How to Prove It A Structured Approach
How to Prove It: A Structured Approach by Daniel J. Velleman, published by Cambridge University Press on July 18, 2019, is a comprehensive guide designed to assist students in mastering the art of mathematical proofs. This third edition spans 468 pages and is presented in English. It addresses the challenges many students face when transitioning from problem-solving to theorem proving, offering a structured approach to understanding the essential techniques required for reading and writing proofs.
Readers will find a wealth of resources, including over 150 new exercises and a new chapter on number theory, which enhance their learning experience. The book begins with foundational concepts in logic and set theory, providing the necessary language for advanced mathematics. It systematically analyzes various techniques for constructing complex proofs, supported by detailed sections that break down the process of proving statements about numbers, sets, relations, and functions. This edition is suitable for anyone interested in logic and proofs, including students of mathematics, computer science, philosophy, and linguistics.
Official synopsis Publisher
Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text’s third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed ‘scratch work’ sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.
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