books tagged “topology”

books tagged “topology”

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The 85 Ways to Tie a Tie: The Science and Aesthetics of Tie Knots
by Thomas Fink, Yong Mao

ISBN 0767906438 (0-7679-0643-8)
Hardcover, Broadway Books

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- The 85 Ways to Tie a Tie: The Science and Aesthetics of Tie Knots: ISBN 0767906438 (0-7679-0643-8)
  Hardcover, Broadway Books
Algebraic Topology
by Allen Hatcher

ISBN 0521795400 (0-521-79540-0)
Softcover, Cambridge Univ Pr

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- Algebraic Topology: ISBN 0521795400 (0-521-79540-0)
  Softcover, Cambridge Univ Pr
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Algebraic Topology
by C. R. F. Maunder

ISBN 0486691314 (0-486-69131-4)
Softcover, Dover Pubns

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Book summary:
Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes, and other topics. Each chapter contains exercises and suggestions for further reading. 1980 corrected edition.
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- Algebraic Topology: ISBN 0486691314 (0-486-69131-4)
  Softcover, Dover Pubns
Algebraic Topology: An Introduction
by William S. Massey

ISBN 0387902716 (0-387-90271-6)
Hardcover, Springer Verlag

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- Algebraic Topology: An Introduction: ISBN 0387902716 (0-387-90271-6)
  Hardcover, Springer Verlag
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The Annotated Flatland: A Romance of Many Dimensions
by Ian Stewart, Edwin Abbott Abbott

ISBN 0738205419 (0-7382-0541-9)
Hardcover, Perseus Books Group

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Book summary:
The product of an agreeably dotty cleric named Edwin Abbott Abbott and first published in 1884, Flatland distills all that the Victorian era knew of higher mathematics--and then some--into a witty, complex novel of ideas.
Ian Stewart, the author of the equally witty sequel, Flatterland--which adds to Abbott's store of science the key discoveries made since--does a superb job of explaining the original book's enigmas, allusions, ironies, implausibilities, and what Douglas Hofstadter would call "metamagical themas." Among other things, Stewart comments on Abbott's comments on such things as the nature/nurture controversy, the fourth dimension and beyond, the role of multidimensional spaces in economic systems, infinite series and perfect squares, celestial mechanics, and other matters close to the hearts of cosmologists and science buffs alike.
Stewart's notes make an entertaining and learned addition to an already classic bit of writing--one that has never been out of print since its first publication. For both devoted Abbott fans and newcomers to his work, this is the edition to have. --Gregory McNamee [via]
More editions of The Annotated Flatland: A Romance of Many Dimensions:
- The Annotated Flatland: A Romance of Many Dimensions: ISBN 0738205419 (0-7382-0541-9)
  Hardcover, Perseus Books Group
Basic Topology
by M. A. Armstrong

ISBN 0387908390 (0-387-90839-0)
Hardcover, Springer London, Limited

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- Basic Topology: ISBN 0387908390 (0-387-90839-0)
  Hardcover, Springer London, Limited
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A Combinatorial Introduction to Topology
by Michael Henle

ISBN 0486679667 (0-486-67966-7)
Softcover, Dover Pubns

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Book summary:
Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some knowledge of differential equations and multivariate calculus required. Many problems and exercises (some solutions) integrated into the text. 1979 edition. Bibliography.
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- A Combinatorial Introduction to Topology: ISBN 0486679667 (0-486-67966-7)
  Softcover, Dover Pubns
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Combinatorial Group Theory: A Topological Approach
by Daniel E. Cohen

ISBN 0521349362 (0-521-34936-2)
Softcover, Cambridge Univ Pr

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Book summary:
In this book, developed from courses taught at the University of London, the author aims to show the value of using topological methods in combinatorial group theory. The topological material is given in terms of the fundamental groupoid, giving results and proofs that are both stronger and simpler than the traditional ones. Several chapters deal with covering spaces and complexes, an important method, which is then applied to yield the major Schreier and Kurosh subgroup theorems. The author presents a full account of Bass-Serre theory and discusses the word problem, in particular, its unsolvability and the Higman Embedding Theorem. Included for completeness are the relevant results of computability theory. [via]
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- Combinatorial Group Theory: A Topological Approach: ISBN 0521349362 (0-521-34936-2)
  Softcover, Cambridge Univ Pr
A Concise Course in Algebraic Topology
by J. Peter May, Peter J. May

