Tagged Questions
11
votes
3answers
99 views
Are there interesting rings without unity?
There are several introductory textbooks which define a ring without any reference to a unity. However, nearly all of the rings one encounters in various branches of mathematics are endowed with a ...
5
votes
2answers
123 views
Analysis without algebra
I once heard someone say that analysis is $99 \%$ algebra. He was, of course, referring to the amount of algebraic manipulations in the exercises from any calculus course.
I know that in topology, ...
7
votes
1answer
99 views
what's the role of fiber bundles play in understanding the base space?
Suppose $\pi: E\to B$ be a fiber bundle, and assume $B$ is connected, I want to know:
1, What do the fiber bundles (e.g., the covering spaces) on $B$ help understand the topology, or the structure on ...
8
votes
2answers
148 views
What was Klein working on when he “replaces his Riemann surface by a metallic surface”?
I am reading The Value of Science by Poincare, and the following paragraph from Chapter I seems rather interesting:
Look at Professor Klein: he is studying one of the most abstract questions of ...
4
votes
4answers
189 views
Examples of partial functions outside recursive function theory?
My math background is very narrow. I've mostly read logic, recursive function theory, and set theory.
In recursive function theory one studies partial functions on the set of natural numbers.
Are ...
25
votes
17answers
3k views
Examples of mathematical induction
What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ ...
1
vote
1answer
156 views
Reference: Compendium of interesting graphs
I've been writing a little about some results on graph theory, and I want some nice examples of applying the results to some interesting finite connected graphs to show how the results might be ...
27
votes
5answers
1k views
False beliefs about Lebesgue measure on $\mathbb{R}$
I'm trying to develop intuition about Lebesgue measure on $\mathbb{R}$ and I'd like to build a list of false beliefs about it, for example: every set is measurable, every set of measure zero is ...
16
votes
3answers
672 views
Examples of math contest problems that can be solved in a 'cheap' way?
What are some examples of math contest problems that can be solved by using a nonrigorous, 'cheap' shortcut?
For instance, a problem on the 2011 AMC went:
A raft and a motorboat left dock A and ...
4
votes
0answers
181 views
Interesting applications of the cofinite topology?
Background: I'm doing some expository writing on intuitionistic logic and I have been toying with the idea of demonstrating its applicability via models where the denotations are taken from a Heyting ...
7
votes
1answer
238 views
When can we say that a theorem has been proven?
I'm taking a Data Structures and Algorithms course for a CS program. The introductory material was all mathematics, mostly a series of formulas that we are to remember. I can work through the formulas ...
115
votes
28answers
8k views
A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language
The following is a quote from Surely you're joking, Mr. Feynman . The question is: are there any interesting theorems that you think would be a good example to tell Richard Feynman, as an answer to ...
