All Questions
495 questions
14
votes
2
answers
7k
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What is the dual concept to "annihilator" called, and do any linear algebra textbooks discuss this concept first?
When introducing dual spaces for the first time, most linear algebra textbooks proceed in what seems to me a rather backwards fashion: the annihilator $\{f\in V^*: f(u)=0\quad \forall u\in U\}$ of a ...
- 491
19
votes
1
answer
2k
views
Resources for teaching arithmetic to calculus students
Every time we teach calculus we discover that a significant portion of our students never understood arithmetic. I don't mean that they can't multiply numbers, but rather that they don't know ...
- 12.1k
27
votes
5
answers
5k
views
Varieties as an introduction to algebraic geometry / How do professional algebraic geometers think about varieties
This really is two questions, but they are kind of related so I would like to ask them at the same time.
Question 1:
In a question asked by Amitesh Datta, BCnrd commented that it is important to ...
CommunityBot
- 1
6
votes
3
answers
4k
views
(How) should I take notes on a subject for self-study? [closed]
Suppose I am interested in really learning / thoroughly reviewing some subject (e.g. the basic theorems of infinite Galois theory, or the classification of compact Lie groups). One approach I might ...
8
votes
12
answers
13k
views
How do I explain the number e to a ten year old? [closed]
Hardly a research level question, but interesting nonetheless, I hope. Pi is easy, but not e. Where could I start?
- 271
10
votes
7
answers
2k
views
Proof that bases etc. exist in early linear algebra course?
I'm currently struggling to teach a 2nd course on linear algebra (in the UK, not at an Oxbridge quality university: the students have done a 1st course which concentrated upon algorithms you can apply ...
CommunityBot
- 1
6
votes
3
answers
1k
views
Publishing with Undergraduates
Is doing research with a student considered to be good for a dossier? Is it okay to have few research publications but a lot of student projects? I am finishing up a grad program and am looking at ...
- 41
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 ...
CommunityBot
- 1
3
votes
6
answers
2k
views
Teach a course in 1 month
I need to teach an intro course on number theory in 1 month. I was just notified. Since I have never studied it, what are good books to learn it quickly?
- 2,368
9
votes
4
answers
2k
views
Applications of Math: Theory vs. Practice
I have a problem: I learned about a lot of the applications of mathematics from academics. Neither they nor I have had much contact with the "real world" to go and see for ourselves how mathematics ...
CommunityBot
- 1
0
votes
1
answer
2k
views
Dual of Zorn's Lemma? [closed]
It seems to me that the dual of Zorn's Lemma should be true: if $S$ is a non-empty partially ordered set and every chain of $S$ has a lower bound in $S$, then $S$ has at least one minimal element.
...
- 39.8k
8
votes
2
answers
679
views
To what extent can algorithms in undergraduate linear algebra be made continuous/polynomial/etc.?
I feel like many of the algorithms that I learned — indeed, that I have taught — in undergraduate linear algebra classes depend sensitively on whether certain numbers are $0$. For example,...
CommunityBot
- 1
18
votes
17
answers
6k
views
What is your favorite isomorphism? [closed]
The other day I was trying to figure out how to explain why isomorphisms are important. I pulled Boyer's A History of Mathematics off the bookshelf and was surprised to find that isomorphism isn't ...
CommunityBot
- 1
5
votes
3
answers
2k
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 ...
CommunityBot
- 1
5
votes
2
answers
2k
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 ...
- 71
7
votes
2
answers
2k
views
Vinogradov's Elements of Number Theory
I can't be the only person here who has fond memories of the problems in Vinogradov's Elements of Number Theory. (For people who have not read it - the text itself is just a concise basic number ...
- 7,442
13
votes
2
answers
3k
views
The probabilistic method - reference to less challenging questions
I am teaching a course in combinatorics and large part of it is dedicated to the probabilistic method especially in the case of graphs. The course is an undergraduate level (almost none of the ...
- 502
2
votes
0
answers
1k
views
Good sources for linear algebra for convex optimization and graph analysis?
What are some good sources for linear algebra for convex optimization and graph analysis?
In Particular, is Gilbert Strang's MIT course suitable, or some other online course? I prefer online courses (...
- 2,383
0
votes
5
answers
2k
views
How to teach addition of negative numbers? [closed]
I have a friend with dyscalculia and was teaching her some some mathematics (namely, solving a linear equation, simplifying certain expressions, and what (affine linear) functions are).
She ...
- 1,882
3
votes
4
answers
2k
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 ...
- 12.6k
7
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 ...
- 2,855
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 ...
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?
- 39.9k
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 ...
CommunityBot
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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 ...
- 2,855
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 ...
- 2,590
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.
- 22.3k
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 ...
CommunityBot
- 1
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 ...
- 39.1k
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 ...
CommunityBot
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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 ...
- 1,180
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 ...
- 761
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 ...
- 50.6k
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.
- 45.7k
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 ...
- 6,734
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 ...
11
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 ...
CommunityBot
- 1
7
votes
2
answers
1k
views
Maximal Ellipsoid
John's Theorem can be stated as "To every compact, convex body, there is a unique inscribed ellipsoid, whose volume is maximal among all inscribed ellipsoids." It goes on to classify this maximal ...
- 31.5k
1
vote
2
answers
1k
views
An "Elementary" Math Question Generalized (Ring Theory Perhaps)
The following question is posed in the book "The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics"
"Prove that if integers a_1, ..., a_n are all distinct, then the ...
- 3,209
14
votes
1
answer
961
views
Founding of homological without quite involving derived categories
I am looking at the foundations of homological algebra, e.g. the introduction
of Ext and Tor, and am unsatisfied. The references I look at start with
"this is called a projective module, this is ...
CommunityBot
- 1
23
votes
4
answers
4k
views
Curriculum reform success stories at an "average" research university
Greetings all,
There's a never-ending story that many of us have sunk our teeth into. How do we go about teaching subjects like calculus and analysis "well?" Most universities that I'm familiar ...
- 403
8
votes
4
answers
2k
views
Choice of adviser
Not sure how to tag this one so feel free to edit and add tags.
When I initially started graduate school my choice for an area of study was quite nebulous. I had only figured out enough to know that ...
- 27.5k
2
votes
2
answers
6k
views
Examples of random variables
I'm looking for a list of examples of random variables to use in teaching a measure-theoretic probability course. For example, the Rademacher functions are an explicit construction of independent ...
- 11.4k
12
votes
3
answers
1k
views
Is formal proof (formalized mathematics) interesting to practicing mathematicians? To educators? [closed]
Formalizing mathematical proofs so that they can be checked for correctness and manipulated by computer is a recurrent proposal, most notably stated in the QED manifesto (1994). The December 2008 ...
- 12.3k
2
votes
0
answers
526
views
How much of math could be taught without using mathematical notation? [closed]
Given that mathematics is not about number, and that it is not even about the cryptic notation used to describe mathematical problems, how much of mathematics could be taught without reference to ...
