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課程名稱 |
加性組合學
Additive Combinatorics |
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開課學期 |
105-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
張鎮華 |
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課號 |
MATH5047 |
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課程識別碼 |
221 U7040 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三4(11:20~12:10)星期五1,2(8:10~10:00) |
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上課地點 |
天數302天數302 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH5047_add_com |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
[1] Chapter 2, Sum set estimates.
[2] Chapter 1, Small sum sets.（equivalent to [1] Chapter 5, Inverse sum set theorems.）
[1] Chapter 8, Incience geometry, and the sum-product proble.
[1] Chapter 4, Fourier-analytic methods, sections 4.1, 4.2 and 4.3.
Fourier analysis proof of Roth theorem.
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課程目標 |
One remarkable feature of additive combinatorics 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 additive combinatorics a rich, fascinating, and multi-faceted subject. There are still many major problems left in the field, and it seems likely that many of these will require a combination of tools from several of the areas mentioned above in order to solve them.
The main purpose of this course is introduce some basic tools in additive combinatorics. We shall demon the Fourier analysis proof of Roth theorem.
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課程要求 |
每周一定要寫作業。 |
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預期每週課後學習時數 |
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Office Hours |
每週三 13:00~17:00 |
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指定閱讀 |
[1] T. Tao and V. Vu, Additive Combinatorics, Cambridge University Press, 2006.
[2] M. B. Nathanson, Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Springer-Verlag, New York, 1996.
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參考書目 |
[1] T. Tao and V. Vu, Additive Combinatorics, Cambridge University Press, 2006.
[2] M. B. Nathanson, Additive Number Theory: Inverse Problems and the Geometry
of Sumsets, Springer-Verlag, New York, 1996.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
作業 |
34% |
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2. |
期中考 |
33% |
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3. |
期末考 |
33% |
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週次 |
日期 |
單元主題 |
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第0週 |
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[1] T. Tao and V. Vu, Additive Combinatorics, Cambridge University Press, 2006.
[2] M. B. Nathanson, Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Springer-Verlag, New York, 1996.
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第1週 |
2/22,2/24 |
[1] Chapter 2, Sum set estimates. |
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第2週 |
3/01,3/03 |
[1] Chapter 2, Sum set estimates. |
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第3週 |
3/08,3/10 |
[1] Chapter 2, Sum set estimates. |
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第4週 |
3/15,3/17 |
[2] Chapter 1, Small sum sets.（equivalent to [1] Chapter 5, Inverse sum set theorems.） |
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第5週 |
3/22,3/24 |
[2] Chapter 1, Small sum sets.（equivalent to [1] Chapter 5, Inverse sum set theorems.） |
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第6週 |
3/29,3/31 |
[2] Chapter 1, Small sum sets.（equivalent to [1] Chapter 5, Inverse sum set theorems.） |
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第7週 |
4/05,4/07 |
緩衝週 |
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第8週 |
4/12,4/14 |
[1] Chapter 8, Incience geometry, and the sum-product proble. |
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第9週 |
4/19,4/21 |
[1] Chapter 8, Incience geometry, and the sum-product proble.
期中考 |
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第10週 |
4/26,4/28 |
[1] Chapter 8, Incience geometry, and the sum-product proble. |
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第11週 |
5/03,5/05 |
自主學習週 |
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第12週 |
5/10,5/12 |
[1] Chapter 4, Fourier-analytic methods, sections 4.1, 4.2 and 4.3. |
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第13週 |
5/17,5/19 |
[1] Chapter 4, Fourier-analytic methods, sections 4.1, 4.2 and 4.3. |
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第14週 |
5/24,5/26 |
1] Chapter 4, Fourier-analytic methods, sections 4.1, 4.2 and 4.3. |
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第15週 |
5/31,6/02 |
Fourier analysis proof of Roth theorem. |
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第16週 |
6/07,6/09 |
Fourier analysis proof of Roth theorem. |
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第17週 |
6/14,6/16 |
Fourier analysis proof of Roth theorem |
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第18週 |
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期末考 |
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