ISBN 0226511839 (0-226-51183-9)
Softcover, Univ of Chicago Pr

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  Softcover, Univ of Chicago Pr
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Counterexamples in Topology
by J. Arthur Seebach, Lynn Arthur Steen

ISBN 048668735X (0-486-68735-X)
Softcover, Dover Pubns

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Book summary:
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.
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- Counterexamples in Topology: ISBN 0387903127 (0-387-90312-7)
  Hardcover, Springer-Verlag
- Counterexamples in Topology: ISBN 048668735X (0-486-68735-X)
  Softcover, Dover Pubns
Differential Forms in Algebraic Topology
by Raoul Bott, Loring W. Tu

ISBN 0387906134 (0-387-90613-4)
Hardcover, Springer

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- Differential Forms in Algebraic Topology: ISBN 0387906134 (0-387-90613-4)
  Hardcover, Springer
Differential Topology
by M. W. Hirsch

ISBN 0387901485 (0-387-90148-5)
Hardcover, Springer

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More editions of Differential Topology:
- Differential Topology: ISBN 3540901485 (3-540-90148-5)
  Hardcover, Springer
- Differential Topology: ISBN 0387901485 (0-387-90148-5)
  Hardcover, Springer
Differential Topology
by V. Guillemin

ISBN 0132126052 (0-13-212605-2)
Hardcover, Prentice Hall

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- Differential Topology: ISBN 0132126052 (0-13-212605-2)
  Hardcover, Prentice Hall
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Dirk Gently's Holistic Detective Agency
by Douglas Adams

ISBN 0671746723 (0-671-74672-3)
Softcover, Pocket Books

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Book summary:
What do a dead cat, a computer whiz-kid, an Electric Monk who believes the world is pink, quantum mechanics, a Chronologist over 200 years old, Samuel Taylor Coleridge (poet), and pizza have in common? Apparently not much; until Dirk Gently, self-styled private investigator, sets out to prove the fundamental interconnectedness of all things by solving a mysterious murder, assisting a mysterious professor, unravelling a mysterious mystery, and eating a lot of pizza -- not to mention saving the entire human race from extinction along the way (at no extra charge). To find out more, read this book (better still, buy it, then read it) -- or contact Dirk Gently's Holistic Detective Agency. 'A thumping good detective-ghost-horror-whodunnit-time travel-romantic-musical-comedy epic.' The author [via]
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Elementary Concepts of Topology
by Paul Alexandroff

ISBN 048660747X (0-486-60747-X)
Softcover, Dover Pubns

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Book summary:
Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.
[via]
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- Elementary Concepts of Topology: ISBN 048660747X (0-486-60747-X)
  Softcover, Dover Pubns
Elementary Differential Topology
by James R. Munkres

ISBN 0691090939 (0-691-09093-9)
Softcover, Princeton Univ Pr

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- Elementary Differential Topology: ISBN 0691090939 (0-691-09093-9)
  Softcover, Princeton Univ Pr
Elements of Algebraic Topology
by James R. Munkres

ISBN 0201627280 (0-201-62728-0)
Softcover, Perseus Books

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More editions of Elements of Algebraic Topology:
- Elements of Algebraic Topology: ISBN 0201045869 (0-201-04586-9)
  Hardcover, Perseus Books
- Elements of Algebraic Topology: ISBN 0201627280 (0-201-62728-0)
  Softcover, Perseus Books
Experiments in Topology
by Stephen Barr

ISBN 0486259331 (0-486-25933-1)
Softcover, Dover Pubns

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More editions of Experiments in Topology:
- Experiments in Topology: ISBN 0690278624 (0-690-27862-4)
  Hardcover, Harpercollins
- Experiments in Topology: ISBN 0486259331 (0-486-25933-1)
  Softcover, Dover Pubns
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Flatland
by Edwin Abbott Abbott

ISBN 1406503436 (1-4065-0343-6)
Softcover, Dodo Pr

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Book summary:
Flatland is one of the very few novels about math and philosophy that can appeal to almost any layperson. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the inhabitants are geometric shapes, and who think the planar world of length and width that they know is all there is. But one inhabitant discovers the existence of a third physical dimension, enabling him to finally grasp the concept of a fourth dimension. Watching our Flatland narrator, we begin to get an idea of the limitations of our own assumptions about reality, and we start to learn how to think about the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. [via]
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Flatland
by A. Square

