Basics of Ramsey Theory

Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey's theorem, van der Waerden's theorem, Schur's theorem, Rado's theorem, the Hales-Jewett theorem, and the Happy End Problem of Erdős and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics.

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.

《Ramsey理論基礎》是一本對於有興趣瞭解當代數學中結合了數論和組合學思想的動態領域的學生而言，作為Ramsey理論的初步介紹的書籍。該書的核心內容包括對於眾所周知的Ramsey定理、van der Waerden定理、Schur定理、Rado定理、Hales-Jewett定理和Erdős和Szekeres的Happy End問題的討論和證明。目標是以具有挑戰性但令人愉快的方式呈現這些內容，並且對於對數學有真正興趣的任何人都具有廣泛的可讀性。

特點包括：
- 適合已成功完成標準微積分課程和標準線性代數課程的本科生。
- 充滿了基本定理的視覺證明。
- 包含許多對本科生易於理解的練習題（附有解答）。
- 可作為數學選修課的教材或輔助教材，適用於對數學有興趣的多樣化學生群體。

Dr. Veselin Jungic is a Teaching Professor at the Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada.

Dr. Jungic is a 3M National Teaching Fellow and a Fellow of the Canadian Mathematical Society. He is a recipient of several teaching awards. Veselin is one of only a few Canadian mathematicians who has been awarded both the Canadian Mathematical Society Pouliot Award (2020) and the Canadian Mathematical Society Teaching Award (2012).

Dr. Jungic's publications range from education related opinion pieces to articles based on his teaching practices to Ramsey theory research and outreach papers.

One of Dr. Jungic's accomplishments is the creation of the Math Catcher Outreach Program. Since the early 2010s, the Program has visited hundreds of classrooms, from kindergarten to grade 12, and created learning resources in multiple Indigenous languages. As an invited speaker, Veselin delivered several dozens of the Math Catcher-related workshops and lectures to teachers, academics, and public at the local, national, and international levels.

Dr. Veselin Jungic是加拿大不列顛哥倫比亞省本拿比的西蒙菲莎大學數學系的教學教授。

Dr. Jungic是3M國家教學獎得主，也是加拿大數學學會的會士。他曾獲得多個教學獎項。Veselin是少數同時獲得加拿大數學學會Pouliot獎（2020年）和加拿大數學學會教學獎（2012年）的加拿大數學家之一。

Dr. Jungic的出版物涵蓋了教育相關的觀點文章、基於他的教學實踐的文章、拉姆齊理論研究和推廣論文。

Dr. Jungic的成就之一是創建了Math Catcher Outreach Program。自2010年代初以來，該計劃已經訪問了從幼稚園到12年級的數百個教室，並創建了多種土著語言的學習資源。作為受邀演講者，Veselin在本地、國家和國際層面上向教師、學者和公眾進行了數十場與Math Catcher相關的工作坊和講座。