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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.



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.



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.



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.



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.



Topoi

Topoi Author R. Goldblatt
ISBN-10 9781483299211
Release 2014-06-28
Pages 565
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The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''. The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.



Set Theory and Logic

Set Theory and Logic Author Robert R. Stoll
ISBN-10 9780486139647
Release 2012-05-23
Pages 512
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Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.



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.



Set Theory and the Continuum Hypothesis

Set Theory and the Continuum Hypothesis Author Paul J. Cohen
ISBN-10 9780486469218
Release 2008-12-09
Pages 154
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This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.



Introduction to Logic

Introduction to Logic Author Alfred Tarski
ISBN-10 9780486318899
Release 2013-07-04
Pages 272
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This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.



The Axiom of Choice

The Axiom of Choice Author Thomas J. Jech
ISBN-10 CORNELL:31924000209357
Release 1973
Pages 202
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The Axiom of Choice has been writing in one form or another for most of life. You can find so many inspiration from The Axiom of Choice also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Axiom of Choice book for free.



Pygmalion

Pygmalion Author SMITH
ISBN-10 9783034857444
Release 2013-12-14
Pages 190
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Pygmalion has been writing in one form or another for most of life. You can find so many inspiration from Pygmalion also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Pygmalion book for free.



The Hedgehog the Fox and the Magister s Pox

The Hedgehog  the Fox  and the Magister s Pox Author Stephen Jay Gould
ISBN-10 9780674061668
Release 2011-10-01
Pages 273
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In his final book, Gould offers a surprising and nuanced study of the complex relationship between our two great ways of knowing: science and the humanities, twin realms of knowledge that have been divided against each other for far too long.



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 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.



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 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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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.