2
votes
3answers
640 views

Assessing effectiveness of (epsilon, delta) definitions [closed]

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in calculus and the student reception of them. The ...
-6
votes
1answer
534 views

V.I. Arnold's high school problem [closed]

According to his interview to the Notices of the AMS, when Vladimir I. Arnold was 12 years old (in 1949) his teacher I.V. Morozkin, gave to his classroom (apparently 6th grade of a soviet primary ...
39
votes
18answers
5k views

How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented 11 years old student and I don't know how I can help him. For ...
38
votes
7answers
4k views

How do you not forget old math?

I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a ...
18
votes
2answers
1k views

Papers better than books?

Not so long ago I took a class called "Discrete analysis". I remember that I couldn't find any "novice" level material on Mobius functions in combinatorics. So then I went to the roots and read Rota's ...
8
votes
7answers
1k views

Review papers in mathematics

Are there review papers, literature reviews in mathematics that describe the recent developments in various fields for a newcomer? Or is the prerequisite knowledge always provided in research ...
2
votes
4answers
955 views

When did you “meet Polya”? [closed]

I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and ...
5
votes
5answers
2k views

What does a mathematician expect from mathematics education? [closed]

Consider that my question is not a personal and/or subjective question. Perhaps, you have hired a mathematics educator in your department and you are interested in finding a way to communicate with ...
8
votes
1answer
684 views

Topology, the board game

Edit: I am reposting this question fom math.stackexchange.com; there may be some professors here who have more experience teaching topology. This is a math education question that I've been thinking ...
5
votes
2answers
651 views

Faculty Handbook: Mentoring Undergraduates in Research and Scholarship

A few days ago I was asked by the director of the Center for Undergraduate Research and Scholarship at Georgia Regents University (formerly known as MCG and Augusta State) to contribute an article for ...
3
votes
1answer
618 views

Math major at 36 [closed]

I decided to go for math at 36. Is this idea possible? I studied literature, political science and international relations and still I am not really sure what I am doing. Since I was kid, I was not ...
19
votes
10answers
2k views

Learning through guided discovery

I have been working through Kenneth P. Bogart's "Combinatorics Through Guided Discovery". You can download it from this page: http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/ I've ...
5
votes
3answers
1k views

Battle of the brains; cultural mathematics

Firstly, I apologize if my question is long. Three years ago, I watched a video with the name Battle of the Brains. It was a wonderful video about challenging some famous peoples to solve some ...
6
votes
2answers
1k views

Advice on doing physics under the umbrella of mathematics and the converse

Note: This is a question directly copied from Theoretical Physics SE primarily to get the advice of people indulged in mathematics. In the current scenario of research in QFT and string theory (and ...
12
votes
17answers
2k views

Short Course Suggestions For High School Students

I am planning to teach a course for talented high school students at a summer camp and I need suggestions for possible topics. The students usually have different backgrounds but most of them are ...
40
votes
14answers
4k views

How to write popular mathematics well?

Recently, some classmates and I were lamenting the fact that our classmates in other disciplines had almost no conception of what we did, despite the large mathematics population at Waterloo. Instead ...
3
votes
2answers
922 views

Is beauty at the high school level even possible? [closed]

This question is a follow up to 74841, and follows from a suggestion by Gian-Carlo Rota that beauty as judged by the educated public differs from that experienced by mathematicians (he gives Euclidean ...
40
votes
44answers
13k views

An example of a beautiful proof that would be accessible at the high school level?

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about ...
35
votes
8answers
4k views

Possibility of an Elementary Differential Geometry Course

I have to admit I'm not sure if this is an appropriate question. It's related to research in math education, but not directly to math. I've found that in talking to professional physicists and ...
192
votes
72answers
77k views

Video lectures of mathematics courses available online for free

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some ...
6
votes
8answers
3k views

Graduate School

How does one apply to graduate school when he has been working for sometime? I am interested in pursuing a PhD in math and making a career switch. Would my work experience benefit my application (I am ...
30
votes
12answers
8k views

Teaching undergraduate students to write proofs

In my experience, there are roughly two approaches to teaching (North American) undergraduates to write proofs: Students see proofs in lecture and in the textbooks, and proofs are explained when ...
55
votes
6answers
2k views

Good ways to engage in mathematics outreach?

