Aspects of Combinatorics and Combinatorial Number Theory discusses various Ramsey-type theorems in combinatorics and combinatorial number theory. While many of the main results are classic, the book describes recent progress and considers unsolved questions in the field. For classical theorems, whenever possible, the author presents different proofs than those offered in Graham, Rothschild, and Spencer's book. For instance, Johnson's proof has been given for Erdoes-Szekeres Theorem, and in establishing that proof, the author makes reference to the other proofs. The first part of the book is primarily concerned with the history, context, and rudiments of the subject, and it requires only a basic maturity in mathematical thinking. The later parts and the remarks following each section describe many rather recent Ramsey-type results in combinatorics with application of topological ideas. These parts require some training in algebra and topology.

Aspects of Combinatorics and Combinatorial Number Theory

Science & Math

Adhikari, S. D.

Mathematics

Narosa

Aspects of Combinatorics And Combinatorial Number Theory

Alpha Science Intl Ltd

This is an elementary introduction to algebra and number theory. Starting with a recalling of the preliminaries of groups, rings and fields, the topics in algebra portion consists of polynomial rings, UFD, PID and Euclidean domains, field extensions, modules and Dedckind domains. In the number theory part, apart from covering elementary congruence results, the laws of quadratic reciprocity and basics of algebraic number fields, this book attempts to give glimpse of various aspects of the subject. Thus, Warning's and Chevally's theorems in the section of finite fields and many results of additive number theory are strewn all over. Some of the additive number theoretic results like derivation of Lagrange's four square theorem from Minkowski's result in geometry of numbers, are given. By adding some remarks and comments, which are beyond the scope of this book, and with the references in the bibliography, attempts are been made to encourage the students to learn beyond this material.

An Introduction to Commutative Algebra And Number Theory

Narosa Pub House

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