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Abstract and Concrete Categories

Abstract and Concrete Categories Author Jiri Adamek
ISBN-10 0486469344
Release 2009-01-01
Pages 517
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This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists Author Benjamin C. Pierce
ISBN-10 0262660717
Release 1991
Pages 100
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Basic Category Theory for Computer Scientists provides a straightforward presentationof the basic constructions and terminology of category theory, including limits, functors, naturaltransformations, adjoints, and cartesian closed categories.

The Universal Coefficient Theorem and Quantum Field Theory

The Universal Coefficient Theorem and Quantum Field Theory Author Andrei-Tudor Patrascu
ISBN-10 9783319461434
Release 2016-09-23
Pages 270
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This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

Category Theory in Context

Category Theory in Context Author Emily Riehl
ISBN-10 9780486820804
Release 2017-03-09
Pages 272
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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Elementary Induction on Abstract Structures

Elementary Induction on Abstract Structures Author Yiannis N. Moschovakis
ISBN-10 9780486152011
Release 2014-06-10
Pages 240
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Well-written research monograph, recommended for students and professionals interested in model theory and definability theory. "Easy to use and a pleasure to read." — Bulletin of the American Mathematical Society. 1974 edition.

Mathematics for the Physical Sciences

Mathematics for the Physical Sciences Author Laurent Schwartz
ISBN-10 9780486466620
Release 2008-04-21
Pages 358
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Concise treatment of mathematical entities employs examples from the physical sciences. Topics include distribution theory, Fourier series, Laplace transforms, wave and heat conduction equations, and gamma and Bessel functions. 1966 edition.

The Surprise Attack in Mathematical Problems

The Surprise Attack in Mathematical Problems Author Louis A. Graham
ISBN-10 9780486820767
Release 2017-03-17
Pages 160
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An unusual problem book that focuses on the method of solution, this collection spotlights 52 problems, each with several approaches to situations involving measurement of geometrical spaces, probabilities, distances, relative motion, more.

The Functions of Mathematical Physics

The Functions of Mathematical Physics Author Harry Hochstadt
ISBN-10 9780486652146
Release 1986
Pages 322
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A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.

A Short Account of the History of Mathematics

A Short Account of the History of Mathematics Author W. W. Rouse Ball
ISBN-10 9780486157849
Release 2012-04-27
Pages 560
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This standard text treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.

The Red Book of Mathematical Problems

The Red Book of Mathematical Problems Author Kenneth S. Williams
ISBN-10 9780486151823
Release 2012-06-29
Pages 192
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DIVHandy compilation of 100 practice problems, hints and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Preface to the First Edition. Sources. 1988 edition. /div

Arrows structures and functors

Arrows  structures  and functors Author Michael A. Arbib
ISBN-10 UOM:39015000487671
Release 1975
Pages 185
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Arrows structures and functors has been writing in one form or another for most of life. You can find so many inspiration from Arrows structures and functors also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Arrows structures and functors book for free.

Elements of the Theory of Functions

Elements of the Theory of Functions Author Konrad Knopp
ISBN-10 9780486165608
Release 2016-10-05
Pages 160
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Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.

The Theory of Linear Viscoelasticity

The Theory of Linear Viscoelasticity Author D. R. Bland
ISBN-10 9780486462691
Release 2016-10-20
Pages 144
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This concise introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed sections present examples of stress-related problems, including sinusoidal oscillation problems, quasi-static problems, and dynamic problems. 1960 edition.

Physics of Fully Ionized Gases

Physics of Fully Ionized Gases Author Lyman Spitzer
ISBN-10 9780486151588
Release 2013-01-18
Pages 192
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An introductory course in theoretical physics is the sole prerequisite for this general but simple introduction to the fields of plasma and fusion research. 1962 edition.

Differential Games

Differential Games Author Rufus Isaacs
ISBN-10 9780486135984
Release 2012-04-26
Pages 416
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Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

Galois Theory

Galois Theory Author Emil Artin
ISBN-10 9780486158259
Release 2012-05-24
Pages 86
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Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Optimal Control and Estimation

Optimal Control and Estimation Author Robert F. Stengel
ISBN-10 9780486134819
Release 2012-10-16
Pages 672
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Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.