most recent 30 from http://mathoverflow.net 2013-05-22T14:20:59Z http://mathoverflow.net/feeds/user/3161 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54430/video-lectures-of-mathematics-courses-available-online-for-free/61030#61030 Alexander Noll 2011-04-08T06:50:43Z 2013-01-08T08:28:08Z

<p><a href="http://qgm.au.dk/video/mc/wall-crossing/" rel="nofollow">Master Class on Wall-Crossing</a>. Lectures given by Maxim Kontsevich.</p>

http://mathoverflow.net/questions/54430/video-lectures-of-mathematics-courses-available-online-for-free/54504#54504 Alexander Noll 2011-02-06T07:08:30Z 2011-02-06T07:08:30Z

<p>The entire master course at ICTP:</p> <p><a href="http://www.ictp.tv/diploma/index2.php?activityid=MTH" rel="nofollow">http://www.ictp.tv/diploma/index2.php?activityid=MTH</a></p>

http://mathoverflow.net/questions/40062/roadmap-for-mirror-symmetry/40192#40192 Alexander Noll 2010-09-27T18:41:20Z 2010-09-27T18:41:20Z

<p>The book <a href="http://books.google.com/books?id=4gvQYrOmRNAC&amp;printsec=frontcover&amp;dq=dirichlet+branes+and+mirror+symmetry&amp;hl=de&amp;ei=n-SgTMXjEsHJswaesP3mDg&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=1&amp;ved=0CCsQ6AEwAA#v=onepage&amp;q&amp;f=false" rel="nofollow">"Dirichlet Branes and Mirror Symmetry"</a> by Aspinwall et. al. seems to fit quite well with your request. It discusses SYZ, Homological Mirror Symmetry and its physical origin.</p>

http://mathoverflow.net/questions/29006/counterexamples-in-algebra/29051#29051 Alexander Noll 2010-06-22T06:29:02Z 2010-06-22T06:29:02Z

<p>In the category of rings, epimorphisms do not have to be surjective: $\mathbb{Z}\hookrightarrow \mathbb{Q}$.</p>

http://mathoverflow.net/questions/23213/does-category-theory-help-understanding-abstract-algebra/23232#23232 Alexander Noll 2010-05-02T05:45:39Z 2010-05-02T05:45:39Z

<p>There is the book <a href="http://books.google.com/books?id=deWkZWYbyHQC&amp;printsec=frontcover&amp;dq=aluffi&amp;hl=de&amp;cd=2#v=onepage&amp;q&amp;f=false" rel="nofollow">Algebra: Chapter 0</a> by Paolo Aluffi that might fit your needs. It is a textbook on algebra (as the title says), but it uses the language of category theory from the beginning. Category theory is mostly used to motivate definitions using universality properties.</p> <p>It is only in the last two chapters that the author introduces more advanced concepts from category theory (functors, abelian categories, etc.).</p>

http://mathoverflow.net/questions/3134/whats-your-favorite-equation-formula-identity-or-inequality/11782#11782 Alexander Noll 2010-01-14T21:52:09Z 2010-01-14T21:52:09Z

<p>$ D_A\star F = 0 $</p> <p>Yang-Mills</p>

http://mathoverflow.net/questions/359/a-reading-list-for-topological-quantum-field-theory/11745#11745 Alexander Noll 2010-01-14T10:20:42Z 2010-01-14T10:20:42Z

<p>There is a new book available, <a href="http://www.amazon.com/Dirichlet-Branes-Symmetry-Mathematics-Monographs/dp/0821838482/ref=sr%5F1%5F1?ie=UTF8&amp;s=books&amp;qid=1263464016&amp;sr=8-1" rel="nofollow">Dirichlet Branes and Mirror Symmetry</a>, written by both mathematicians and physicists. It contains a chapter on TQFT written by Moore and Segal which is based on <a href="http://arxiv.org/abs/hep-th/0609042" rel="nofollow">this paper</a>. This book is supposed to be written such that mathematicians are able to understand it, and I think that the authors achieved this goal.</p>

http://mathoverflow.net/questions/11427/looking-for-reference-on-gauge-fields-as-connections/11431#11431 Alexander Noll 2010-01-11T13:39:45Z 2010-01-12T09:48:06Z

<p>The books that I liked by far the most are the two volumes on <a href="http://www.amazon.com/Topology-Geometry-Gauge-fields-Foundations/dp/0387949461/ref=sr%5F1%5F1?ie=UTF8&amp;s=books&amp;qid=1263216770&amp;sr=8-1" rel="nofollow">Topology, Geometry and Gauge Field</a>s by Gregory Naber. It has a very nice introductory chapter which tells you why one should care about connection and then starts topology from the scratch. The second book ends with a short introduction to Seiberg-Witten gauge theory (to be found on <a href="http://www.pages.drexel.edu/~gln22/" rel="nofollow">his homepage</a>, "Introduction to Donaldson and Seiberg-Witten Theories").</p> <p>I also enjoyed John Morgan's lectures on Gauge theory in the book "Gauge theory and topology of four-manifolds".</p>

http://mathoverflow.net/questions/23213/does-category-theory-help-understanding-abstract-algebra/23232#23232 Alexander Noll 2010-05-02T11:52:25Z 2010-05-02T11:52:25Z

If you mentioned it already, I'm sorry. I cannot find a reference to the book in your answer, however. The text is designed for graduate students, but I think that it is readable for undergraduates as well. I used this book to learn abstract algebra for the first time, and at least for me it worked.

http://mathoverflow.net/questions/11427/looking-for-reference-on-gauge-fields-as-connections/11431#11431 Alexander Noll 2010-01-12T09:48:41Z 2010-01-12T09:48:41Z

Sorry, again. The link directly to the pdf does not seem to work.

http://mathoverflow.net/questions/11427/looking-for-reference-on-gauge-fields-as-connections/11431#11431 Alexander Noll 2010-01-11T17:26:19Z 2010-01-11T17:26:19Z

Sorry for the unclarity: Not the book is available on his homepage, only the appendix to Seiberg-Witten Gauge theory.