Basics of Ramsey theory
著者
書誌事項
Basics of Ramsey theory
Chapman & Hall/CRC, 2023
- :hbk
大学図書館所蔵 件 / 全6件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and index
内容説明・目次
内容説明
Features
Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course.
Filled with visual proofs of fundamental theorems.
Contains numerous exercises (with their solutions) accessible to undergraduate students.
Serves as both a textbook or as a supplementary text in an elective course in combinatorics and aimed at a diverse group of students interested in mathematics.
目次
1. Introduction: Pioneers and Trailblazers. 1.1. Complete Disorder is Impossible. 1.2 Paul Erdos. 1.3. Frank Plumpton Ramsey. 1.4 Ramsey Theory. 2. Ramsey's Theorem. 2.1. The Pigeonhole Principle. 2.2. Acquaintances and Strangers. 2.3. Ramsey's Theorem for Graphs. 2.4. Ramsey's Theorem: Infinite Case. 2.5. Ramsey's Theorem: General Case. 2.6. Exercises. 3. van der Waerden's Theorem. 3.1. Bartel van der Waerden. 3.2. van der Waerden's Theorem: 3-Term Arithmetic Progressions. 3.3. Proof of van der Waerden's Theorem. 3.4. van der Waerden's Theorem: How Far and Where? 3.5. van der Waerden's Theorem: Some Related Questions. 3.6. Exercises. 4. Schur's Theorem and Rado's Theorem. 4.1 Issai Schur. 4.2. Schur's Theorem. 4.3. Richard Rado. 4.4 Rado's Theorem. 4.5. Exercises. 5. The Hales-Jewett Theorem. 5.1. Combinatorial Lines. 5.2. Generalized Tic-Tac-Toe Game. 5.3. The Hales-Jewett Theorem. 5.4. Exercises. 6. Happy End Problem. 6.1. The Happy End Problem: Triangles, Quadrilaterals, and Pentagons. 6.2. The Happy End Problem - General Case. 6.3. Erdos-Szekeres' Upper and Lower Bounds. 6.4. Progress on the Conjecture OF Erdos and Szekeres. 6.5. Exercises. 7. Solutions.
「Nielsen BookData」 より