Feasible Mathematics Ii

Author : Peter Clote,Jeffrey B. Remmel
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 52,7 Mb
Release : 2013-03-13
Category : Computers
ISBN : 9781461225669

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Feasible Mathematics II by Peter Clote,Jeffrey B. Remmel Pdf

Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa tion device, such as a 'lUring machine or boolean circuit. Feasible math ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.

Author : Peter Clote,Jeffrey B. Remmel
Publisher : Unknown
Page : 447 pages
File Size : 47,9 Mb
Release : 1995
Category : Computational complexity
ISBN : 3764336757

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Feasible Mathematics II by Peter Clote,Jeffrey B. Remmel Pdf

Author : S.R. Buss,P.J. Scott
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 54,7 Mb
Release : 2013-03-07
Category : Computers
ISBN : 9781461234661

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Feasible Mathematics by S.R. Buss,P.J. Scott Pdf

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions of complexity classes, on finite model theory, on models of feasible computation for real numbers, on vector spaces and on recursion theory. The vVorkshop on Feasible Mathematics was sponsored by the Mathematical Sciences Institute and was held at Cornell University, June 26-28, 1989.

Author : Samuel Buss,P. J. Scott
Publisher : Unknown
Page : 364 pages
File Size : 50,6 Mb
Release : 2014-05-30
Category : Electronic
ISBN : 1461234670

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Feasible Mathematics by Samuel Buss,P. J. Scott Pdf

Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 52,5 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066

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Mathematics for Computer Science by Eric Lehman,F. Thomson Leighton,Albert R. Meyer Pdf

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Author : Samuel R. Buss,Philip J. Scott
Publisher : Unknown
Page : 350 pages
File Size : 55,8 Mb
Release : 1990
Category : Computational complexity
ISBN : 3764334835

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Feasible Mathematics by Samuel R. Buss,Philip J. Scott Pdf

Author : Juris Hartmanis
Publisher : SIAM
Page : 65 pages
File Size : 51,7 Mb
Release : 1978-01-01
Category : Mathematics
ISBN : 9780898710274

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Feasible Computations and Provable Complexity Properties by Juris Hartmanis Pdf

An overview of current developments in research on feasible computations; and its relation to provable properties of complexity of computations.

Author : Brian Hopkins
Publisher : MAA
Page : 342 pages
File Size : 51,8 Mb
Release : 2009
Category : Computers
ISBN : 0883851849

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Resources for Teaching Discrete Mathematics by Brian Hopkins Pdf

Hopkins collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs.

Author : H Neunzert
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400929791

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Proceedings of the Second European Symposium on Mathematics in Industry by H Neunzert Pdf

"Mathematics in Industry" - since the volume containing the proceedings of the 1985 Oberwolfach conference was published*), this subject has become more fashionable in Europe, America and also in the third world. The Europeans have come closer to each other: They formed a European Consortium for Mathematics in Industry, abbreviated ECMI. This ECMI supported mainly by mathematicians from Amsterdam, Bari, Eindhoven, Firenze, Kaiserslautem, Limerick, Linz, Paris, Oxford and Trondheim has become a legal entity with a rapidly growing number of members. It has organized a common, really European postgraduate programme, establishes contact between industry and universities and organizes other confer ences everywhere in the world. Industrial mathematics is a special method to get interesting problems; a special attitude of curiosity for technical or economical questions; a general rather broad knowledge in all branches of mathematics; but it always remains real mathematics. Our first proceedings contained many articles about "why and how to start". Now we are more selfconfident about our ideas: These proceedings include only exam ples of "how to do". It is a pleasure to see how many different kinds of good mathematics are applied to so many different problems from industry. Part of the selection criteria for this volume was that some of the applications of what is usually considered ivory tower mathematics be represented.

Author : Michael Harris
Publisher : Princeton University Press
Page : 468 pages
File Size : 48,6 Mb
Release : 2017-05-30
Category : Mathematics
ISBN : 9780691175836

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Mathematics without Apologies by Michael Harris Pdf

An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

Author : Disha Experts
Publisher : Disha Publications
Page : 599 pages
File Size : 46,8 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9789388919890

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10 in One Study Package for CBSE Mathematics Class 12 with Objective Questions & 3 Sample Papers 3rd Edition by Disha Experts Pdf

Author : Paul W. Beame,Samuel R. Buss
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 40,6 Mb
Release : 2024-06-26
Category : Mathematics
ISBN : 0821870823

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Proof Complexity and Feasible Arithmetics by Paul W. Beame,Samuel R. Buss Pdf

Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can be made but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether or not NP is equal to co-NP. In addition, these have important implications for the efficiency of automated reasoning systems. The last dozen years have seen several breakthroughs in the study of these resource requirement. Papers in this volume represent the proceedings of the DIMACS workshop on "Feasible Arithmetics and Proof Complexity" held in April 1996 in Rutgers, NJ, as part of the DIMACS Institute's Special Year on Logic and Algorithms. This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.

Author : James Bergin
Publisher : Routledge
Page : 713 pages
File Size : 52,8 Mb
Release : 2015-01-09
Category : Business & Economics
ISBN : 9781317820161

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Mathematics for Economists with Applications by James Bergin Pdf

Mathematics for Economists with Applications provides detailed coverage of the mathematical techniques essential for undergraduate and introductory graduate work in economics, business and finance. Beginning with linear algebra and matrix theory, the book develops the techniques of univariate and multivariate calculus used in economics, proceeding to discuss the theory of optimization in detail. Integration, differential and difference equations are considered in subsequent chapters. Uniquely, the book also features a discussion of statistics and probability, including a study of the key distributions and their role in hypothesis testing. Throughout the text, large numbers of new and insightful examples and an extensive use of graphs explain and motivate the material. Each chapter develops from an elementary level and builds to more advanced topics, providing logical progression for the student, and enabling instructors to prescribe material to the required level of the course. With coverage substantial in depth as well as breadth, and including a companion website at www.routledge.com/cw/bergin, containing exercises related to the worked examples from each chapter of the book, Mathematics for Economists with Applications contains everything needed to understand and apply the mathematical methods and practices fundamental to the study of economics.

Author : A.H. van der Burgh,J Simonis
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401118149

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Topics in Engineering Mathematics by A.H. van der Burgh,J Simonis Pdf

This volume presents a selection of expository papers on various topics in engineering mathematics. The papers concern model problems relating to, amongst others, the automobile and shipping industries, transportation networks and wave propagation. Among the methods treated are numerical methods, such as the finite element method and Newton's method, Karmarkar's interior point method and generalizations, and recurrence and induction in computer science. This volume will be of great interest to applied mathematicians, physicists and engineers interested in recent developments in engineering mathematics. The papers are written with an emphasis on exposition and should be accessible to all members of scientific community interested in modeling and solving real-life problems.

Author : H.K. Dass, Rama Verma & Bhagwat S. Sharma
Publisher : S. Chand Publishing
Page : 128 pages
File Size : 49,8 Mb
Release : 2024-06-26
Category : Mathematics
ISBN : 9788121938464

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S.Chand’S Mathematics For Class IX Term II by H.K. Dass, Rama Verma & Bhagwat S. Sharma Pdf

S. Chand’s Mathematics books for Classes IX and X are completely based on CCE pattern of CBSE. The book for Term I covers the syllabus from April to September and the book for Term II covers the syllabus from October to March.