REAL VARIABLES WITH BASIC METRIC SPACE TOPOLOGY DOVER BOOKS ON MATHEMATICS

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Author : Robert B. Ash
ISBN : 9780486472201
Genre : Mathematics
File Size : 43.29 MB
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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.

Author : John G. Hocking
ISBN : 9780486141091
Genre : Mathematics
File Size : 37.71 MB
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Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.

Author : David A. Sprecher
ISBN : 9780486153254
Genre : Mathematics
File Size : 73.69 MB
Format : PDF, ePub
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Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.

Author : Paul Alexandroff
ISBN : 9780486155067
Genre : Mathematics
File Size : 46.76 MB
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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Author : John D. Baum
ISBN : 9780486668260
Genre : Mathematics
File Size : 31.61 MB
Format : PDF
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Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Author : Ian Stewart
ISBN : 9780486150963
Genre : Mathematics
File Size : 61.18 MB
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Twelve essays take a playful approach to mathematics, investigating the topology of a blanket, the odds of beating a superior tennis player, and how to distinguish between fact and fallacy.

Author : Kenneth S. Williams
ISBN : 9780486151823
Genre : Mathematics
File Size : 21.76 MB
Format : PDF, Kindle
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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.

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 : 9780486158259
Genre : Mathematics
File Size : 77.15 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.

Author : Robert F. Stengel
ISBN : 9780486134819
Genre : Mathematics
File Size : 78.50 MB
Format : PDF
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Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.