User michael wan - MathOverflow

Answer by Michael Wan for Reference book for commutative algebra

2011-01-23T08:15:13Z

There is a new (released December 2010) Springer GTM by Kemper, which looks like it might fit the bill. I haven't read it, but I'd be interested to hear from someone who did.

References regarding a connection between recursion theory and sheaves

2010-05-19T22:08:28Z

In Manin's A Course in Mathematical Logic for Mathematicians, he defines (p.201) a structure $(\mathcal{E},R)$ given an enumerable set $E \subset (\mathbb{Z}^+)^n$ by:

$\mathcal{E}$ is the set of all enumerable subsets of $E$.
For each $E' \in \mathcal{E}$, $R(E')=\{f|domain(f)=E', f:E'\rightarrow (\mathbb{Z}^+) \text{ is recursive}\}.$

He then demonstrates (cumulating on p. 205-6) that there is an analogy between $(\mathcal{E},R)$ and (his quotes) "a topological space together with a sheaf", and a way to define "recursive Cech cohomology of groups" of some complexes that arise from $(\mathcal{E},R)$. He then claims that "it would be interesting to study such cohomology groups".

My question: is this a well known construction/analogy? Has it been studied further? Are there any relevant references?

Basic question about differential forms and physics.

2010-05-18T04:20:38Z

When, if ever, can we view a differential form, e.g. like $dx \wedge dy$, as the similar looking expression used in physics to represent the product of "infinitesimals" e.g. $dx$ $dy$? In particular, I'm wondering why differential forms are anti-symmetric, e.g. $dx \wedge dy=-dy \wedge dx$, whereas in physics we often are happy to write $dx$ $dy=dy$ $dx$. Am I misunderstanding something basic?

Answer by Michael Wan for Alternative Undergraduate Analysis Texts

2009-12-31T17:58:37Z

Charles Pugh's Real Mathematical Analysis covers a wide range, starting from real numbers, topology, and basic 1D calculus, and then moving into multivariable calculus, function spaces, and Lebesgue measure/integration, all in a compact 450 pages. The writing is clear and quirky, and there are lots of interesting and hard problems.

Answer by Michael Wan for Undergraduate Differential Geometry Texts

2009-12-05T06:18:56Z

There's a cheap Dover book by Kreyszig. It's old, and has the advantage/disadvantage of mentioning tensors (in index notation), connections, and many other things that Pressley leaves out completely.

Oh, and if this is for a course, the book has solutions to all of it's problems in the back.

Comment by Michael Wan

2010-05-19T04:05:24Z

Thanks for the reply. It is a bit over my head, but appropriate for the level of MO so I can't complain.

Comment by Michael Wan

2010-05-19T04:00:34Z

Thanks, this was clear and helpful.