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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.

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.

Mathematics for the Physical Sciences

Mathematics for the Physical Sciences Author Laurent Schwartz
ISBN-10 9780486466620
Release 2008
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.

Lapses in Mathematical Reasoning

Lapses in Mathematical Reasoning Author V. M. Bradis
ISBN-10 9780486816579
Release 2016-10-28
Pages 224
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Designed as a method for teaching correct mathematical thinking to high school students, this book contains a brilliantly constructed series of what the authors call "lapses," erroneous statements that are part of a larger mathematical argument. These lapses lead to sophism or mathematical absurdities. The ingenious idea behind this technique is to lead the student deliberately toward a clearly false conclusion. The teacher and student then go back and analyze the lapse as a way to correct the problem. The authors begin by focusing on exercises in refuting erroneous mathematical arguments and their classification. The remaining chapters discuss examples of false arguments in arithmetic, algebra, geometry, trigonometry, and approximate computations. Ideally, students will come to the correct insights and conclusions on their own; however, each argument is followed by a detailed analysis of the false reasoning. Stimulating and unique, this book is an intriguing and enjoyable way to teach students critical mathematical reasoning skills.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics Author Arthur Godon Webster
ISBN-10 9780486805153
Release 2016-06-15
Pages 464
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A classic treatise on partial differential equations, this comprehensive work by one of America's greatest early mathematical physicists covers the basic method, theory, and application of partial differential equations. In addition to its value as an introductory and supplementary text for students, this volume constitutes a fine reference for mathematicians, physicists, and research engineers. Detailed coverage includes Fourier series; integral and elliptic equations; spherical, cylindrical, and ellipsoidal harmonics; Cauchy's method; boundary problems; the Riemann-Volterra method; and many other basic topics. The self-contained treatment fully develops the theory and application of partial differential equations to virtually every relevant field: vibration, elasticity, potential theory, the theory of sound, wave propagation, heat conduction, and many more. A helpful Appendix provides background on Jacobians, double limits, uniform convergence, definite integrals, complex variables, and linear differential equations.

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.

Mathematical Logic

Mathematical Logic Author Joel W. Robbin
ISBN-10 9780486450186
Release 2006-07-07
Pages 212
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Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds — including mathematics, philosophy, linguistics, computer science, and engineering. It features numerous exercises of varying levels of difficulty, many with solutions. A survey of the propositional calculus is followed by chapters on first-order logic and first-order recursive arithmetic. An examination of the arithmetization of syntax follows, along with a review of the incompleteness theorems and other applications of the Liar Paradox. The text concludes with a study of second-order logic and an appendix on set theory that will prove valuable to students with little or no mathematical background.

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.

Mathematical Recreations of Lewis Carroll

Mathematical Recreations of Lewis Carroll Author Lewis Carroll
ISBN-10 9780486204932
Release 1958-06-01
Pages 261
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Charles L. Dodgson was a Mathematical Lecturer at Oxford, better known as Lewis Carroll. This collection of mathematical puzzles was compiled in 1893, following years of insomnia. Dodgson claimed to have solved every puzzle, without pencil and paper, during his sleepness nights. This incredible feat is difficult to comprehend, even for such a genius. The complexity and good humor of the problems and tales are suggestive of his well-loved "Alice in Wonderland". Dodgson also hints at his pioneering the field of symbolic logic.

The Continuum and Other Types of Serial Order

The Continuum and Other Types of Serial Order Author Edward V. Huntington
ISBN-10 9780486161075
Release 2017-05-25
Pages 96
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Based on the Dedekind-Cantor ordinal theory, this classic presents the best systematic elementary account of modern theory of the continuum as a type of serial order. 119 footnotes. 1917 edition.

The Mathematics of Games of Strategy

The Mathematics of Games of Strategy Author Melvin Dresher
ISBN-10 9780486150062
Release 2012-11-14
Pages 208
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This text offers an exceptionally clear presentation of the mathematical theory of games of strategy and its applications to many fields including economics, military, business, and operations research.

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

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.

Principles of Topology

Principles of Topology Author Fred H. Croom
ISBN-10 9780486810447
Release 2016-03-17
Pages 336
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Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.

Figures for Fun

Figures for Fun Author Yakov Perelman
ISBN-10 9780486803456
Release 2015-03-02
Pages 144
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"Does your brain need a workout? Are you wondering what to do? Well this could be the book for you! This is a great book for anyone who is looking for a challenge and, if you get too stuck, the author kindly also provided the answers at the end of each chapter!" — Splashes Into Books Give your mind a playful workout with this collection of more than 100 inventive puzzles. Finding the solutions requires only minimal mathematical knowledge and will test your imagination as well as your brainpower. The motley collection ranges from conundrums and mathematical stunts to practical situations involving counting and measuring. Chess problems, magic squares, and a host of other intriguing scenarios will amuse and challenge puzzle enthusiasts and fans of recreational mathematics. Answers appear at the end of each chapter. These puzzles are the inventions of a gifted Soviet mathematician, Yakov Perelman, whose popular science books on astronomy, physics, and mathematics inspired generations of readers. Perelman's distinctive style, abounding in wit and ingenuity, adds a special flair to his timeless riddles and brainteasers.