The Nuts And Bolts Of Proofs An Introduction To Mathematical Proofs

The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * The "List of Symbols" has been extended.* Set Theory section has been strengthened with more examples and exercises.* Addition of "A Collection of Proofs"

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. Jumps right in with the needed vocabulary to get 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

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. 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 invaluable. 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

This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology

This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.