Combinatorial Analysis

Course Description and Grading Breakdown
This term we will study three topics. We will spend the first five weeks of the course on the probabilistic method in combinatorics. The next two weeks will be spent on the Szemeredi regularity theorem and applications. The final three weeks will be spent on an introduction to additive combinatorics. There will be four problem sets assigned, two for the first topic and one for each of the others. Each set will count equally and the final grade in the course will be determined entirely based on the homework.


Course Meeting Time and Location
Tuesday and Thursday
1:00 - 2:25 pm
255 Linde

Course Instructor Contact Information and Office Hours
164 Linde Hall
Wednesday 7-8

Course Schedule and Textbook

For the first five weeks of the course, the textbook will be the 3rd edition of Alon and Spencer's text "The Probabilistic Method" There is a fourth edition, but the third edition is available from the library as an electronic resource. Textbook >
 Date Topic 
   
   


Course Policies
Late work - 


Assignments
 Date Posted Assignment  Due Date 
1/10/19 Problem Set 1 1/24/19
1/27/19 Problem Set 2 2/7/19
2/19/19 Problem Set 3 3/4/19
     
Solutions to Problem Set 2 can be found on pages 138-144 here. As Ben Krause says, it builds character. Bourgain





Notes

Here are Croot's notes on the Szemeredi Regularity Theorem: Croot   

Here are notes of Shagnik Das on applications of the regularity lemma. Das
Here is a survey of Conlon and Fox on graph removal lemmas. Conlon-Fox

Here are some notes for a lecture to Chinese high school students. Ignore the part about logistics of studying mathematics. [This was supposed to please their parents.] The
mathematical part will form the basis for my first lecture on additive combinatorics. NetsChina1


Collaboration Table
  Homework Exams
You may consult:    
Course textbook (including answers in the back) YES YES
Other books YES NO
Solution manuals NO NO
Internet YES NO
Your notes (taken in class) YES YES
Class notes of others YES NO
Your hand copies of class notes of others YES YES
Photocopies of class notes of others YES NO
Electronic copies of class notes of others YES NO
Course handouts YES YES
Your returned homework / exams YES YES
Solutions to homework / exams (posted on webpage) YES YES
Homework / exams of previous years NO NO
Solutions to homework / exams of previous years NO NO
Emails from TAs YES NO
You may:

Discuss problems with others YES NO
Look at communal materials while writing up solutions YES NO
Look at individual written work of others NO NO
Post about problems online NO NO
For computational aids, you may use:

Calculators YES* NO
Computers YES* NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

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Caltech Math,
Feb 12, 2019, 12:07 PM
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Caltech Math,
Feb 21, 2019, 9:50 AM
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croot.pdf
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Caltech Math,
Feb 12, 2019, 12:07 PM
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ps1.pdf
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Caltech Math,
Jan 10, 2019, 9:08 AM
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ps2.pdf
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Caltech Math,
Jan 27, 2019, 12:04 PM
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ps3.pdf
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Caltech Math,
Feb 19, 2019, 8:26 AM