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seen Jun 23 at 16:11

Dec
30
comment Books to learn physics, being a math major
These are some of the most elegant books ever written on the subject of physics.
Dec
24
comment Prove the existence of a largest integer less than or equal to a rational number
I like this answer because it doesn't make use of the extra properties which $\mathbb{R}$ has. It seems preferable to me to avoid special properties of $\mathbb{R}$ to prove this fact which certainly remains true if we totally ignore the existence of $\mathbb{R}$.
Dec
17
asked An example of computing Ext
Dec
13
comment Please demonstrate decomposition of a torus into two cells
A blind calculation that gives you the number of cells you need: Take a cell decomposition of $S^1$ (one 0-cell and one 1-cell). Then the torus $S^1\times S^1$ has as cells the products of the cells of the two $S^1$ factors, so we get one 0-cell, two 1-cells, and one 2-cell.
Dec
13
answered What's Combinatorial Proof/Object/etc.?
Dec
11
revised Motivating Cohomology
added 4 characters in body; added 1 characters in body
Dec
11
revised Motivating Cohomology
added 92 characters in body; added 152 characters in body
Dec
11
comment Motivating Cohomology
"And you get so much information for free just by knowing that certain maps are ring homomorphisms rather than graded abelian group homomorphisms. I can't think of a good example off the top of my head, but I know there is one." One example might be that any diffeomorphism of $\mathbb{CP}^2$ preserves the orientation of that manifold. The cohomology ring is $\mathbb{Z}[u]/u^3$ and the top cohomology group is generated by $u^2$.
Dec
11
revised Motivating Cohomology
added 255 characters in body
Dec
11
answered Motivating Cohomology
Dec
11
comment Motivating Cohomology
By the way, are you looking for motivations of *co*homology specifically or just the entire gamut of homology, cohomology theories? Your title suggests the former, but in your question you mention "topology is fine until we get to homology," which seems to suggest the latter.
Dec
11
comment Motivating Cohomology
Bott and Tu's Differential Forms in Algebraic Topology provides a great introduction to de Rham cohomology, which I've always found intuitive and concrete.
Dec
10
accepted Homology and Euler characteristics of the classical Lie groups
Dec
8
comment Is there a general formula for solving 4th degree equations?
"However, if you allow special theta values (a new operation, not among the standard ones!) then yes, you can actually write down the solutions of arbitrary polynomials this way." Do you know of a reference which expands on this point?
Dec
6
accepted Examples of advanced results and ideas explained in a down-to-earth way
Dec
6
asked Homology and Euler characteristics of the classical Lie groups
Dec
4
comment Best Intermediate/Advanced Computer Science book
This question could be more appropriate here: cstheory.stackexchange.com
Dec
4
comment Examples of advanced results and ideas explained in a down-to-earth way
By accurate I mean more or less that false statements aren't made. Some popular treatments attain their accessible level by communicating half-truths. Again, Feynman's QED is a good example of what I mean: it doesn't cover the details, and it won't teach you how to do the calculations yourself, but it does communicate the ideas of the subject, it does explain some of its more striking applications, and it doesn't make false statements.
Dec
4
asked Examples of advanced results and ideas explained in a down-to-earth way
Dec
3
comment Is value of $\pi = 4$?
The downvote came from me. I added it soon after you posted your answer when there weren't any other answers to complement yours. My rationale was that, based on how I've seen other people (not here) attempt to answer this question, anything less than a completely rigorous demonstration would not suffice simply because almost any intuitive explanation seems plausible in this instance. I later tried to remove the downvote when I realized there were a variety of answers and that yours complemented the others nicely, but because an hour had elapsed I was not (and am not) able to do so.