How To Read And Do Proofs
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How to Prove It
Author: Daniel J. Velleman
language: en
Publisher: Cambridge University Press
Release Date: 2006-01-16
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write 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 a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
How to Read and Do Proofs
An essential reference for anyone grappling with advanced mathematics, this Fourth Edition helps readers master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once the reader has a firm grasp of the technique, they'll be better equipped to read, understand and actually do proofs. They'll also learn when each technique is likely to be successful, based on the form of the theorem. (Midwest).
Mathematical Reasoning
Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. For learners making the transition form calculus to more advanced mathematics.