All Questions
495 questions
14
votes
11
answers
35k
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
...
1
vote
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 ...
30
votes
15
answers
5k
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 ...
13
votes
7
answers
35k
views
Real analysis has no applications?
I'm teaching an undergrad course in real analysis this Fall and we are using the text "Real Mathematical Analysis" by Charles Pugh. On the back it states that real analysis involves no "applications ...
24
votes
15
answers
5k
views
Applications of connectedness
In an «advanced calculus» course, I am talking tomorrow about connectedness (in the context of metric spaces, including notably the real line).
What are nice examples of applications of the idea of ...
154
votes
7
answers
85k
views
Where to buy premium white chalk in the U.S., like they have at RIMS? [closed]
While not a research-level math question, I'm sure this is a question of interest to many research-level mathematicians, whose expertise I seek.
At RIMS (in Kyoto) in 2005, they had the best white ...
8
votes
3
answers
2k
views
The harmonic (series) beetle: live illustrations of mathematical theorems
In my analysis class I use the following problem to illustrate the divergence
of the harmonic series (consider this as a hint for solving it).
Exercise.
A beetle creeps along a 1-meter infinitely ...
12
votes
5
answers
2k
views
Introducing Cryptology to Undergraduates
This summer I am going to give some lectures to some REU students. I am still tossing around ideas for what I am going to talk about, but one thing I would at least like to give one or two lectures on,...
- 4,842
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 ...
14
votes
1
answer
3k
views
An elementary proof that the degree of a map of spheres determines its homotopy type
I'm helping to teach an undergraduate algebraic topology course (out of Hatcher's textbook). We have recently defined the degree of a map of spheres using homology, and the professor and I thought it ...
- 7,338
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
13k
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 ...
12
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. ...
4
votes
2
answers
750
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 ...
5
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 ...
- 61
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.
...
13
votes
11
answers
5k
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 ...
- 16k
1072
votes
296
answers
351k
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 ...
21
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 ...
- 12.1k
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.
- 71
74
votes
21
answers
25k
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 ...
- 21k
7
votes
3
answers
3k
views
The etale fundamental group of a field
Background and motivation:
I am teaching the "covering space" section in an introductory algebraic topology course. I thought that, in the last five minutes of my last lecture, I might briefly sketch ...
- 7,338
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 ...
42
votes
13
answers
20k
views
How to draw knots with LaTeX?
I am writing an exam for my students, and the topic is intro knots theory. I have no idea how to put knots into the file, but I know many MO users who can draw amazing diagrams in their papers.
Can ...
- 30.5k
21
votes
7
answers
3k
views
What should be taught in a 1st course on Riemann Surfaces?
I am teaching a topics course on Riemann Surfaces/Algebraic Curves next term. The course is aimed at 1st and 2nd year US graduate students who have have taken basic coursework in algebra and manifold ...
- 3,284
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 ...
14
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 ...
16
votes
9
answers
4k
views
How to motivate the skein relations?
I am teaching an advanced undergraduate class on topology. We are doing introductory knot theory at the moment. One of my students asked how do we know to use this skein relation to compute all these ...
- 30.5k
57
votes
11
answers
13k
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 ...
- 1,042
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 ...
- 1,042
61
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 ...
15
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 ...
2
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 ...
- 150
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 ...
333
votes
34
answers
96k
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 ...
40
votes
16
answers
11k
views
"Homotopy-first" courses in algebraic topology
A first course in algebraic topology, at least the ones I'm familiar with, generally gets students to a point where they can calculate homology right away. Building the theory behind it is generally ...
21
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
897
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 ...
8
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 ...
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.
- 163
12
votes
1
answer
775
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 ...
2
votes
4
answers
6k
views
Undergraduate Derivation of Fundamental Solution to Heat Equation
It is well known that the 1-dimensional heat equation $$\frac{\partial}{\partial t} u(x,t)=a\cdot\frac{\partial^2}{\partial x^2} {u(x,t)}$$ has the fundamental solution $$K(x,t)=\frac{1}{\sqrt{4\pi a ...
- 5,935
208
votes
72
answers
51k
views
What are your favorite instructional counterexamples?
Related: question #879, Most interesting mathematics mistake. But the intent of this question is more pedagogical.
In many branches of mathematics, it seems to me that a good counterexample can be ...
7
votes
3
answers
3k
views
Specializing early
Topic: this is a mathematics education question (but applies to other sciences too).
Assumptions: my first assumption is that most mathematical concepts used in research are not intrinsically more ...
51
votes
6
answers
5k
views
What does it take to run a good learning seminar?
I'm thinking about running a graduate student seminar in the summer. Having both organized and participated in such seminars in the past, I have witnessed first-hand that, contrary to what one might ...
6
votes
6
answers
7k
views
Interesting applications of max-flow and linear programming
Max-flow and linear programming are two big hammers in algorithm design: each are expressive enough to represent many poly-time solvable problems. Some problems are obvious applications of max-flow: ...
16
votes
13
answers
4k
views
Do you find your students are less competent in basic algebra and arithmetic, and, if so, do you believe that this is due to overuse of calculators at an early level? [closed]
So first I gave my class the quiz problem: Compute $$\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 $...
4
votes
0
answers
652
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 ...
- 65
18
votes
12
answers
10k
views
Looking for an introductory textbook on algebraic geometry for an undergraduate lecture course
I am now supposed to organize a tiny lecture course on algebraic geometry for undergraduate students who have an interest in this subject.
I wonder whether there are some basic algebraic geometry ...