課程資訊

Combinatorics (Ⅱ)

100-1

MATH7702

221 U3300

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001combinatorics2

The course basicaly follows the book “Additice Combinatorics” edited by Granville et al. [1], using Tao and Vu’s book [2] as an important addition. It will start at the classical theorem of arithmetic progressions by van der Waerden, and try to end at Szemeredi’s theorem, at least for the case of k = 3. Various tools as well as related topics will also be touched.

Additive combinatorics is currently a highly active area of resaerch for several reasons, for example its many applications to additive number theory. One remarkable feature of the field is the use of tools from many diverse fields of mathematics, including elementary combinatorics, harmonic analysis, convex geometry, incidence geometry, graph theory, probability, algebraic geometry, and ergodic theory; this wealth of perspectives makes addivitive combinatorics a rich, fascinating, and multi-faceted subject. The purpose of this course is to introduce basic tools in this subject.

Office Hours

[1] A. Granville, M. B. Nathanson and J. Solymosi ed., Additive Combinatorics,
AMS, 2007.
[2] T. Tao and V. Vu, Additive Combinatorics, Cambridge University Press, 2006.
[3] K. Soundararajan, Additive Combinatorics, Lecture Notes, Winter 2007.
[4] R. L. Graham, Rudiments of Ramsey Theory, AMS, 1979.

[1] A. Granville, M. B. Nathanson and J. Solymosi ed., Additive Combinatorics, AMS, 2007.
[2] T. Tao and V. Vu, Additive Combinatorics, Cambridge University Press, 2006.
[3] K. Soundararajan, Additive Combinatorics, Lecture Notes, Winter 2007.
[4] R. L. Graham, Rudiments of Ramsey Theory, AMS, 1979.

(僅供參考)

 No. 項目 百分比 說明 1. 作業 30% 2. 期中考試 35% 3. 期末考試 35%

 課程進度
 週次 日期 單元主題 第1週 9/13,9/16 Introduction / van der Waerden's theorem 第2週 9/20,9/23 van der Waerden's theorem / Hales-Jewett's theorem 第3週 9/27,9/30 Dynamical proof of van der Waerden's theorem 第4週 10/04,10/07 The Furstenberg correspondence principle vs Szemered's theorem 第5週 10/11,10/14 Princeton Lecture Note [4]---Chapters 2 and 5, Semeredi's regularity lemma 第6週 10/18,10/21 Princeton Lecture Note [4]----Chapter 6,Roth's proof for Szemeredi's theorem with k = 3 第7週 10/25,10/28 Chapter 2 in Tao and Vu [2]: Sum set estimates 第8週 11/01,11/04 Chapter 2 in Tao and Vu [2]: Sum set estimates 第9週 11/08,11/11 Chapter 2 in Tao and Vu [2]: Sum set estimates 第10週 11/15,11/18 Chapter 2 in Tao and Vu [2]: Sum set estimates 第11週 11/22,11/25 Chapter 9 in tao and Vu: Algebraic Method 第12週 11/29,12/02 Chapter 9 in tao and Vu: Algebraic Method 第13週 12/06,12/09 (P1) Scetion 5.1 up to Theorem 5.7. ----- (P2) Section 5.1 from Proposition 5.8. 第14週 12/13,12/16 (P2) Section 5.1 from Proposition 5.8. -----(P3) Section 5.2 up to Corollary 5.16. 第15週 12/20,12/23 (P4) Scetion 5.2 from Theorem 5.17. 第16週 12/27,12/30 (P5) Section 5.3. 第17週 1/03,1/06 (P6) Section 5.4. 第18週 1/10, 1/13 (P7) Section 5.5.