An Introduction To Mathematical Reasoning (Numbers, Sets And Functions)

An Introduction To Mathematical Reasoning (Numbers, Sets And Functions)

This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.Review"A student planning to study advanced mathematics would be well served by first mastering the material in this book...a rigorous study of sevearl fundamental topics pervasive in mathematics, including sets, functions, cardinality, combinatorics, and modular arithmetic." D.S. Larson, ChoiceBook DescriptionThe purpose of this book is to introduce the basic ideas of mathematical proof and reasoning to students starting university mathematics.Book DescriptionThe purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.