ISBN 1883938775 (1-883938-77-5)
Softcover, Dry Bones Pr

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- Flatland: ISBN 1883938775 (1-883938-77-5)
  Softcover, Dry Bones Pr
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Flatterland
by Ian Stewart

ISBN 073820675X (0-7382-0675-X)
Softcover, Basic Books

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Book summary:
In 1884, an amiably eccentric clergyman and literary scholar named Edwin Abbott Abbott published an odd philosophical novel called Flatland, in which he explored such things as four-dimensional mathematics and gently satirized some of the orthodoxies of his time. The book went on to be a bestseller in Victorian England, and it has remained in print ever since.
With Flatterland, Ian Stewart, an amiable professor of mathematics at the University of Warwick, updates the science of Flatland, adding literally countless dimensions to Abbott's scheme of things ("Your world has not just four dimensions," one of his characters proclaims, "but five, fifty, a million, or even an infinity of them! And none of them need be time. Space of a hundred and one dimensions is just as real as a space of three dimensions"). Along his fictional path, Stewart touches on Feynman diagrams, superstring theory, time travel, quantum mechanics, and black holes, among many other topics. And, in Abbott's spirit, Stewart pokes fun at our own assumptions, including our quest for a Theory of Everything.
You can't help but be charmed by a book with characters named Superpaws, the Hawk King, the Projective Lion, and the Space Hopper and dotted with doggerel such as "You ain't nothin' but a hadron / nucleifyin' all the time" and "I can't get no / more momentum." And, best of all, you can learn a thing or two about modern mathematics while being roundly entertained. That's no small accomplishment, and one for which Stewart deserves applause. --Gregory McNamee [via]
More editions of Flatterland:
- Flatterland: ISBN 0738204420 (0-7382-0442-0)
  Hardcover, Perseus Books Group
- Flatterland: ISBN 073820675X (0-7382-0675-X)
  Softcover, Basic Books
The Fourth Dimension
by Rudy V. B. Rucker

ISBN 0395344204 (0-395-34420-4)
Hardcover, Houghton Mifflin

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- The Fourth Dimension: ISBN 0395344204 (0-395-34420-4)
  Hardcover, Houghton Mifflin
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The Fourth Dimension: A Guided Tour of the Higher Universes
by Rudolf V. B. Rucker, Martin Gardner, David Povilaitis

ISBN 0395393884 (0-395-39388-4)
Softcover, Houghton Mifflin Company

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Book summary:
A detailed description of what the fourth dimension would be like.
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- The Fourth Dimension: A Guided Tour of the Higher Universes: ISBN 0395393884 (0-395-39388-4)
  Softcover, Houghton Mifflin Company
General Topology
by John L. Kelley

ISBN 0387901256 (0-387-90125-6)
Hardcover, Springer Verlag

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- General Topology: ISBN 0387901256 (0-387-90125-6)
  Hardcover, Springer Verlag
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General Topology
by Stephen Willard

ISBN 0486434796 (0-486-43479-6)
Softcover, Dover Pubns

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Book summary:
Among the best available reference introductions to general topology, this volume encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by 9 sections on connectivity properties, topological characterization theorems, and homotopy theory. Includes 340 exercises. 1970 edition. 27 figures.
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- General Topology: ISBN 0486434796 (0-486-43479-6)
  Softcover, Dover Pubns
General Topology
by Willard Stephen

ISBN 0201087073 (0-201-08707-3)
Hardcover, Addison-Wesley

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- General Topology: ISBN 0201087073 (0-201-08707-3)
  Hardcover, Addison-Wesley
The Geometry of Physics: An Introduction
by Theodore Frankel

ISBN 0521539277 (0-521-53927-7)
Softcover, Cambridge Univ Pr

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Book summary:
This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism, thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should also be of interest to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study. [via]
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Introduction to Metric and Topological Spaces
by Wilson Alexander Sutherland

ISBN 0198531613 (0-19-853161-3)
Softcover, Oxford Univ Pr

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Book summary:
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics.

Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments.

