Course notes: Difference between revisions

Latest revision as of 11:41, 4 October 2014

This page collects math notes I've taken, mostly course notes. I've also written some TeXnical notes and scripts.

I provide the source for most of my notes for a couple of reasons.

It feels good for some reason.
If you're curious about how to typeset something you've seen in these notes, you can download the source and have a look.
Somebody might download all my notes, correct the errors and unclear presentation, and then send them back to me. It's not likely, but it could happen.
If a bomb drops on my house and I lose all my stuff, maybe somebody can give me a copy of my notes.
The source is much faster to download and compile if you're on a slow connection.

Since I've learned about it, I've started using Subversion (svn) for everything. If you actually make corrections in any of the notes, I recommend doing it through svn. If you don't yet know how to use svn, I wrote an svn crash course just for you.

My notes	What?	Who?	When?	Additional Resources
pdf svn tgz	Geometric Invariant Theory	Vera Serganova	Fall 2009
pdf svn tgz	Homological Algebra	Peter Teichner	Spring 2008
pdf svn tgz	Deformation Theory Workshop, MSRI	Max Lieblich Martin Olsson Brian Osserman Ravi Vakil	Summer 2007	Other peoples' notes can be found here and here.
pdf svn tgz	Math 274, Stacks	Martin Olsson	Spring 2007
pdf tex	Math 215A, Algebraic Topology	Peter Teichner	Fall 2006
pdf tgz	Math 274, Commutative Rings	Tsit Yuen Lam	Fall 2006
pdf tgz	Math 261A, Lie Groups and Lie Algebras	Nicolai Reshetikhin Vera Serganova Richard Borcherds	Spring 2006
pdf tgz	Math 242, Symplectic Geometry	Alan Wienstein	Fall 2005
	Math 252, Representation Theory	Vera Serganova	Fall 2005	Vera Serganova's Representation Theorey notes William Crawley-Boevey's lectures on representations of quivers
pdf tgz	Math 256B, Algebraic Geometry	Paul Vojta	Spring 2005	Paul Vojta's handouts and solutions William Stein's notes and solutions Richard Borcherds's selected solutions Bryden Cais's notes and solutions Jinhyun Park's solutions Mark Haiman's Math 256AB page

I gave a couple of talks on toric varieties in a student seminar. If my notes make sense to you, you're welcome to use them.

My notes (pdf, tgz), made from Tony's notes, of Yonathan's prelim workshop on analysis.

One of my favorite facts about right adjoint functors is that they commute with limits.

Sestina's and primes, an easy problem Richard Dore and I worked out our first year in grad school, which I wrote up for some reason.

In 2007, I talked about the Salamander Lemma in MCF, and later blogged about it on the Secret Blogging Seminar. My reference was George Bergman's preprint, On diagram-chasing in double complexes (which wasn't yet on the arxiv at the time).

More moved notes

Aspects of Moduli:

Tom Bridgeland	Stability in triangulated categories	pdf
Kai Behrend	Foundations of Donaldson-Thomas theory	pdf
Alessio Corti	Foundations of Donaldson-Thomas theory	pdf
Valery Alexeev	Moduli of higher-dimensional varieties	pdf
Martin Olsson	Logarithmic structures with a view towards moduli	pdf
All in one (chronologically)	pdf tgz

Quantum Field Theory, my notes from

Nicolai Reshetikhin's course	pdf
Peter Teichner's course	pdf
Richard Borcherd's course	pdf
All in one (chronologically)	pdf tgz dir

For more QFT stuff, see Chris Schommer-Pries' QFT site for Fall 2007. (doesn't exist any more?)

For those who just want to get some notes, just download the pdf file. For those who want to look at the souce, download the tgz (tar-ed and gzip-ped) file, which has all the tex source in it. You'll find that the main file (QFT.tex) is quite boring. The actual lecture notes are in the other files and the top matter (like macro definitions) is in QFTPreamble.tex. As far as I know, the command \input{abcdefg} gives exactly the same result as pasting in the contents of the file abcdefg.tex (note that abcdefg.tex should be in the same directory as the main file).

If you have notes that I'm missing or if you have a correct/clear explanation for something which is incorrect/unclear, let me know (either tell me what you'd like to modify, give me some notes to go on, or update the tex yourself and send me a copy). Real (mathematical) errors should be fixed because it would be immoral to let them propagate (er ... that is, sit there), and typographical errors hardly take any time to fix, so you shouldn't be shy about telling me about them.

