The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides a basic introduction to mathematical proofs, techniques for reading and writing proofs, and discussion of theorems such as if and only if, equivalence, existence, and uniqueness. It also covers counter examples, mathematical induction, composite statements, and equality of numbers and includes review exercises. Undergraduate students in engineering and physical science will find it accessible and invaluable.

Format: Paperback / softback
Length: 416 pages
Publication date: 21 March 2023
Publisher: Elsevier Science & Technology

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition is a comprehensive guide that delves into the fundamental principles of mathematical proofs and their operational mechanisms. This edition offers a comprehensive exploration of the logic behind mathematical proofs, providing students with the tools they need to understand and execute them effectively.

The book begins by introducing the basic concepts of proof, including the definition of a proof, the structure of a proof, and the different types of proofs. It then proceeds to discuss techniques for both reading and writing proofs, such as proving if/then statements by contrapositive and proofing by contradiction. Additionally, the book covers the negation statement, the conjunction (and/or), and examines various theorems, including the if and only-if, equivalence theorems, existence theorems, and uniqueness theorems.

One of the key features of this edition is its emphasis on the use of counter examples, mathematical induction, composite statements including multiple hypotheses and multiple conclusions, and equality of numbers. These topics are essential for developing a strong foundation in proof techniques and are often overlooked in other introductory texts. The book also provides mathematical topics for practicing proof techniques, such as the Cartesian products, indexed families, functions, and relations.

The final chapter of the book includes review exercises on various topics, allowing students to consolidate their knowledge and test their understanding of the material. These exercises are designed to reinforce the concepts covered throughout the book and are suitable for undergraduate students in engineering and physical science.

Overall, The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition is an invaluable resource for students seeking to develop their skills in mathematical proof. With its comprehensive coverage of proof techniques, logical reasoning, and mathematical topics, this edition provides students with the foundation they need to excel in their studies and pursue careers in fields that require advanced mathematical knowledge.

Weight: 860g
Dimension: 237 x 194 x 26 (mm)
ISBN-13: 9780323990202
Edition number: 5 ed