The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book. [via]
More editions of Introduction to Metric and Topological Spaces:
- Introduction to Metric and Topological Spaces: ISBN 0198531559 (0-19-853155-9)
  Hardcover, Oxford Univ Pr
- Introduction to Metric and Topological Spaces: ISBN 0198531613 (0-19-853161-3)
  Softcover, Oxford Univ Pr
Introduction to Topological Manifolds
by John M. Lee

ISBN 0387950265 (0-387-95026-5)
Softcover, Springer Verlag

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- Introduction to Topological Manifolds: ISBN 0387950265 (0-387-95026-5)
  Softcover, Springer Verlag
Introduction to Topology
by Theodore W. Gamelin, Robert Everist Greene

ISBN 0486406806 (0-486-40680-6)
Softcover, Dover Pubns

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More editions of Introduction to Topology:
- Introduction to Topology: ISBN 0030624762 (0-03-062476-2)
  Hardcover, Cengage Learning
- Introduction to Topology: ISBN 0486406806 (0-486-40680-6)
  Softcover, Dover Pubns
Introduction to Topology
by Bert Mendelson

ISBN 0486663523 (0-486-66352-3)
Softcover, Dover Pubns

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- Introduction to Topology: ISBN 0486663523 (0-486-66352-3)
  Softcover, Dover Pubns
Introduction to Topology and Modern Analysis
by George F. Simmons

ISBN 1575242389 (1-57524-238-9)
Hardcover, Krieger Pub Co

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Book summary:
This material is intended to contribute to a wider appreciation of the mathematical words "continuity and linearity". The book's purpose is to illuminate the meanings of these words and their relation to each other. [via]
More editions of Introduction to Topology and Modern Analysis:
- Introduction to Topology and Modern Analysis: ISBN 0898745519 (0-89874-551-9)
  Hardcover, Krieger Publishing Company
- Introduction to Topology and Modern Analysis: ISBN 1575242389 (1-57524-238-9)
  Hardcover, Krieger Pub Co
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Introductory Real Analysis
by S.V. Fomin, A.N. Kolmogorov

ISBN 0486612260 (0-486-61226-0)
Softcover, Dover Pubns

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Book summary:
Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition.
[via]
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- Introductory Real Analysis: ISBN 0486612260 (0-486-61226-0)
  Softcover, Dover Pubns
Intuitive Topology
by V.V. Prasolov, A. Sossinsky

ISBN 0821803565 (0-8218-0356-5)
Softcover, Amer Mathematical Society

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- Intuitive Topology: ISBN 0821803565 (0-8218-0356-5)
  Softcover, Amer Mathematical Society
K-Theory
by D.W. Anderson, M.F. Atiyah

ISBN 0201407922 (0-201-40792-2)
Softcover, Perseus Books

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More editions of K-Theory:
- K-Theory: ISBN 0201093944 (0-201-09394-4)
  Hardcover, Perseus Books
- K-Theory: ISBN 0201407922 (0-201-40792-2)
  Softcover, Perseus Books
The Knot Book : An Elementary Introduction to the Mathematical Theory of Knots
by Colin C. Adams

ISBN 0821836781 (0-8218-3678-1)
Softcover, Amer Mathematical Society

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Book summary:
In February 2001, scientists at the Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicament--a neat trick worthy of an inorganic Houdini, but more, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and enfold themselves.
A knot seems a simple, everyday thing, at least to anyone who wears laced shoes or uses a corded telephone. In the mathematical discipline known as topology, knots are anything but simple: at 16 crossings of a "closed curve in space that does not intersect itself anywhere", a knot can take one of 1,388,705 permutations, and more are possible. All this thrills mathematics professor Colin Adams, whose primer The Knot Book offers an engaging if often challenging introduction to the mysterious, often unproven, but, he suggests, ultimately knowable nature of knots of all kinds--whether nontrivial, satellite, torus, cable or hyperbolic. As perhaps befits its subject, Adams's prose is sometimes... well, tangled ("A knot is amphicheiral if it can be deformed through space to the knot obtained by changing every crossing in the projection of the knot to the opposite crossing.") but his book is great fun for puzzle and magic buffs, and a useful reference for students of knot theory and other aspects of higher mathematics. --Gregory McNamee [via]
More editions of The Knot Book : An Elementary Introduction to the Mathematical Theory of Knots:
Knotted Doughnuts and Other Mathematical Entertainments
by Martin Gardner

