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˜A œframework for priority arguments par Lerman,, M. Publication : New York Cambridge University Press 2010 . xvi, 176 pages , "This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner"--Provided by publisher. 24 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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A transition to abstract mathematics: learning mathematical thinking and writing par Maddox, Randall. Publication : [S.l.] Academic Press 2009 . 356 p. , Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. * Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction * Explains identification of techniques and how they are applied in the specific problem * Illustrates how to read written proofs with many step by step examples * Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter * The Instructors Guide and Solutions Manual points out which exercises simply must be either assigned or at least discussed because they undergird later results. 24 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Gentzen calculi for modal propositional logic par Poggiolesi, Francesca Publication : Dordrecht | New York Springer 2011 . 222 pages 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Hybrid logic and its proof-theory par Braüner, Torben. Publication : Dordrecht | New York Springer. 2011 . xiii, 231 pages 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Mathematical thinking and writing A transition to higher mathematics par Maddox, Randall B. Publication : [S.l.] Academic Press 2002 . 304 p. , The 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 significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision. 25 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Methods of cut-elimination par Baaz, Matthias. Publication : Dordrecht ; | Heidelberg | New York : Springer 2011 . vi, 287 pages 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Set theory : boolean-valued models and independence proofs par Bell, John L. Publication : Oxford Clarendon Press 2005 . 1 vol. (VIII-191 p.) , This second edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory ,. It provides an exposition of some of the most important results in set theory obtained in the 20th century - the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the second edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It also includes recent developments in the field and numerous exercises, along with the enlarged and entirely updated background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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The nuts and bolts of proofs / par Cupillari, Antonella. Publication : . 1 online resource (xii, 179 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780120885091,

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Lectures on the Curry-Howard isomorphism / par Sørensen, Morten Heine. Publication : . 1 online resource (xiv, 442 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780444520777,  http://www.sciencedirect.com/science/publication?issn=0049237X&volume=149,

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Logic in algebraic form : Three languages and theories / par Craig, William, Publication : . 1 online resource (viii, 204 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780444104779,

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Proof theory / par Takeuti, Gaisi, Publication : . 1 online resource (vii, 372 pages) , Based on a series of lectures given at the Symposium on Intuitionism and Proof Theory held at Buffalo in the summer of 1968. | Includes index. Disponibilité :  http://www.sciencedirect.com/science/book/9780444104922,

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Statistical learning with sparsity : the lasso and generalizations / par Hastie, Trevor. Publication : Boca Raton : CRC Press, Taylor & Francis Group, 2015 . xv, 351 pages : , "A Chapman & Hall book." 25 cm. Date : 2015 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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