@@ Line 1: / Line 1: @@
 This page collects math notes I've taken, mostly course notes. I've also written some [[TeXnical notes]] and [[scripts]].
-[I'm currently moving content here from [http://math.berkeley.edu/~anton/index.php?m1=writings my old page]]
+I provide the source for most of my notes for a couple of reasons.
+#It feels good for some reason.
+#If you're curious about how to typeset something you've seen in these notes, you can download the source and have a look.
+#Somebody might download all my notes, correct the errors and unclear presentation, and then send them back to me. It's not likely, but it could happen.
+#If a bomb drops on my house and I lose all my stuff, maybe somebody can give me a copy of my notes.
+#The source is much faster to download and compile if you're on a slow connection.
+Since I've learned about it, I've started using [http://en.wikipedia.org/wiki/Subversion_(software) Subversion (svn)] for everything. If you actually make corrections in any of the notes, I recommend doing it through svn. If you don't yet know how to use svn, I wrote an [http://stacky.net/old-webpage/svnguide.html svn crash course] just for you.
 {| class="wikitable"
@@ Line 10: / Line 17: @@
 |When?
 |Additional Resources
+|-
+|[http://stacky.net/files/written/GIT/GIT.pdf pdf][svn://sheafy.net/courses/git_fa2009 svn][http://stacky.net/files/written/GIT/GITSource.tgz tgz]
+|Geometric Invariant Theory
+|[http://math.berkeley.edu/~serganov/ Vera Serganova]
+|Fall 2009
+|
 |-
 |[http://stacky.net/files/written/Halg/Halg.pdf pdf][svn://sheafy.net/courses/halg_sp2008 svn][http://stacky.net/files/written/Halg/HalgSource.tgz tgz]
-|[http://math.berkeley.edu/~teichner/Courses/253.html Homological Algebra]
+|Homological Algebra
 |[http://math.berkeley.edu/~teichner Peter Teichner]
 |Spring 2008
@@ Line 19: / Line 32: @@
 |[http://stacky.net/files/written/defthy07/defthy07.pdf pdf][svn://sheafy.net/defthy_su07 svn][http://stacky.net/files/written/defthy07/DefThySource.tgz tgz]
 |[http://www.msri.org/people/members/defthy07/ Deformation Theory Workshop, MSRI]
-|[http://www.math.princeton.edu/~lieblich/ Max Lieblich][http://math.berkeley.edu/%7Emolsson Martin Olsson][http://math.berkeley.edu/~osserman/ Brian Osserman] [http://math.stanford.edu/~vakil/ Ravi Vakil]
+|[http://www.math.princeton.edu/~lieblich/ Max Lieblich]<br>
+[http://math.berkeley.edu/%7Emolsson Martin Olsson]<br>
+[http://math.berkeley.edu/~osserman/ Brian Osserman]<br>
+[http://math.stanford.edu/~vakil/ Ravi Vakil]
 |Summer 2007
 |Other peoples' notes can be found [http://www.msri.org/people/members/defthy07/lectures.html here] and [http://math.stanford.edu/~vakil/defthy/ here].
@@ Line 30: / Line 46: @@
 |-
 |[http://stacky.net/files/written/AlgTopology/AlgebraicTopologyNotes.pdf pdf][http://stacky.net/files/written/AlgTopology/AlgebraicTopologyNotes.tex tex]
-|Math 215A, [http://math.berkeley.edu/%7Eteichner/Courses/215A.html Algebraic Topology]
+|Math 215A, Algebraic Topology
 |[http://math.berkeley.edu/%7Eteichner/ Peter Teichner]
 |Fall 2006
@@ Line 43: / Line 59: @@
 |[http://stacky.net/files/written/LieGroups/LieGroups.pdf pdf][http://stacky.net/files/written/LieGroups/LieGroupsSource.tgz tgz]
 |Math 261A, Lie Groups and Lie Algebras
-|[http://math.berkeley.edu/%7Ereshetik/ Nicolai Reshetikhin] [http://math.berkeley.edu/%7Eserganov/ Vera Serganova] [http://math.berkeley.edu/%7Ereb/ Richard Borcherds]