ISBN 0716717999 (0-7167-1799-9)
Softcover, W H Freeman & Co

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More editions of Knotted Doughnuts and Other Mathematical Entertainments:
- Knotted Doughnuts and Other Mathematical Entertainments: ISBN 0716717948 (0-7167-1794-8)
  Hardcover, W.H. Freeman
- Knotted Doughnuts and Other Mathematical Entertainments: ISBN 0716717999 (0-7167-1799-9)
  Softcover, W H Freeman & Co
Lecture Notes on Elementary Topology and Geometry
by I. M. Singer

ISBN 0387902023 (0-387-90202-3)
Hardcover, Springer Verlag

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More editions of Lecture Notes on Elementary Topology and Geometry:
- Lecture Notes on Elementary Topology and Geometry: ISBN 0387902023 (0-387-90202-3)
  Hardcover, Springer Verlag
Mathematical Tourist: New and Updated Snapshots of Modern Mathematics
by Ivars Peterson

ISBN 0716732505 (0-7167-3250-5)
Softcover, W H Freeman & Co

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Book summary:
When the first edition of Ivars Peterson's The Mathematical Tourist was published in 1988, the New York Times called it "a rich array of ideas, drawing on virtually every branch of mathematics and bunging in plenty of late-breaking developments to boot." Now Peterson has expanded this popular book to feature another decade of mathematical progress, including new sections on crystal structure, string theory, mathematicians' use of computers, chaos theory, and Fermat's Last Theorem. Most of the other sections have been reworked and reworded as well, and there are many new illustrations. One thing that has not changed is the clarity of Peterson's writing and his almost unparalleled ability to make mathematical ideas themselves interesting, without focusing on the lives and personalities of mathematicians. Martin Gardner called the first edition "a travel guide that the professional mathematician will read with as much excitement and pleasure as the veriest amateur ... a masterpiece of popular exposition," and this second edition is no less. --Mary Ellen Curtin [via]
More editions of Mathematical Tourist: New and Updated Snapshots of Modern Mathematics:
- The Mathematical Tourist : New and Updated Snapshots of Modern Mathematics: ISBN 0805071598 (0-8050-7159-8)
  Softcover, Holt & Company, Henry
- Mathematical Tourist: New and Updated Snapshots of Modern Mathematics: ISBN 0716732505 (0-7167-3250-5)
  Softcover, W H Freeman & Co
The Mathematical Tourist: Snapshots of Modern Mathematics
by Ivars Peterson

ISBN 0716720647 (0-7167-2064-7)
Softcover, W H Freeman & Co

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Book summary:
When the first edition of Ivars Peterson's The Mathematical Tourist was published in 1988, the New York Times called it "a rich array of ideas, drawing on virtually every branch of mathematics and bunging in plenty of late-breaking developments to boot." Now Peterson has expanded this popular book to feature another decade of mathematical progress, including new sections on crystal structure, string theory, mathematicians' use of computers, chaos theory, and Fermat's Last Theorem. Most of the other sections have been reworked and reworded as well, and there are many new illustrations. One thing that has not changed is the clarity of Peterson's writing and his almost unparalleled ability to make mathematical ideas themselves interesting, without focusing on the lives and personalities of mathematicians. Martin Gardner called the first edition "a travel guide that the professional mathematician will read with as much excitement and pleasure as the veriest amateur ... a masterpiece of popular exposition," and this second edition is no less. --Mary Ellen Curtin [via]
More editions of The Mathematical Tourist: Snapshots of Modern Mathematics:
- The Mathematical Tourist: Snapshots of Modern Mathematics: ISBN 0716719533 (0-7167-1953-3)
  Hardcover, Freeman
- The Mathematical Tourist: Snapshots of Modern Mathematics: ISBN 0716720647 (0-7167-2064-7)
  Softcover, W H Freeman & Co
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Morse Theory
by John W. Milnor

ISBN 0691080089 (0-691-08008-9)
Softcover, Princeton Univ Pr

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Book summary:
One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory.
Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master."
Milnor has published five books with Princeton University Press.
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More editions of Morse Theory:
- Morse Theory: ISBN 0691080089 (0-691-08008-9)
  Softcover, Princeton Univ Pr
On Knots
by Louis H. Kauffman

