abstract and concrete categories the joy of cats dover books on mathematics

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Abstract And Concrete Categories

Author : Jiri Adamek
ISBN : 0486469344
Genre : Mathematics
File Size : 58. 12 MB
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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

Author : Andrei-Tudor Patrascu
ISBN : 9783319461434
Genre : Science
File Size : 90. 40 MB
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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.

Mathematics For The Physical Sciences

Author : Laurent Schwartz
ISBN : 9780486466620
Genre : Mathematics
File Size : 23. 46 MB
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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.

Lectures On The Mathematical Method In Analytical Economics

Author : Jacob T. Schwartz
ISBN : 9780486828039
Genre : Business & Economics
File Size : 37. 94 MB
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An early but still useful and frequently cited contribution to the science of mathematical economics, this volume is geared toward graduate students in the field. Prerequisites include familiarity with the basic theory of matrices and linear transformations and with elementary calculus. Author Jacob T. Schwartz begins his treatment with an exploration of the Leontief input-output model, which forms a general framework for subsequent material. An introductory treatment of price theory in the Leontief model is followed by an examination of the business-cycle theory, following ideas pioneered by Lloyd Metzler and John Maynard Keynes. In the final section, Schwartz applies the teachings of previous chapters to a critique of the general equilibrium approach devised by Léon Walras as the theory of supply and demand, and he synthesizes the notions of Walras and Keynes. 1961 edition.

The Surprise Attack In Mathematical Problems

Author : Louis A. Graham
ISBN : 9780486820767
Genre : Mathematics
File Size : 30. 82 MB
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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 Red Book Of Mathematical Problems

Author : Kenneth S. Williams
ISBN : 9780486151823
Genre : Mathematics
File Size : 81. 62 MB
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Handy 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.

Physics Of Fully Ionized Gases

Author : Lyman Spitzer
ISBN : 9780486151588
Genre : Science
File Size : 63. 36 MB
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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.

A Short Account Of The History Of Mathematics

Author : W. W. Rouse Ball
ISBN : 9780486157849
Genre : Mathematics
File Size : 88. 82 MB
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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.

Differential Games

Author : Rufus Isaacs
ISBN : 9780486135984
Genre : Mathematics
File Size : 75. 53 MB
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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

Author : Emil Artin
ISBN : 9780486158259
Genre : Mathematics
File Size : 84. 77 MB
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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.

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