommendations? I'm not concerned about the "adjustment" to the grad ...
57 votes
11 answers
12k views

Interesting results in algebraic geometry accessible to 3rd year undergraduates

On another thread I asked how I could encourage my final year undergraduate colleagues to take an algebraic geometry or complex analysis courses during their graduate studies. Willie Wong proposed me ...
ifk's user avatar
  • 1,034
6 votes
1 answer
5k views

How would You encourage graduate students to learn algebraic geometry and/or complex analysis? [closed]

Hello, I am the 3rd year undegraduate student of mathematics. After I obtain a bachelor degree I want to study maths at graduate level, especially algebraic geometry and complex analysis. This fields ...
ifk's user avatar
  • 1,034
62 votes
13 answers
9k views

How do you approach your child's math education? [closed]

My son is one year old, so it is perhaps a bit too early to worry about his mathematical education, but I do. I would like to hear from mathematicians that have older children: What do you wish you'd ...
16 votes
5 answers
3k views

Why is a topology made up of 'open' sets? Part II [closed]

Because the display was getting quite cluttered, I thought I'd post a second part to this question separately. I hope the Gods of Math Overflow don't take too much offense. I'll go now into some ...
3 votes
2 answers
1k views

How should I find a tutor for math-overflow level mathematics? [closed]

Searching for maths tutors online finds people willing to teach up to A-level. I'm looking for help at a more advanced level. At the moment I'm trying to teach myself category theory from downloaded ...
Paul Crowley's user avatar
36 votes
7 answers
2k views

Informal online seminars or reading groups via videoconferencing?

Does the following exist, and if not, does anyone besides me wish it did? A web site where a mathematician (say) could find other mathematicians who want to study the same book or paper, and arrange ...
325 votes
34 answers
92k views

Why is a topology made up of 'open' sets? [closed]

I'm ashamed to admit it, but I don't think I've ever been able to genuinely motivate the definition of a topological space in an undergraduate course. Clearly, the definition distills the essence of ...
22 votes
9 answers
2k views

How do you motivate a precise definition to a student without much proof experience?

When introducing students to highly technical definitions for seemingly intuitive concepts (e.g., homotopy, continuity), how do you motivate the necessity of the definition? On the one hand, you ...
50 votes
4 answers
4k views

What algorithm in algebraic geometry should I work on implementing?

This summer my wife and one of my friends (who are both programmers and undergraduate math majors, but have not learned any algebraic geometry) want to learn some algebraic geometry from me, and I ...
2 votes
1 answer
889 views

Text/structure for an analysis course for students with pre-existing understanding of some applied aspects of analysis

Greetings, I'm teaching a one-off course (perhaps never to be repeated) in a curriculum that's in transition, and I'm looking for advice on a textbook, or stories from people who have taught similar ...
9 votes
4 answers
4k views

How to teach introductory statistic course to students with little math background?

Next semester I will teach an elementary statistic course for the first time (which I am actually quite excited about). A brief description can be found here. I am told to expect very little math ...
Hailong Dao's user avatar
  • 30.3k
6 votes
7 answers
5k views

Best way to teach concept of real numbers using a hands-on activity?

I know a middle school math teacher looking for some suggestions for hands-on activities to teach the concept of real numbers. I'm new to this site, so this may be a little off topic.
mshafrir's user avatar
  • 163
12 votes
1 answer
755 views

Teaching Methods and Evaluating them

Hey, As a lowly graduate student, I'm on a committee (I'm not sure how important my role really is) trying to evaluate how effective different approaches teaching undergraduates. We are looking at ...
202 votes
72 answers
49k views

What are your favorite instructional counterexamples?

Related: question #879, Most interesting mathematics mistake. But the intent of this question is more pedagogical. In many branches of mathematics, it seems to me that a good counterexample can be ...
8 votes
3 answers
3k views

Specializing early

Topic: this is a mathematics education question (but applies to other sciences too). Assumptions: my first assumption is that most mathematical concepts used in research are not intrinsically more ...
6 votes
6 answers
7k views

Interesting applications of max-flow and linear programming

Max-flow and linear programming are two big hammers in algorithm design: each are expressive enough to represent many poly-time solvable problems. Some problems are obvious applications of max-flow: ...
16 votes
13 answers
4k views

Do you find your students are less competent in basic algebra and arithmetic, and, if so, do you believe that this is due to overuse of calculators at an early level? [closed]

So first I gave my class the quiz problem: Compute $$\lim_{h\rightarrow 0} \frac{\frac{1}{3+h} - \frac{1}{3}}{h}.$$ Upon finding that they could not do that (no real surprize) I asked them to compute $...
5 votes
0 answers
651 views

Probability in Math Education [closed]

Why is probability an under-emphasized subject in most math programs? Why does it seem that the hot topics these days are category theory and algebra? What do you think about the following: A student ...
Rob Doty's user avatar
19 votes
10 answers
6k views

Research Experience for Undergraduates: Summer Programs

Some time ago, I found this list of REU programs held in 2009. The main aspects that characterize such programs are: (a) a great deal of lectures on specific topics; and, admittedly more importantly,...
163 votes
28 answers
54k views

Cool problems to impress students with group theory [closed]

Since this forum is densely populated with algebraists, I think I'll ask it here. I'm teaching intermediate level algebra this semester and I'd like to entertain my students with some clever ...
59 votes
34 answers
13k views

Are there any books that take a 'theorems as problems' approach?

Are there any books that present theorems as problems? To be more specific, a book on elementary group theory might have written: "Theorem: Each group has exactly one identity" and then show a proof ...
9 votes
4 answers
9k views

Applications of Euler-Cauchy ODEs

The Euler-Cauchy ODE (2nd order, homogeneous version) is: $$ x^2 y'' + a x y' + b y = 0 $$ Looking in various books on ODEs and a random walk on a web search (i.e. I didn't click on every link, but ...
Andrew Stacey's user avatar
12 votes
2 answers
2k views

Teaching and students

Sometimes I get stumped by students' questions in my classes I teach. I am an algebraist by training and have just started teaching. Sometimes I have to teach analysis courses. My question is: Is it ...
Rachel J's user avatar
  • 129