ISBN 0691084351 (0-691-08435-1)
Softcover, Princeton Univ Pr

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- On Knots: ISBN 0691084351 (0-691-08435-1)
  Softcover, Princeton Univ Pr
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Quantum Fields and Strings: A Course for Mathematicians
by John W. Morgan, Edward Witten, Pierre Deligne, Daniel S. Freed, David R. Morrison, Lisa C. Jeffrey, David Kazhdan, Pavel Etingof

ISBN 0821820133 (0-8218-2013-3)
Softcover, Amer Mathematical Society

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Book summary:
Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics.
In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose is eloquently stated in a letter written by Robert MacPherson: "The goal is to create and convey an understanding, in terms congenial to mathematicians, of some fundamental notions of physics ... [and to] develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra."
These volumes are a written record of the program. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the program. The book also includes problems and solutions worked out by the editors and other leading participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures. These two volumes present the first truly comprehensive introduction to this field aimed at a mathematics audience. They offer a unique opportunity for mathematicians and mathematical physicists to learn about the beautiful and difficult subjects of quantum field theory and string theory. [via]
More editions of Quantum Fields and Strings: A Course for Mathematicians:
- Quantum Fields and Strings: A Course for Mathematicians: ISBN 0821820141 (0-8218-2014-1)
  Softcover, Amer Mathematical Society
- Quantum Fields and Strings: A Course for Mathematicians: ISBN 0821820133 (0-8218-2013-3)
  Softcover, Amer Mathematical Society
Quantum Fields and Strings: A Course for Mathematicians
by Pierre Deligne

ISBN 0821820125 (0-8218-2012-5)
Softcover, Amer Mathematical Society

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- Quantum Fields and Strings: A Course for Mathematicians: ISBN 0821820125 (0-8218-2012-5)
  Softcover, Amer Mathematical Society
Stable Homotopy and Generalized Homology
by J. F. Adams

ISBN 0226005240 (0-226-00524-0)
Softcover, Univ of Chicago Pr

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- Stable Homotopy and Generalized Homology: ISBN 0226005240 (0-226-00524-0)
  Softcover, Univ of Chicago Pr
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Topological Methods in Euclidean Spaces
by Gregory L. Naber

ISBN 0486414523 (0-486-41452-3)
Softcover, Dover Pubns

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Book summary:
Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem, the Lefschetz Fixed Point Theorem, the Stone-Weierstrass Theorem, and Morse functions. Includes new section of solutions to selected problems.
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More editions of Topological Methods in Euclidean Spaces:
- Topological Methods in Euclidean Spaces: ISBN 0486414523 (0-486-41452-3)
  Softcover, Dover Pubns
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Topological Spaces: From Distance to Neighborhood
by Gerard Buskes, Arnoud Van Rooij, A. C. M. Van Rooij

ISBN 0387949941 (0-387-94994-1)
Hardcover, Springer Verlag

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Book summary:
gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology. [via]
More editions of Topological Spaces: From Distance to Neighborhood:
- Topological Spaces: From Distance to Neighborhood: ISBN 0387949941 (0-387-94994-1)
  Hardcover, Springer Verlag
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Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity
by Claude Berge, E. M. Patterson

ISBN 0486696537 (0-486-69653-7)
Softcover, Dover Pubns

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Book summary:
Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.
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More editions of Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity:
- Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity: ISBN 0486696537 (0-486-69653-7)
  Softcover, Dover Pubns
Topological Vector Spaces
by H. H. Schaefer

ISBN 0387900268 (0-387-90026-8)
Hardcover, Springer

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Book summary:
Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate. This second edition has been thoroughly revised and includes a new chapter on C^* and W^* algebras. [via]
More editions of Topological Vector Spaces:
- Topological Vector Spaces: ISBN 0387987266 (0-387-98726-6)
  Hardcover, Springer Verlag
- Topological Vector Spaces: ISBN 0387900268 (0-387-90026-8)
  Hardcover, Springer
Topology: An Introduction With Application to Topological Groups
by George McCarty

