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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. |

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. |

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. |

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. |

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. |

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. |

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. |

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. |

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. |

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 |

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. |

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. |

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. |

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. |

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. |

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. |

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. |