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Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 1461208033
Category : Science
Languages : en
Pages : 304
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Book Description
The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain geometrical problems posed by the ancient Greeks cannot be solved by ruler and compass alone. The second part presents some fundamental topics of interest from the past two centuries, including proof of G del's incompleteness theorem, together with a discussion of its implications.
Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 1461208033
Category : Science
Languages : en
Pages : 304
Get Book Here
Book Description
The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain geometrical problems posed by the ancient Greeks cannot be solved by ruler and compass alone. The second part presents some fundamental topics of interest from the past two centuries, including proof of G del's incompleteness theorem, together with a discussion of its implications.
Author: I︠U︡riĭ V. Matii︠a︡sevich
Publisher: MIT Press
ISBN: 9780262132954
Category : Computers
Languages : en
Pages : 296
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Book Description
This book presents the full, self-contained negative solution of Hilbert's 10th problem.
Author: Alexandra Shlapentokh
Publisher: Cambridge University Press
ISBN: 9780521833608
Category : Mathematics
Languages : en
Pages : 342
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Book Description
Publisher description
Author: Sarvadaman Chowla
Publisher: CRC Press
ISBN: 9780677001401
Category : Mathematics
Languages : en
Pages : 144
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Book Description
Author: Julia Robinson
Publisher: American Mathematical Soc.
ISBN: 9780821805756
Category : Mathematics
Languages : en
Pages : 388
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Book Description
This volume presents all the published works -- spanning more than thirty years -- of Julia Bowman Robinson. These papers constitute important contributions to the theory of effectively calculable functions and to its applications. Outstanding among the latter are Robinson's proof of the effective unsolvability of the decision problem for the rational number field (and, consequently of that for the first-order theory of all fields), and her work that provided the central step toward the negative solution of Hilbert's Tenth Problem. These results provide upper bound for what one can hope to obtain in the way of positive solutions to the decision problem for special classes of fields and for special classes of diophantine equations, respectively. Besides thematic unity, Robinson's papers are distinguished by their clarity of purpose and accessibility to non-specialists as well as specialists. The volume also includes an extensive biographical memoir on the life and work of Robinson, who will be remembered not only for her distinctive and vital contributions, but also as the first woman to be elected to the mathematical section of the National Academy of Sciences and as the first woman to be President of the American Mathematical Society.
Author: Richard E. Hodel
Publisher: Courier Corporation
ISBN: 0486497852
Category : Mathematics
Languages : en
Pages : 514
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Book Description
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Author: Robert Tubbs
Publisher: Springer
ISBN: 9811026459
Category : Mathematics
Languages : en
Pages : 91
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Book Description
This exposition is primarily a survey of the elementary yet subtle innovations of several mathematicians between 1929 and 1934 that led to partial and then complete solutions to Hilbert’s Seventh Problem (from the International Congress of Mathematicians in Paris, 1900). This volume is suitable for both mathematics students, wishing to experience how different mathematical ideas can come together to establish results, and for research mathematicians interested in the fascinating progression of mathematical ideas that solved Hilbert’s problem and established a modern theory of transcendental numbers.
Author: Jeremy Gray
Publisher: Oxford University Press, USA
ISBN: 9780198506515
Category : Mathematics
Languages : en
Pages : 340
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Book Description
David Hilbert was arguably the leading mathematician of his generation. He was among the few mathematicians who could reshape mathematics, and was able to because he brought together an impressive technical power and mastery of detail with a vision of where the subject was going and how it should get there. This was the unique combination which he brought to the setting of his famous 23 Problems. Few problems in mathematics have the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving individual ones such as Fermat's last theorem, and several remain unsolved including the Riemann hypotheses, which has eluded all the great minds of this century. A hundred years on, it is timely to take a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this fascinating new book, Jeremy Gray and David Rowe consider what has made this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. The book is written in a clear and lively manner and will appeal both to the general reader with an interest in mathematics and to mathematicians themselves.
Author: Gerald E. Sacks
Publisher: World Scientific
ISBN: 9789812564894
Category : Mathematics
Languages : en
Pages : 712
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Book Description
This invaluable book is a collection of 31 important both inideas and results papers published by mathematical logicians inthe 20th Century. The papers have been selected by Professor Gerald ESacks. Some of the authors are Gdel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin.
Author: David Harel
Publisher: MIT Press
ISBN: 9780262263023
Category : Computers
Languages : en
Pages : 492
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Book Description
This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.
