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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 ProofsEnglish | 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. 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 Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry 12 June 2010 Mathematical Problems and Proofs: Combinatorics, Number Theory, and GeometryPublisher: 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 The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some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. Mathematical Proofs - A Transition to Advanced Mathematics, 3rd Edition 10 September 2013 Mathematical Proofs - A Transition to Advanced Mathematics, 3rd EditionISBN: 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. Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion 2 June 2013 Proofs of the Cantor-Bernstein Theorem: A Mathematical ExcursionPublished: 2013-02-22 | ISBN: 3034802234 | PDF | 452 pages | 3 MB Proofs From The Book 9 April 2010 Proofs from THE BOOKSpringer | 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 Introduction to Topology (Student Mathematical Library, V. 14) 20 September 2010 Introduction to Topology (Student Mathematical Library, V. 14)American Mathematical Society 2001 | 149 | ISBN: 0821821628 | PDF | 11 Mb
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on its style. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have important generalizations are presented." ...Math Made Visual Creating Images For 6 April 2010 Math Made Visual: Creating Images for Understanding MathematicsThe Mathematical Association of America | English | 2006-04-10 | ISBN: 0883857464 | 172 pages | PDF | 11 MB Is it possible to make mathematical drawings that help to understand mathematical idea, prooifs and arguments? The authors of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called "proofs without words." Hundreds of these have been published in "Mathematics Magazine" and "The College Mathematics Journal," as well as in other journals, books and on the Internet. Normalization, Cut-Elimination, and the Theory of Proofs 3 August 2011 Normalization, Cut-Elimination, and the Theory of Proofs 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. ... 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 TheoremsEnglish | 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. |