ISBN 0486450821 (0-486-45082-1)
Hardcover, Dover Pubns

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More editions of Topology: An Introduction With Application to Topological Groups:
- Topology: An Introduction With Application to Topological Groups: ISBN 0486656330 (0-486-65633-0)
  Softcover, Dover Pubns
- Topology: An Introduction With Application to Topological Groups: ISBN 0486450821 (0-486-45082-1)
  Hardcover, Dover Pubns
Topology: An Introduction to the Point-Set and Algebraic Areas
by Donald W. Kahn

ISBN 0486686094 (0-486-68609-4)
Softcover, Dover Pubns

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- Topology: An Introduction to the Point-Set and Algebraic Areas: ISBN 0486686094 (0-486-68609-4)
  Softcover, Dover Pubns
Topology
by Gail S. Young, John G. Hocking

ISBN 0486656764 (0-486-65676-4)
Softcover, Dover Pubns

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More editions of Topology:
- Topology: ISBN 0486656764 (0-486-65676-4)
  Softcover, Dover Pubns
Topology
by Horst Schubert

ISBN 0356020770 (0-356-02077-0)
Hardcover, Macdonald & Co

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- Topology: ISBN 0356020770 (0-356-02077-0)
  Hardcover, Macdonald & Co
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Topology
by James Munkres

ISBN 0131816292 (0-13-181629-2)
Hardcover, Prentice Hall

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Book summary:
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications. [via]
More editions of Topology:
- Topology: ISBN 0131816292 (0-13-181629-2)
  Hardcover, Prentice Hall
Topology; A First Course
by James Raymond Munkres

ISBN 0139254951 (0-13-925495-1)
Hardcover, Prentice Hall

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- Topology; A First Course: ISBN 0139254951 (0-13-925495-1)
  Hardcover, Prentice Hall
Topology
by K. Jänich, S. Levy

ISBN 0387908927 (0-387-90892-7)
Hardcover, Springer

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- Topology: ISBN 0387908927 (0-387-90892-7)
  Hardcover, Springer
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Topology and Geometry
by Glen E. Bredon

ISBN 0387979263 (0-387-97926-3)
Hardcover, Springer Verlag

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Book summary:
This book is intended as a textbook for a first-year graduate course onalgebraic topology, with as strong flavoring in smooth manifold theory.Starting with general topology, it discusses differentiable manifolds,cohomology, products and duality, the fundamental group, homology theory,and homotopy theory. It covers most of the topics all topologists willwant students to see, including surfaces, Lie groups and fibre bundle theory.With a thoroughly modern point of view, it is the first truly new textbookin topology since Spanier, almost 25 years ago. Although the book is comprehensive,there is no attempt made to present the material in excessive generality,except where generality improves the efficiency and clarity of the presentation. [via]
More editions of Topology and Geometry:
- Topology and Geometry: ISBN 3540979263 (3-540-97926-3)
  Hardcover, Springer-Verlag
- Topology and Geometry: ISBN 0387979263 (0-387-97926-3)
  Hardcover, Springer Verlag
Topology from the Differentiable Viewpoint
by John W. Milnor

ISBN 0691048339 (0-691-04833-9)
Softcover, Princeton Univ Pr

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More editions of Topology from the Differentiable Viewpoint:
- Topology from the Differentiable Viewpoint: ISBN 0813901812 (0-8139-0181-2)
  Softcover, Univ of Virginia Pr
- Topology from the Differentiable Viewpoint: ISBN 0691048339 (0-691-04833-9)
  Softcover, Princeton Univ Pr
The Topology of Fibre Bundles
by Norman Steenrod

ISBN 0691005486 (0-691-00548-6)
Softcover, Princeton Univ Pr

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More editions of The Topology of Fibre Bundles:
- The Topology of Fibre Bundles: ISBN 0691005486 (0-691-00548-6)
  Softcover, Princeton Univ Pr
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A User's Guide to Spectral Sequences
by John McCleary, B. Bollobas, W. Fulton, A. Katok, F. Kirwan

ISBN 0521567599 (0-521-56759-9)
Softcover, Cambridge University Press

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Book summary:
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra. [via]
More editions of A User's Guide to Spectral Sequences:
- A User's Guide to Spectral Sequences: ISBN 0521561418 (0-521-56141-8)
  Hardcover, Cambridge Univ Pr
- A User's Guide to Spectral Sequences: ISBN 0521567599 (0-521-56759-9)
  Softcover, Cambridge University Press

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