Mathematical Reasoning: Writing and Proof

Livro digital

Título:
Mathematical Reasoning: Writing and Proof

Autor:
Ted Sundstrom

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Many mathematics and computer science students struggle with the leap from computation to proof — the moment a course stops asking "what is the answer?" and starts asking "how do you know?" This book addresses that transition head-on, opening with conditional statements and the structure of direct proofs before introducing the full grammar of logical reasoning: operators, quantifiers, negations, and open sentences. The progression is deliberate. Chapters 1 through 3 build the core proof toolkit — direct proofs, proof by contradiction, case analysis, and the division algorithm with congruence — before dedicating an entire chapter to mathematical induction, including other induction forms and its connection to recursion. Chapter 5 enters set theory with the same rigor: not just defining sets, but proving set relationships from the ground up. Updated to Version 3 in December 2024 by Ted Sundstrom, Professor Emeritus at Grand Valley State University, and previously published by Pearson Education, this textbook is now freely available under a Creative Commons CC BY-NC-SA license. Each concept is paired with worked examples and structured exercises, making it equally effective for self-study or as a course companion for students taking their first steps into mathematical abstraction.