An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library) by Matthew Katz (PDF)

Description

This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey’s theorem for graphs and hypergraphs, van der Waerden’s theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.

User’s Reviews

Editorial Reviews: Review This little book is a gem. It is advertised as having minimal prerequisites. Such statements are often made but less often accurate, but the claim seems entirely truthful here. The authors have taken pains to develop, as necessary, what background material is used in the book…and have written this book in a clear, conversational tone that is certain to engage student interest. –Mark Hunacek, MAA Reviews About the Author Matthew Katz: Pennsylvania State University, University Park, PA, Jan Reimann: Pennsylvania State University, University Park, PA

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Have read about half the book – the material and the writing style are both superb. The explanation of the ideas is very clear, and the exercises are insightful. The authors have taken great pains to ensure that the book is self contained, and all proofs are spelt out in detail. Overall a wonderful reading experience.The first chapter contains Ramsey theory of finite sets, and gives two proofs of Ramsey’s theorem. The second chapter presents the Ramsey theory of infinite sets, and the authors include material on set theory, cardinals and ordinals needed to understand it. The third chapter starts with a great presentation of van der Waerden’s theorem, leading into questions of computability. The final chapter deals with metamathematics, what is provable etc.

⭐I’ve been working through this book with a friend, we cover 20-30 pages in our weekly syncs.The material is simply amazing, geared to people with an interest in logic/set theory, but the proofs use concepts from other disciplines, e.g,. real analysis, combinatorics, all of which are developed in the book itself.It’s a nice combination of nuggets and broader theory. The authors make good use of examples, the writing is informal but still rigorous.It should be accessible to anyone with undergrad math training (it’s not suitable for amateurs).Pro tip: don’t skip the proofs that are left as exercises.

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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library) PDF Free Download
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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library) 2018 PDF Free Download
Download An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library) PDF
Free Download Ebook An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library)