How to Prove It: A Structured Approach (3rd Edition)

Download How to Prove It: A Structured Approach (3rd Edition) written by Daniel J. Velleman in PDF format. This book is under the category Mathematics and bearing the isbn/isbn13 number 110842418X; 1108439535/9781108424189/ 9781108439534. You may reffer the table below for additional details of the book.

$19.99

SKU: ef0917ea498b Category: Tags: ,

Specifications

book-author

Daniel J. Velleman

publisher

Cambridge University Press; 3rd Edition

file-type

PDF

pages

469 pages

language

English

asin

B07TBM9LW6

isbn10

110842418X; 1108439535

isbn13

9781108424189/ 9781108439534


Book Description

Proofs are important in advanced mathematics and theoretical computer science, but many students struggle the first time they take a subject that relies heavily on evidence. The third edition of this best-selling textbook teaches students how to shift from solving problems to proving theorems by teaching them how to read and write proofs. How to Prove It: A Structured Approach; 3rd Edition (PDF) introduces students to the realm of advanced mathematics through the mastering of proofs, with over 150 new tasks and a new chapter on number theory. To familiarize readers with the language of mathematics and how it is inferred, the ebook begins with basic ideas of logic and sets theory. These principles serve as the foundation for an examination of approaches for constructing intricate proofs step by step, with detailed’scratch work’ parts exposing the mechanism of proofs involving numbers, relations, sets, and functions. This ebook will be valuable to everyone interested in logic and proofs, including computer scientists, linguists, philosophers, and, of course, mathematicians, as it assumes no prior knowledge beyond normal high school mathematics.

NOTE: This item only comes with the publication How to Prove It: A Structured Approach, 3rd Edition, in PDF format. There are no access codes included.

Table of contents


Table of contents :
Half Title page
Title page
Copyright page
Dedication
Contents
Preface to the Third Edition
Introduction
1 Sentential Logic
1.1 Deductive Reasoning and Logical Connectives
1.2 Truth Tables
1.3 Variables and Sets
1.4 Operations on Sets
1.5 The Conditional and Biconditional Connectives
2 Quantificational Logic
2.1 Quantifiers
2.2 Equivalences Involving Quantifiers
2.3 More Operations on Sets
3 Proofs
3.1 Proof Strategies
3.2 Proofs Involving Negations and Conditionals
3.3 Proofs Involving Quantifiers
3.4 Proofs Involving Conjunctions and Biconditionals
3.5 Proofs Involving Disjunctions
3.6 Existence and Uniqueness Proofs
3.7 More Examples of Proofs
4 Relations
4.1 Ordered Pairs and Cartesian Products
4.2 Relations
4.3 More About Relations
4.4 Ordering Relations
4.5 Equivalence Relations
5 Functions
5.1 Functions
5.2 One-to-One and Onto
5.3 Inverses of Functions
5.4 Closures
5.5 Images and Inverse Images: A Research Project
6 Mathematical Induction
6.1 Proof by Mathematical Induction
6.2 More Examples
6.3 Recursion
6.4 Strong Induction
6.5 Closures Again
7 Number Theory
7.1 Greatest Common Divisors
7.2 Prime Factorization
7.3 Modular Arithmetic
7.4 Euler’s Theorem
7.5 Public-Key Cryptography
8 Infinite Sets
8.1 Equinumerous Sets
8.2 Countable and Uncountable Sets
8.3 The Cantor-Schrӧder-Bernstein Theorem
Appendix: Solutions to Selected Exercises
Suggestions for Further Reading
Summary of Proof Techniques
Index

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