+|[http://math.berkeley.edu/%7Ereshetik/ Nicolai Reshetikhin]<br> [http://math.berkeley.edu/%7Eserganov/ Vera Serganova]<br> [http://math.berkeley.edu/%7Ereb/ Richard Borcherds]
 |Spring 2006
 |
@@ Line 61: / Line 77: @@
 [http://www.maths.leeds.ac.uk/%7Epmtwc/ William Crawley-Boevey]'s lectures on [http://www.maths.leeds.ac.uk/%7Epmtwc/quivlecs.pdf representations of quivers]
 |-
-|[http://stacky.net/files/written/AlgebraicGeometry/AlgebraicGeometryNotes.pdf pdf] [http://stacky.net/files/written/AlgebraicGeometry/AlgebraicGeometryNotes.tgz tgz]
+|[http://stacky.net/files/written/AlgebraicGeometry/AlgebraicGeometryNotes.pdf pdf] [http://stacky.net/files/written/AlgebraicGeometry/AlgebraicGeometrySource.tgz tgz]
 |Math 256B, Algebraic Geometry
 |[http://math.berkeley.edu/~vojta/ Paul Vojta]
 |Spring 2005
-|[http://math.berkeley.edu/%7Evojta/ Paul Vojta]'s [http://stacky.net/files/written/VojtaSolutions/ handouts and solutions]<br>
+|[http://math.berkeley.edu/%7Evojta/ Paul Vojta's] [http://stacky.net/files/written/VojtaSolutions/ handouts and solutions]<br>
+[http://modular.ucsd.edu/ William Stein's] [http://modular.ucsd.edu/AG.html notes and solutions]<br>
+[http://math.berkeley.edu/%7Ereb/ Richard Borcherds's] selected [http://math.berkeley.edu/%7Ereb/courses/alggeom/ solutions]<br>
+[http://math.arizona.edu/~cais/ Bryden Cais's] [http://math.arizona.edu/~cais/CourseNotes/AlgGeom04/ notes] and [http://math.arizona.edu/~cais/CourseNotes/AlgGeom04/Hartshorne_Solutions.pdf solutions]<br>
+[http://mathsci.kaist.ac.kr/~jinhyun/ Jinhyun Park's] [http://mathsci.kaist.ac.kr/~jinhyun/sol2/hart.html solutions]<br>
+[http://math.berkeley.edu/%7Emhaiman/index.html Mark Haiman]'s [http://math.berkeley.edu/%7Emhaiman/math256/index.html Math 256AB page]
+|}
-[http://www.maths.bath.ac.uk/%7Emapmlg/ Marco Lo Giudice]'s [http://www.maths.bath.ac.uk/%7Emapmlg/Documents/MyNotes.pdf notes]<br>
+I gave a couple of talks on toric varieties in a student seminar. If [http://stacky.net/files/written/toric.pdf my notes] make sense to you, you're welcome to use them.
-[http://modular.ucsd.edu/ William Stein]'s [http://modular.ucsd.edu/AG.html notes and solutions]<br>
+My notes ([http://stacky.net/files/written/AnalysisPrelim/AnalysisPrelim.pdf pdf], [http://stacky.net/files/written/AnalysisPrelim/AnalysisPrelim.tgz tgz])<span style="text-decoration: underline;"></span>, made from [http://math.rice.edu/~av15/ Tony's] notes, of Yonathan's prelim workshop on analysis.
-[http://math.berkeley.edu/%7Ereb/ Richard Borcherds'] selected [http://math.berkeley.edu/%7Ereb/courses/alggeom/ solutions]<br>
+One of my favorite facts about right adjoint functors is that they [http://stacky.net/files/written/AdjointsCommuteLimits.pdf commute with limits].
-[http://www.math.lsa.umich.edu/%7Ebcais/ Bryden Cias'] [http://www.math.lsa.umich.edu/%7Ebcais/CourseNotes/AlgGeom04/ notes] and [http://www.math.lsa.umich.edu/%7Ebcais/CourseNotes/AlgGeom04/Hartshorne_Solutions.pdf solutions]<br>
+[http://stacky.net/files/written/sestina.pdf Sestina's and primes], an easy problem Richard Dore and I worked out our first year in grad school, which I wrote up for some reason.
-[http://www.math.uchicago.edu/%7Ejinhyun/ Jinhyun Park]'s [http://www.math.uchicago.edu/%7Ejinhyun/sol2/hart.html solutions]<br>
