most recent 30 from http://mathoverflow.net 2013-05-19T08:22:23Z http://mathoverflow.net/feeds/user/817 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/761/undergraduate-level-math-books/9445#9445 Adrian Petrescu 2009-12-20T22:39:55Z 2011-05-10T23:02:38Z

<p>I liked <a href="http://books.google.ca/books?id=bj1kOY8gOfcC&amp;dq=elements+of+abstract+algebra&amp;printsec=frontcover&amp;source=bl&amp;ots=sMDMivxMQ6&amp;sig=5XAar4HPSaqw0XRPBwt0Om4ibhA&amp;hl=en&amp;ei=SKcuS4fEJsbilAePleCkBw&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=1&amp;ved=0CAoQ6AEwAA#v=onepage&amp;q=&amp;f=false" rel="nofollow">Elements of Abstract Algebra</a> by Allan Clark, which is mainly a problem book with a moderate amount of exposition, but the problems are so well-chosen that a diligent undergraduate student working through all of them will come out with a solid knowledge of group theory, classical ring theory, and Galois theory.</p>

http://mathoverflow.net/questions/31879/are-there-other-nice-math-books-close-to-the-style-of-tristan-needham/32211#32211 Adrian Petrescu 2010-07-16T17:53:24Z 2010-07-16T17:53:24Z

<p>It's not exactly as visual as <em>Visual Complex Analysis</em>, but Michael Spivak's <a href="http://www.amazon.com/Comprehensive-Introduction-Differential-Geometry-Vol/dp/0914098705/ref=pd_sim_b_1" rel="nofollow">A Comprehensive Introduction to Differential Geometry</a> has a lot of the same appeal to intuition and conversational style. (Well, I've only read Volume 1, there's a total of 5, but if they're anything like other Spivak books I've read, this holds true of them as well).</p> <hr> <p><img src="http://ec1.images-amazon.com/images/G/01/ciu/0b/84/b820d250fca05ed75ca26010.L.jpg" alt="Cover of Volume 1"></p>

http://mathoverflow.net/questions/14574/your-favorite-surprising-connections-in-mathematics/14617#14617 Adrian Petrescu 2010-02-08T07:09:07Z 2010-02-16T23:55:09Z

<p>This is probably not the most serious of applications, but I found the equivalence (in game theory) of the determinacy of Nash's board game Hex with the Brouwer Fixed Point theorem to be a surprising, if somewhat lighthearted, connection.</p> <p>You can read <a href="http://www.jstor.org/pss/2320146" rel="nofollow">David Gale's paper</a>.</p>

http://mathoverflow.net/questions/9218/probabilistic-proofs-of-analytic-facts/9252#9252 Adrian Petrescu 2009-12-18T07:40:32Z 2009-12-18T07:40:32Z

<p><a href="http://www.jstor.org/pss/2318544" rel="nofollow">This paper</a> (Prime Numbers and Brownian Motion, by Patrick Billingsley) is perhaps more about proving number theoretic facts than analytical, but at least to me they have a very analytical flavor anyway, and was the first thing to come into my mind when I read your question. I think you would find it interesting.</p>

http://mathoverflow.net/questions/5145/completeness-under-uniform-continuity Adrian Petrescu 2009-11-12T03:28:59Z 2009-11-12T03:28:59Z

<p>We say that a metric space where every convergent sequence converges to something in the space is called "complete" and has useful properties, but is there a specific name for spaces which fail to be complete, but have at least the condition that every <strong>uniformly</strong> convergent sequence converges to something in the space?</p> <p>Like, for instance, the metric space of polynomials over R is not complete as far as I know, but if you restrict yourself to uniformly convergent sequences, then you always get a polynomial. Is there a name for that, or are these types of spaces just not that interesting?</p>

http://mathoverflow.net/questions/7330/which-math-paper-maximizes-the-ratio-importance-length/7891#7891 Adrian Petrescu 2011-10-30T05:25:01Z 2011-10-30T05:25:01Z

Link: <a href="http://courses.engr.illinois.edu/ece586/TB/Nash-NAS-1950.pdf" rel="nofollow">courses.engr.illinois.edu/ece586/TB/&hellip;</a>

http://mathoverflow.net/questions/48477/never-appeared-forthcoming-papers/48533#48533 Adrian Petrescu 2010-12-07T06:24:25Z 2010-12-07T06:24:25Z

According to Knuth, 4A was completed and sent to the printer today (December 6th, 2010)

http://mathoverflow.net/questions/20430/is-there-an-explicit-example-of-a-complex-number-which-is-not-a-period/20435#20435 Adrian Petrescu 2010-09-08T06:50:29Z 2010-09-08T06:50:29Z

From the abstract: &quot;In particular we prove that periods can be effectively approximated by elementary rational Cauchy sequences. As an application, we exhibit a computable real number which is not a period.&quot; So it definitely does have other importance; it probably just pops out a construction of a non-period as an easy corollary or something.

http://mathoverflow.net/questions/35677/binary-decimal-expansion-of-algebraic-numbers Adrian Petrescu 2010-08-15T18:24:02Z 2010-08-15T18:24:02Z

Depending on the answers you get, this may turn out to be MO-suitable. In case it's not, however, the other &quot;better&quot; math forum for it would be <a href="http://math.stackexchange.com/" rel="nofollow">math.stackexchange.com</a>.

http://mathoverflow.net/questions/33402/how-to-test-if-the-difference-between-probabilities-is-statistically-significant Adrian Petrescu 2010-07-26T14:46:18Z 2010-07-26T14:46:18Z

In about 4 hours, a new Stack Exchange site focusing on statistics will become public: <a href="http://stats.stackexchange.com/" rel="nofollow">stats.stackexchange.com</a> I think your question will be better-suited there.

http://mathoverflow.net/questions/30511/ebook-readers-for-mathematics/30520#30520 Adrian Petrescu 2010-07-04T17:44:57Z 2010-07-04T17:44:57Z

It should also be mentioned that the latest software update for the Kindle, 2.5.3, now allows zooming of PDFs, which makes it even more useful especially for PDFs that have two pages scanned per the same image. I use it for reading textbooks and papers all the time and it is a very comfortable experience.

http://mathoverflow.net/questions/5145/completeness-under-uniform-continuity Adrian Petrescu 2009-11-12T03:38:06Z 2009-11-12T03:38:06Z

I could be misunderstanding, but I'm not saying that the polynomials themselves are uniformly convergent, rather that the SEQUENCE of polynomials converges uniformly (to another polynomial) under the usual metric. Does this clear it up?