| Edition |
4th ed. |
| Description |
1 online resource (ix, 283 pages) |
|
text txt rdacontent |
|
computer c rdamedia |
|
online resource cr rdacarrier |
| Summary |
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. 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. |
| Contents |
Chapter 1: Getting Started Introduction and Basic Terminology General Suggestions -- Chapter 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 Contradiction -- Chapter 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 Numbers -- Chapter 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 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. |
| Note |
Includes index. |
| Bibliography |
Includes bibliographical references (pages 278-280) and index. |
| Subject |
Proof theory.
|
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Théorie de la preuve.
|
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Proof theory
|
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Beweistheorie
|
| ISBN |
9780123822178 (electronic bk.) |
|
0123822173 (electronic bk.) |
| Standard No. |
AU@ 000049014141 |
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CHBIS 006990420 |
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CHBIS 009942983 |
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CHNEW 001010422 |
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CHVBK 179590022 |
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CHVBK 302218246 |
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DEBBG BV042310452 |
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DEBSZ 405340893 |
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NZ1 14536444 |
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NZ1 15192371 |
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AU@ 000075336280 |
|
