課程資訊
 課程名稱 組合學二Combinatorics (Ⅱ) 開課學期 103-2 授課對象 理學院  數學研究所 授課教師 張鎮華 課號 MATH7702 課程識別碼 221 U3300 班次 學分 3 全/半年 半年 必/選修 選修 上課時間 星期三3(10:20~11:10)星期五3,4(10:20~12:10) 上課地點 天數101天數101 備註 總人數上限：60人 Ceiba 課程網頁 http://ceiba.ntu.edu.tw/1032MATH7702_Comb_II 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 This course is to introduce additive combinatorics. It basically follows the lecture note by Terence Tao [01], with necessary modification at need. It will start at the combinatorial estimates relating to the sums, differences, and products of finite sets. We will also cover related objects such as arithmetic progressions, from the classical theorem by van der Waerden to the Szemeredi’s theorem for the case of k = 3. Various tools as well as related topics will also be touched. 課程目標 The aim of this course is to tour the highlights of arithmetic combinatorics -the combinatorial estimates relating to the sums, differences, and products of finite sets, or to related objects such as arithmetic progressions. The material here is of course mostly combinatorial, but we will also exploit the Fourier transform at times. We will also discuss the recent applications of this theory to geometric combinatorics problems, and in particular the Kakeya problem. 課程要求 代數導論。 預期每週課後學習時數 Office Hours 參考書目 待補 指定閱讀 [01] Lecture Note by Terence Tao. [02] T. Tao and V. Vu, Additive Combinatorics, Cambridge University Press, 2006. [03] K. Soundararajan, Additive Combinatorics, Lecture Notes, Winter 2007. [04] A mini course on additive combinatorics, Princeton, 2007. [05] S. Lovett, Additive Combinatorics and its Applications in Theoretical Computer Science, 2013. [06] A. Granville, M. B. Nathanson and J. Solymosi ed., Additive Combinatorics, AMS, 2007. [09] R. L. Graham, Rudiments of Ramsey Theory, AMS, 1979. [11] H. Furstenberg and B. Weiss, Toplological dynamics and combinatorial number theory, J. Analyse Math. 34 (1978), 61-85. 評量方式(僅供參考)
 課程進度
 週次 日期 單元主題 第1週 2/25,2/27 Lecture Notes 1 (6/27 補假。) 第2週 3/04,3/06 (3/4 出國，補課。) 第4週 3/18,3/20 Lecture Notes 2 第6週 4/01,4/03 (4/1 溫書假，4/3 補假。) 第7週 4/08,4/10 Lecture Notes 3 第9週 4/22,4/24 (4/22 交大評鑑，補課。) 第10週 4/29,5/01 Lecture Notes 4 第12週 5/13,5/15 Lecture Notes 6 第17週 6/17,6/19 (6/19 補假。)