# 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.

# Proof in Geometry

Title | Proof in Geometry PDF eBook |

Author | A. I. Fetisov |

Publisher | Courier Corporation |

Pages | 130 |

Release | 2012-06-11 |

Genre | Mathematics |

ISBN | 0486154920 |

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This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.

# Proofs and Refutations

Title | Proofs and Refutations PDF eBook |

Author | Imre Lakatos |

Publisher | Cambridge University Press |

Pages | 190 |

Release | 1976 |

Genre | Mathematics |

ISBN | 9780521290388 |

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

# Reverse Mathematics

Title | Reverse Mathematics PDF eBook |

Author | John Stillwell |

Publisher | Princeton University Press |

Pages | 198 |

Release | 2019-09-24 |

Genre | Mathematics |

ISBN | 0691196419 |

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This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.

# An Introduction to Proof Theory

Title | An Introduction to Proof Theory PDF eBook |

Author | Paolo Mancosu |

Publisher | Oxford University Press |

Pages | 336 |

Release | 2021-08-12 |

Genre | Philosophy |

ISBN | 0192649299 |

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An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.