Greetings all, I have often heard that it would be good if we as a community did more in the way of mathematics outreach: more to explain what it is we do to the community at large, more to expose ...
1
vote
1answer
862 views

Best examples of physics providing insight into math [duplicate]

Possible Duplicates: Examples where physical heuristics led to incorrect answers? Examples of using physical intuition to solve math problems V. I. Arnold argues ...
76
votes
26answers
10k views

How To Present Mathematics To Non-Mathematicians?

(Added an epilogue) I started a job as a TA, and it requires me to take a five sessions workshop about better teaching in which we have to present a 10 minutes lecture (micro-teaching). In the last ...
9
votes
4answers
2k views

A learning roadmap for Additive combinatorics.

Hello, I'd love to learn more about the field of additive combinatorics. From what I've understand, there's a book by Tao and Vu out on the subject, and it looks fun, but I think I lack the ...
0
votes
5answers
1k views

If you could redesign a high school mathematics curriculum from the ground up, what would you include? [closed]

Let's assume that we also get to redesign our high school mathematics teachers as well, in the sense that we can assume that they know and can teach whatever material we choose to cover. This is ...
17
votes
16answers
4k views

Journals for undergraduates

Are there math journals that are aimed for undergraduates? I don't mean here journals where students can publish their papers, but journals that publish introductory articles that an undergraduate can ...
20
votes
1answer
1k views

Community experiences writing Lamport's structured proofs

About two years ago, I came across this paper by Lamport http://research.microsoft.com/en-us/um/people/lamport/pubs/lamport-how-to-write.pdf on writing proofs hierarchically. It changed how I wrote ...
5
votes
3answers
1k views

Graphical representation of mathematical structures (in the spirit of unified modeling language)

In software engineering the unified modeling language ("UML") is a well established technique for providing overview of complex systems and an efficient means of communicating about them. There are ...
4
votes
2answers
1k views

How to study a math text [closed]

Hello, recently I've been trying various attempts regarding how to approach a math book to learn in the best way. Should one memorize the theorems and proofs so that one can recite them? I tend to ...
9
votes
4answers
1k views

Problem suggestions for polymath for undergraduates research

I'm inspired by the polymath project. It might be great for few undergraduates to work together on a research topic. What are some research problems with the following properties(Experimental ...
2
votes
5answers
2k views

Learning Roadmap for Software Engineer

Hi, I did some browsing around here on MathOverflow, but I feel that my question is different enough from others that it warrants its own question. Background: I'm a computer science major, with a ...
6
votes
4answers
1k 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 ...
15
votes
9answers
3k 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 ...
23
votes
7answers
4k 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
4answers
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 ...
23
votes
14answers
3k views

Making sure that you have comprehended a concept

Hi, 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 ...
32
votes
12answers
7k 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 ...
3
votes
2answers
2k views

Which area of mathematics is the hardest to learn ? [closed]

I was asked this question by a friend's daughter a few days back, and I was interested to see what people here think. I realize of course that this is quite subjective, but still, I get the impression ...
18
votes
4answers
3k 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 ...
11
votes
5answers
10k 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 ...
5
votes
1answer
2k views

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

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 ...
44
votes
13answers
5k 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 ...
3
votes
2answers
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 ...
4
votes
6answers
3k 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: ...
14
votes
5answers
4k views

How seriously do professors take teaching evaluations?

Do they ever know who writes them? How seriously do departments take teaching evaluations? If a professor knows which student wrote a particular evaluation....would they be biased (e.g. be nicer, ...
6
votes
1answer
1k views

In studying maths, do you tend to go through books one at a time? [closed]

Or do you read a lot of books on the same subject (say Topology)? Consider these two cases: Case 1: Suppose you want to study point set topology. You pick up a good book and work thoroughly on it. ...
24
votes
20answers
6k views

Nontrivial question about fibonacci numbers?

I'm looking for a nontrivial, but not super difficult question concerning Fibonacci numbers. It should be at a level suitable for an undergraduate course. Here is a (not so good) example of the sort ...
14
votes
12answers
5k views

How seriously should a graduate student take teaching evaluations?

Pretty much the question in the title. If a grad student gets bad reviews as a TA, how much does that hurt them later? How much do good reviews help? What if the situation is more complex? (For ...