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課程名稱 |
圖論二
Graph Theory (Ⅱ) |
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開課學期 |
112-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
戴尚年 |
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課號 |
MATH7704 |
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課程識別碼 |
221EU3460 |
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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 |
必修 |
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上課時間 |
星期二8,9(15:30~17:20)星期五5(12:20~13:10) |
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上課地點 |
天數102天數102 |
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備註 |
本課程以英語授課。
總人數上限：80人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
This course will introduce students to the problems and methods of extremal
combinatorics. The fundamental extremal problem asks how large a structure can be
without containing a forbidden substructure. This very flexible problem arises in many
different settings and enjoys several applications. A variety of methods have been
developed to tackle them, and this course will pay special attention to the probabilistic,
linear algebraic and (briefly) topological methods. |
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課程目標 |
The first half of the course will continue from the previous semester’s Graph Theory
course, taking a deeper look into Ramsey and Turán Theory. The second half will
cover problems from extremal set theory, including the central theorems of Erdős-Ko-
Rado and Sperner. Alongside the important results, equal attention will be paid to
the development of methods used to prove them. |
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課程要求 |
Successful completion of Graph Theory I (or an equivalent course)
Familiarity with linear algebra and (discrete) probability
Some knowledge of topology would be a bonus, but is not required |
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預期每週課後學習時數 |
4-6 hours |
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Office Hours |
另約時間 備註： Feel free to schedule office hours by asking before/after lectures or sending an e-mail. You should also post any questions in the NTU COOL Discussions forum. |
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指定閱讀 |
The course will be self-contained, with notes provided online |
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參考書目 |
Sources for supplemental reading:
- “The probabilistic method” (Alon-Spencer)
- “Extremal Combinatorics” (Jukna)
- “A Course in Combinatorics” (Van Lint-Wilson)
- "Graph Theory” (Diestel)
- “Linear Algebra Methods in Combinatorics” (Babai-Frankl) |
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評量方式
(僅供參考) |
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