The Nuts and Bolts of Proofs
An Introduction to Mathematical Proofs
By- Antonella Cupillari, Pennsylvania State Erie, Behrend College, U.S.A.
The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.
Paperback, 296 Pages
Published: January 2012
Imprint: Academic Press
ISBN: 978-0-12-382217-8
Contents
Chapter 1: Getting Started
Introduction and Basic Terminology
General SuggestionsChapter 2: Basic Techniques to Prove If/Then Statements
What Does "If/Then" Mean?
Direct Proof
The Negation of a Statement, And/Or
Proof by Contrapositive
Proof by ContradictionChapter 3: Special kinds of Theorems
"If and only if" or Equivalence Theorems
Use of Counterexamples
Mathematical Induction
Existence Theorems
Uniqueness Theorems
Composite Statements
Equality of NumbersChapter 4: Some mathematical topics on which to practice proof techniques
Basic Set Theory
About Functions
Relations
The Basics of Groups
Limits
Cardinality and Sizes of InfinityChapter 5: Review Exercises
Solutions for the Exercises at the End of the Sections and the Review Exercises
Exercises Without Solutions
Collection of Proofs
Solutions for the Exercises at the End of the Sections
Solutions for the Review ExercisesOther Books on the Subject of Proofs and Mathematical Writing
