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The Nuts and Bolts of Proofs
An Introduction to Mathematical Proofs
Demonstrates the construction of proofs to help students develop the skills they need to transition to higher-level, more abstract math courses
Antonella Cupillari (Author)
9780323990202
Paperback / softback, published 21 March 2023
416 pages
23.5 x 19 x 2.6 cm, 0.86 kg
The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides basic logic of mathematical proofs and how they work. The book offers techniques for both reading and writing proofs, discusses techniques in proving if/then statements by contrapositive and proofing by contradiction, includes the negation statement, and/or, examines various theorems, such as the if and only-if, equivalence theorems, existence theorems, and the uniqueness theorems. In addition, the use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are also covered. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book accessible as well as invaluable.
1. Getting Started
2. Basic Techniques to Prove If/Then Statements
3. Special Kinds of Theorems
4. Some Mathematical Topics on Which to Practice Proof Techniques
5. Review Exercises
Subject Areas: Mathematical logic [PBCD]
