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

$19.99

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.

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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 play a key role in advanced mathematics and theoretical computer science; yet many learners struggle the first time they take a course in which shreds of evidence play a significant role. This bestselling textbook’s 3rd edition helps students transition from solving problems to proving theorems by teaching them the techniques required to read and write proofs. Featuring more than 150 new exercises and a new chapter on number theory; How to Prove It: A Structured Approach; 3rd Edition; (PDF) presents students to the world of advanced mathematics through the mastery of proofs. The ebook begins with the basic concepts of logic and sets theory to acquaint students with the language of mathematics and how it is inferred. These concepts are used as the ground for an analysis of techniques that can be used to build up complicated proofs step by step; using detailed ‘scratch work’ sections to expose the machinery of proofs about numbers; relations; sets; and functions. Assuming no background beyond standard high school mathematics; this ebook will be useful to anyone interested in logic and proofs: computer scientists; linguists; philosophers; and; of course; mathematicians.

NOTE: The product only includes the ebook How to Prove It: A Structured Approach; 3rd Edition; in PDF. No access codes are included.

Additional information

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

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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