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Proof Logic and Formalizationby Michael Detlefsen
Routledge 1992; US$ 135.00A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification. more...
Tracking Reasonby Jody Azzouni
Oxford University Press 2006; US$ 24.95When ordinary people - mathematicians among them - take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. This book investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. more...
Lectures on the Curry-Howard Isomorphismby Morten Heine Sørensen; Pawel Urzyczyn
Elsevier 2006; US$ 150.00The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov,... more...
Mathematical Thinking and Writingby Randall Maddox
Elsevier 2001; US$ 107.00The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most... more...
The Nuts and Bolts of Proofsby Antonella Cupillari
Elsevier 2005; US$ 51.95The 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" more...
Handbook of Proof Theoryby S.R. Buss
Elsevier 1998; US$ 182.00This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science. more...
Math Proofs Demystifiedby 'Stan Gibilisco
McGraw-Hill 2005; US$ 19.95Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not uncommon to have philosophy and law students grappling with proofs. This book is the perfect resource for demystifying the techniques and principles that govern the mathematical proof area, and is done with the standard “Demystified” level, questions and answers, and accessibility. more...
The Moment of Proofby Donald C. Benson
Oxford University Press, USA 2000; US$ 25.95When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many and varied. The book is packed with intriguing conundrums--Loyd's Fifteen Puzzle, the Petersburg Paradox, the Chaos Game, the Monty Hall Problem, the Prisoners' Dilemma--as well as many mathematical curiosities. We learn how to perform... more...
Logic in algebraic formby William Craig
Elsevier Science & Technology 2000; US$ 250.00Provability, Computability and Reflection more...