100% mathematical proof
著者
書誌事項
100% mathematical proof
Wiley, c1996
- : pbk
- タイトル別名
-
One hundred percent mathematical proof
A hundred percent mathematical proof
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注記
Includes index
内容説明・目次
内容説明
Proof has been, and remains, one of the concepts which characterizes mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, this text seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principal techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, and constructive and non-constructive proofs. Many examples of proofs are presented and some common student errors are explained. The exercises assume only a secondary school background in mathematics, although examples from analysis and modern algebra are included.
目次
- Proofs: Mathematical and Non-Mathematical
- Propositional Logic
- Predicate Logic
- Axiom Systems and Formal Proof
- Direct Proof
- Direct Proofs: Variations
- Existence and Uniqueness Proofs
- Further Proof Techniques
- Mathematical Induction
- Appendix
- References and Further Reading
- Hints and Solutions to Selected Exercises
- Index.
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