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Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems

4 July 2013

**Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems**

English | ISBN: 9810215843 | 1994 | 400 pages | PDF | 8 MB

This book begins by introducing the area method, and recent results in automating the area method. It can either be used as a geometry text for students and geometers, or be regarded as a monograph on machine proofs in geometry. By automating the area method, this book presents a systematic way of proving geometry theorems using traditional methods. The authors aim to make learning and teaching geometry easier through this book.

4 July 2013

English | ISBN: 9810215843 | 1994 | 400 pages | PDF | 8 MB

This book begins by introducing the area method, and recent results in automating the area method. It can either be used as a geometry text for students and geometers, or be regarded as a monograph on machine proofs in geometry. By automating the area method, this book presents a systematic way of proving geometry theorems using traditional methods. The authors aim to make learning and teaching geometry easier through this book.

Normalization, Cut-Elimination, and the Theory of Proofs

3 August 2011

**Normalization, Cut-Elimination, and the Theory of Proofs**

Gentzen's cut-elimination theorem is widely used as a tool for meta-mathematical investigations. It is sometimes claimed however that the theorem and its proof have interest which is independent of these applications and derives from the information they supply about the structure of proofs in general. Ungar investigates this claim in the context of first order logic. Ungar gives an account of Gentzen's theorem for various formalisms and discusses the difficulties involved in treating these different versions uniformly, as instances of a single theorem which is not tied to a particular system of rules. By extending the theorem to a natural deduction calculus whose derivations are allowed to have more than one conclusion, Ungar argues that the different versions of the theorem are more or less natural specializations of a single result whose significance can be understood in terms of the proofs represented by formal derivations. A concluding discussion focuses on the relationship between proofs and formal derivations, and the role proofs may play as part of a general theory of evidence. ...

3 August 2011

1992 | 236 | ISBN: 0937073830 | DJVU | 3 Mb

Gentzen's cut-elimination theorem is widely used as a tool for meta-mathematical investigations. It is sometimes claimed however that the theorem and its proof have interest which is independent of these applications and derives from the information they supply about the structure of proofs in general. Ungar investigates this claim in the context of first order logic. Ungar gives an account of Gentzen's theorem for various formalisms and discusses the difficulties involved in treating these different versions uniformly, as instances of a single theorem which is not tied to a particular system of rules. By extending the theorem to a natural deduction calculus whose derivations are allowed to have more than one conclusion, Ungar argues that the different versions of the theorem are more or less natural specializations of a single result whose significance can be understood in terms of the proofs represented by formal derivations. A concluding discussion focuses on the relationship between proofs and formal derivations, and the role proofs may play as part of a general theory of evidence. ...

Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

12 June 2010

**Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry**

Publisher: Springer 1998 | 214 Pages | ISBN: 0306459671 | PDF | 6 MB

A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians.

12 June 2010

Publisher: Springer 1998 | 214 Pages | ISBN: 0306459671 | PDF | 6 MB

A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians.

The Nuts and Bolts of Proofs, Third Edition - An Introduction to Mathematical Proofs

23 September 2013

**The Nuts and Bolts of Proofs, Third Edition - An Introduction to Mathematical Proofs**

English | 2005 | ISBN: 0120885093 | 193 pages | PDF | 6 MB

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.

23 September 2013

English | 2005 | ISBN: 0120885093 | 193 pages | PDF | 6 MB

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.

Proofs From The Book

9 April 2010

**Proofs from THE BOOK**

Springer | 2009-11-23 | ISBN: 3642008550 | 274 pages | PDF | 14 MB

"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999

9 April 2010

Springer | 2009-11-23 | ISBN: 3642008550 | 274 pages | PDF | 14 MB

"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999

Gary Halbert - Hurricane Andrew Seminar

20 January 2012

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20 January 2012

Gary Halbert - Hurricane Andrew Seminar

English + 11 DVDS + 6.32 GB

English + 11 DVDS + 6.32 GB

Mathematical Proofs - A Transition to Advanced Mathematics, 3rd Edition

10 September 2013

**Mathematical Proofs - A Transition to Advanced Mathematics, 3rd Edition**

ISBN: 0321797094 | 2012 | PDF | 416 pages | 3 MB

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own.

10 September 2013

ISBN: 0321797094 | 2012 | PDF | 416 pages | 3 MB

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own.

Introduction to Mathematical Structures and Proofs (2nd edition)

3 March 2013

**Introduction to Mathematical Structures and Proofs (2nd edition)**

Larry J. Gerstein

Published: 2012-06-06 | ISBN: 1461442648 | PDF | 414 pages | 3 MB

3 March 2013

Larry J. Gerstein

Published: 2012-06-06 | ISBN: 1461442648 | PDF | 414 pages | 3 MB

Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion

2 June 2013

**Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion**

Published: 2013-02-22 | ISBN: 3034802234 | PDF | 452 pages | 3 MB

2 June 2013

Published: 2013-02-22 | ISBN: 3034802234 | PDF | 452 pages | 3 MB

Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes

20 May 2011

**Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes**

Here is a third trip around the mathematical circle, and, at least for some time, it must be the last such trip. I cannot deny that it has been fun making these trips, but there are so many other, and more serious, things I wish to write that it is high time I set the mathematical stories and anecdotes aside—with somewhat more than half of my collection now in print. Except for the first quadrant and the tail end of the fourth quadrant, the items in this third set of stories are classified by geography, in contrast to the classification by chronology in In Mathematical Circles and by subject matter in Mathematical Circles Revisited. ...

20 May 2011

1972 | 186 | ISBN: 0871501546 | DJVU | 2 Mb

Here is a third trip around the mathematical circle, and, at least for some time, it must be the last such trip. I cannot deny that it has been fun making these trips, but there are so many other, and more serious, things I wish to write that it is high time I set the mathematical stories and anecdotes aside—with somewhat more than half of my collection now in print. Except for the first quadrant and the tail end of the fourth quadrant, the items in this third set of stories are classified by geography, in contrast to the classification by chronology in In Mathematical Circles and by subject matter in Mathematical Circles Revisited. ...