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  About site: http://www.math.ucla.edu/~tao/254a.1.03w/

Title: Math/Number Theory - Some Highlights of Arithmetic Combinatorics Lecture notes and resources on combinatorial number theory by Terence Tao.
Some_Number-Theoretical_Constants Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.

Somos_Polynomials Related to Somos sequences and elliptic theta functions.

The_Somos_Sequence_Site Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.

Square-free_Gaps Algorithm and source code for the calculation of square-free numbers and gaps.

Transcendental_Numbers Maple worksheets, lecture notes and links to other resources by John Cosgrove.

The_Valuation_Theory_Home_Page A forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research.


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Math 254AMATH 254ASome highlights of arithmetic combinatorics MW 3-4:30, MS 6221Terence Tao, tao@math.ucla.edu,x64844, MS 5622 A brief summary of the course can be foundhere.Lecture notes: Lecture notes 1: Cauchy-Davenportinequality, Plunnecke's theorem, sum set estimates. Errata to Q2: |A|, |B| need to be assumedto be at least 2. Errata to Q10(a):"translates of B" should read "translates of B-B". Errata to Q11:"and some subset A' such that |A'|>= (1-delta) |A| and" should read"such that for every subset A' with |A'|>= (1-delta)|A|, we have". Thanks to Roman Sasyk for pointing out theseerrata. Lecture notes 2: Freiman's theorem (both inthe torsion and torsion-free cases), Gowers-Walters theorem, Chang'srefinement of Freiman's theorem Lecture notes 3: Gowers' quantitative Balog-Szemeredi theorem; applications to the Kakeya problem; applications to a multilinear convolution integral. Errata to Q4: The theorem as stated is false; it is best to forget this question entirely. Lecture notes 4: Roth's theorem for APs of length 3; Gowers' proof of Szemeredi's theorem for APs of length 4. Lecture notes 5: Behrend's example; Bourgain's refinement of Roth's theorem. Lecture notes 6: Crossing numbers and Szemeredi's theorem; Elekes's sum-product theorem; Bourgain-Katz-Tao sum-product theorem; finite field Szemeredi-Trotter and distance set problem results. Further reading: Theweb page of Ben Green, including hislecture notes on Freiman's theorem. The webpage of Tim Gowers. The webpage of Imre Ruzsa. VanVu's grad course home page on combinatorial number theory (a courserunning in parallel with ours wich much overlap of topics, but adifferent mathematical perspective).
 

Lecture

notes

and

resources

on

combinatorial

number

theory

by

Terence

Tao.

http://www.math.ucla.edu/~tao/254a.1.03w/

Some Highlights of Arithmetic Combinatorics 2008 November

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Lecture notes and resources on combinatorial number theory by Terence Tao.

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