Algebraic Topology

Homology and Cohomology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486462390

Category: Mathematics

Page: 272

View: 6142

Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
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Algebraic Topology

Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 9780486691312

Category: Mathematics

Page: 375

View: 7611

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
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Homology Theory on Algebraic Varieties

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486799905

Category: Mathematics

Page: 128

View: 345

Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and relative cycles. 1958 edition.
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Cohomology Operations and Applications in Homotopy Theory

Author: Robert E. Mosher,Martin C. Tangora

Publisher: Courier Corporation

ISBN: 0486466647

Category: Mathematics

Page: 214

View: 673

Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
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Topology

Author: John Gilbert Hocking,Gail S. Young

Publisher: Courier Corporation

ISBN: 0486656764

Category: Mathematics

Page: 374

View: 3727

Designed as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.
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Lectures on the Mathematical Method in Analytical Economics

Author: Jacob T. Schwartz

Publisher: Courier Dover Publications

ISBN: 0486835596

Category: Mathematics

Page: 304

View: 4492

Early but still useful contribution to the science of mathematical economics explores the Leontif model and the technological basis of production, theory of business cycles, and neoclassical equilibrium theory. 1961 edition.
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Topology and Geometry for Physicists

Author: Charles Nash,Siddhartha Sen

Publisher: Courier Corporation

ISBN: 0486318362

Category: Mathematics

Page: 320

View: 5523

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.
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Transcendental and Algebraic Numbers

Author: A. O. Gelfond

Publisher: Courier Dover Publications

ISBN: 0486802256

Category: Mathematics

Page: 208

View: 975

Primarily an advanced study of the modern theory of transcendental and algebraic numbers, this treatment by a distinguished Soviet mathematician focuses on the theory's fundamental methods. The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory. The problem of approximating algebraic numbers is also studied as a case in the theory of transcendental numbers. Topics include the Thue-Siegel theorem, the Hermite-Lindemann theorem on the transcendency of the exponential function, and the work of C. Siegel on the transcendency of the Bessel functions and of the solutions of other differential equations. The final chapter considers the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme, which provides a helpful guide to understanding the proof's progression.
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Topological Methods in Galois Representation Theory

Author: Victor P. Snaith

Publisher: Courier Corporation

ISBN: 0486782271

Category: Mathematics

Page: 320

View: 3472

This advanced monograph on Galois representation theory by a renowned algebraist covers abelian and nonabelian cohomology of groups, characteristic classes of forms and algebras, explicit Brauer induction theory, more. 1989 edition.
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The Functions of Mathematical Physics

Author: Harry Hochstadt

Publisher: Courier Corporation

ISBN: 0486652149

Category: Science

Page: 322

View: 6529

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.
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Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

View: 1761

Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.
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Curvature and Homology

Author: Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 048640207X

Category: Mathematics

Page: 395

View: 5378

This systematic and self-contained treatment examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. It generalizes the theory of Riemann surfaces to that of Riemannian manifolds. Includes four helpful appendixes. "A valuable survey." — Nature. 1962 edition.
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Selected Topics in the Classical Theory of Functions of a Complex Variable

Author: Maurice Heins

Publisher: Courier Corporation

ISBN: 0486800695

Category: Mathematics

Page: 176

View: 2801

Elegant and concise, this text explores properties of meromorphic functions, Picard theorem, harmonic and subharmonic functions, applications, and boundary behavior of the Riemann mapping function for simply connected Jordan regions. 1962 edition.
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An Introduction to the Theory of Elasticity

Author: R. J. Atkin,N. Fox

Publisher: Courier Corporation

ISBN: 0486150992

Category: Science

Page: 272

View: 2838

Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.
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The Cumulative Book Index

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 8002

A world list of books in the English language.
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