+In 2007, I talked about the Salamander Lemma in [http://math.berkeley.edu/~mcf MCF], and later [http://sbseminar.wordpress.com/2007/11/13/anton-geraschenko-the-salamander-lemma/ blogged about it] on the [http://sbseminar.wordpress.com/ Secret Blogging Seminar]. My reference was [http://math.berkeley.edu/~gbergman/ George Bergman]'s preprint, [http://arxiv.org/abs/1108.0958 On diagram-chasing in double complexes] (which wasn't yet on the arxiv at the time).
+==More moved notes==
+[http://docs.google.com/View?docid=dsrd28g_14rgs6ptht Aspects of Moduli]:
+{|class="wikitable"
+|-
+|Tom Bridgeland
+| Stability in triangulated categories
+| [http://stacky.net/files/written/AspectsModuli/TB.pdf pdf]
+|-
+|Kai Behrend
+| Foundations of Donaldson-Thomas theory
+| [http://stacky.net/files/written/AspectsModuli/KB.pdf pdf]
+|-
+|Alessio Corti
+| Foundations of Donaldson-Thomas theory
+| [http://stacky.net/files/written/AspectsModuli/AC.pdf pdf]
+|-
+|Valery Alexeev
+| Moduli of higher-dimensional varieties
+| [http://stacky.net/files/written/AspectsModuli/VA.pdf pdf]
+|-
+|Martin Olsson
+| Logarithmic structures with a view towards moduli
+| [http://stacky.net/files/written/AspectsModuli/MO.pdf pdf]
+|-
+|All in one (chronologically)
+| [http://stacky.net/files/written/AspectsModuli/AspectsModuli.pdf pdf] [http://stacky.net/files/written/AspectsModuli/AspectsModuliSource.tgz tgz]
+|}
-[http://math.berkeley.edu/%7Emhaiman/index.html Mark Haiman]'s [http://math.berkeley.edu/%7Emhaiman/math256/index.html Math 256AB page]
+Quantum Field Theory, my notes from
+{|class="wikitable"
+|-
+|[http://math.berkeley.edu/~reshetik/ Nicolai Reshetikhin]'s [http://math.berkeley.edu/~reshetik/topics/CFT-TQFT.pdf course]
+|[http://stacky.net/files/written/QFT/NR.pdf pdf]
+|-
+|[http://math.berkeley.edu/~teichner Peter Teichner's] course
+|[http://stacky.net/files/written/QFT/PT.pdf pdf]
+|-
+|[http://math.berkeley.edu/~reb/ Richard Borcherd's] course
+|[http://stacky.net/files/written/QFT/RB.pdf pdf]
+|-
+|All in one (chronologically)
+| [http://stacky.net/files/written/QFT/QFT.pdf pdf] [http://stacky.net/files/written/QFT/QFTSource.tgz tgz] [http://stacky.net/files/written/QFT/ dir]
 |}
+For more QFT stuff, see [http://sites.google.com/site/chrisschommerpriesmath/ Chris Schommer-Pries'] QFT site for Fall 2007. (doesn't exist any more?)
+For those who just want to get some notes, just download the pdf file. For those who want to look at the souce, download the tgz (<code>tar</code>-ed and <code>gzip</code>-ped) file, which has all the tex source in it. You'll find that the main file (<code>QFT.tex</code>) is quite boring. The actual lecture notes are in the other files and the top matter (like macro definitions) is in <code>QFTPreamble.tex</code>. As far as I know, the command <code>\input{abcdefg}</code> gives exactly the same result as pasting in the contents of the file <code>abcdefg.tex</code> (note that <code>abcdefg.tex</code> should be in the same directory as the main file).
+If you have notes that I'm missing or if you have a correct/clear explanation for something which is incorrect/unclear, let me know (either tell me what you'd like to modify, give me some notes to go on, or update the tex yourself and send me a copy). Real (mathematical) errors should be fixed because it would be immoral to let them propagate (er ... that is, sit there), and typographical errors hardly take any time to fix, so you shouldn't be shy about telling me about them.&nbsp;