User michael wan - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T08:03:40Z http://mathoverflow.net/feeds/user/2028 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16416/reference-book-for-commutative-algebra/52928#52928 Answer by Michael Wan for Reference book for commutative algebra Michael Wan 2011-01-23T08:15:13Z 2011-01-23T08:15:13Z <p>There is a new (released December 2010) Springer GTM by <a href="http://www.amazon.com/Course-Commutative-Algebra-Graduate-Mathematics/dp/3642035442" rel="nofollow">Kemper</a>, which looks like it might fit the bill. I haven't read it, but I'd be interested to hear from someone who did. </p> http://mathoverflow.net/questions/25287/references-regarding-a-connection-between-recursion-theory-and-sheaves References regarding a connection between recursion theory and sheaves Michael Wan 2010-05-19T22:08:28Z 2010-05-19T22:08:28Z <p>In Manin's <em><a href="http://books.google.com/books?id=8NTWRFD5lZ8C&amp;lpg=PR2&amp;dq=manin%2520logic&amp;pg=PR2#v=onepage&amp;q&amp;f=false" rel="nofollow">A Course in Mathematical Logic for Mathematicians</a></em>, he defines (p.201) a structure $(\mathcal{E},R)$ given an enumerable set $E \subset (\mathbb{Z}^+)^n$ by:</p> <ol> <li>$\mathcal{E}$ is the set of all enumerable subsets of $E$.</li> <li>For each $E' \in \mathcal{E}$, $R(E')=\{f|domain(f)=E', f:E'\rightarrow (\mathbb{Z}^+) \text{ is recursive}\}.$</li> </ol> <p>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". </p> <p>My question: is this a well known construction/analogy? Has it been studied further? Are there any relevant references? </p> http://mathoverflow.net/questions/25089/basic-question-about-differential-forms-and-physics Basic question about differential forms and physics. Michael Wan 2010-05-18T04:20:38Z 2010-05-18T14:30:54Z <p>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?</p> http://mathoverflow.net/questions/10282/alternative-undergraduate-analysis-texts/10298#10298 Answer by Michael Wan for Alternative Undergraduate Analysis Texts Michael Wan 2009-12-31T17:58:37Z 2009-12-31T17:58:37Z <p>Charles Pugh's <a href="http://www.amazon.com/Real-Mathematical-Analysis-Charles-Chapman/dp/0387952977/ref=sr%5F1%5F1?ie=UTF8&amp;s=books&amp;qid=1262281966&amp;sr=8-1" rel="nofollow">Real Mathematical Analysis</a> 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.</p> http://mathoverflow.net/questions/7834/undergraduate-differential-geometry-texts/7844#7844 Answer by Michael Wan for Undergraduate Differential Geometry Texts Michael Wan 2009-12-05T06:18:56Z 2009-12-05T06:18:56Z <p>There's a cheap Dover book by <a href="http://www.amazon.com/Differential-Geometry-Erwin-Kreyszig/dp/0486667219/ref=sr%5F1%5F1?ie=UTF8&amp;s=books&amp;qid=1259993562&amp;sr=8-1" rel="nofollow">Kreyszig</a>. It's old, and has the advantage/disadvantage of mentioning tensors (in index notation), connections, and many other things that Pressley leaves out completely. </p> <p>Oh, and if this is for a course, the book has solutions to all of it's problems in the back.</p> http://mathoverflow.net/questions/25089/basic-question-about-differential-forms-and-physics/25105#25105 Comment by Michael Wan Michael Wan 2010-05-19T04:05:24Z 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. http://mathoverflow.net/questions/25089/basic-question-about-differential-forms-and-physics/25098#25098 Comment by Michael Wan Michael Wan 2010-05-19T04:00:34Z 2010-05-19T04:00:34Z Thanks, this was clear and helpful.