Descuento:
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35,53 €Chapter 1. Getting Started
Introduction and Basic Terminology
General Suggestions
Chapter 2. Basic Techniques to Prove If/Then Statements
What Does “If/Then” Mean?
The Negation of a Statement: AND/OR
Proof by Contrapositive
Proof by Contradiction
Chapter 3. Special Kinds of Theorems
“If and Only If” or “Equivalence Theorems”
Use of Counter Examples
Mathematical Induction
Existence Theorems
Uniqueness Theorems
Composite Statements
Equality of Numbers
Chapter 4. Some Mathematical Topics on Which to Practice Proof Techniques
Basic Set Theory and Indexed Families
About Functions
Relations
The Basics of Groups
Limits
Sizes of Infinity
Chapter 5. Review Exercises
Exercises without Solutions
Collection of “Proofs”
Solutions for the Exercises at the End of the Sections and the Review Exercises
Solutions for the Exercises at the End of the Sections
Solutions for the Review Exercises
Other Books on the Subject of Proofs and Mathematical Writing
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.
Features:
• Jumps right in with the needed vocabulary-gets students thinking like mathematicians from the beginning
• Offers a large variety of examples and problems with solutions for students to work through on their own
• Includes a collection of exercises without solutions to help instructors prepare assignments
• Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics
Author
Antonella Cupillari, Pennsylvania State Erie, Behrend College, U.S.A.
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