# Proofs from THE BOOK

Title | Proofs from THE BOOK PDF eBook |

Author | Martin Aigner |

Publisher | Springer Science & Business Media |

Pages | 194 |

Release | 2013-06-29 |

Genre | Mathematics |

ISBN | 3662223430 |

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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.

# Book of Proof

Title | Book of Proof PDF eBook |

Author | Richard H. Hammack |

Publisher | |

Pages | 314 |

Release | 2016-01-01 |

Genre | Mathematics |

ISBN | 9780989472111 |

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This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

# How to Prove It

Title | How to Prove It PDF eBook |

Author | Daniel J. Velleman |

Publisher | Cambridge University Press |

Pages | 401 |

Release | 2006-01-16 |

Genre | Mathematics |

ISBN | 0521861241 |

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Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

# Introduction to Proof in Abstract Mathematics

Title | Introduction to Proof in Abstract Mathematics PDF eBook |

Author | Andrew Wohlgemuth |

Publisher | Courier Corporation |

Pages | 385 |

Release | 2014-06-10 |

Genre | Mathematics |

ISBN | 0486141683 |

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The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.

# Proofs Without Words

Title | Proofs Without Words PDF eBook |

Author | Roger B. Nelsen |

Publisher | MAA |

Pages | 166 |

Release | 1993 |

Genre | Logic, Symbolic and mathematical |

ISBN | 9780883857007 |

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# Introduction · to Mathematical Structures and · Proofs

Title | Introduction · to Mathematical Structures and · Proofs PDF eBook |

Author | Larry Gerstein |

Publisher | Springer Science & Business Media |

Pages | 355 |

Release | 2013-11-21 |

Genre | Science |

ISBN | 1468467085 |

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This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.

# Mathematical Proofs

Title | Mathematical Proofs PDF eBook |

Author | Gary Chartrand |

Publisher | Pearson |

Pages | 0 |

Release | 2013 |

Genre | Proof theory |

ISBN | 9780321797094 |

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This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory.