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An offshoot of geometry, topology originated during the 19th century. A simple definition has often been used:
topology is the study of those properties that an object retains under deformation--specifically, bending, stretching and squeezing, but not
breaking or tearing. Thus, a triangle is topologically equivalent to a circle but not to a straight line segment. Similarly, a solid cube made of
modeling clay could be deformed into a ball by kneading. It could not, however, be molded into a solid torus (ring) unless a hole were bored
through it or two surfaces were joined together. A solid cube is therefore not topologically equivalent to a finger ring.
More precisely, if there are given two geometric objects or sets of points and if some two-way transformation (or operation or mapping) takes
each point p of either set into one and only one point p' of the other and if the transformation is continuous in the sense that points close to p become points close to p', then the transformation is called a homeomorphism and the two sets are said to be
topologically equivalent. Topology is, then, the study of properties that remain invariant under homeomorphisms. (from the Encyclopedia Brittanica).
1. Topology from the Differentiable Viewpoint
by John W. Milnor
2. Counterexamples in Topology
by Lynn Arthur Steen, J. Arthur Seebach (Contributor)
3. Algebraic Topology
by C. R. F. Maunder
4. Structural Equations With Latent Variables (Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics Section)
by Kenneth A. Bollen, William Bollen
5. Topology; A First Course
by James Raymond, Munkres
6. Topology : An Introduction to the Point-Set and Algebraic Areas
by Donald W. Kahn
7. Elements of Algebraic Topology
by James R. Munkres
8. From Calculus to Cohomology : De Rham Cohomology and Characteristic Classes
by I. H. Madsen, et al
9. A Basic Course in Algebraic Topology (Graduate Texts in Mathematics, Vol 127)
by William S. Massey, et al
10. Elements of the Topology of Plane Sets of Points
by M. H. A. Newman
11. A General Topology Workbook
by Iain T. Adamson
12. Algebraic Topology : A First Course (Graduate Texts in Mathematics, Vol 153)
by William Fulton
13. Curvature and Homology
by Samuel I. Goldberg
14. Algebraic Topology
by Edwin H. Spanier
15. Introduction to Algebraic Topology (Graduate Texts in Mathematics, Vol 119)
by Joseph J. Rotman
16. Differential Topology
by Alan Pollack, Victor W. Guillemin
17. Spin Geometry (Princeton Mathematical Series, 38)
by H. Blaine Lawson, Marie-Louise Michelsohn (Editor)
18. Introduction to Symplectic Topology (Oxford Mathematical Monographs)
by Dusa McDuff, D. Salamon (Contributor)
19. Algebraic Topology
by Marvin J. Greenberg, J. R. Harper
20. Topology of Fibre Bundles (Princeton Mathematical Series)
by Steenrod, Norman Steenrod
21. Combinatorial Topology
by P. S. Aleksandrov, P. Alexandrov
22. The Mathematics of Time : Essays on Dynamical Systems, Economic Processes, and Related Topics
by Stephen, Smale
23. Topology of 4-Manifolds (Princeton Mathematical Series, No 39)
by Michael Freedman, Frank C. Quinn (Contributor)
24. Differential Equations : Geometric Theory
by Solomon Lefschetz
25. The Four-Color Theorem : History, Topological Foundations, and Idea of Proof
by Rudolf Fritsch, et al
26. Set Topology
by R. Vaidyanathaswamy
27. The Foundations of Topological Graph Theory
by C. Paul Bonnington, C. H. C. Little (Contributor)
28. Knots and Surfaces
by T. Porter(Contributor), N. D. Gilbert
29. Braid Group, Knot Theory and Statistical Mechanics II (Advanced Series in Mathematical Physics, Vol 17)
by M.L. Ge(Editor), C. N. Yang
30. Representations and Cohomology : Basic Representation Theory of Finite Groups and Associative Algebras (Repr of 1995 Ed) (Cambridge Studies in advance
by D. Benson
31. Representations and Cohomology : Cohomology of Groups and Modules (Cambridge Studies in Advanced Mathematics, 31)
by D. J. Benson
32. Contemporary Design Theory : A Collection of Surveys (Wiley-Interscience Series in Discrete Mathematics and Optimization)
by Jeffrey H. Dinitz, Douglas R. Stinson (Editor)
33. Introductory Structural Analysis
by Chu-Kia Wang, Charles G. Salmon
34. Introduction to General Topology
by George L. Cain
35. High-Dimensional Knot Theory : Algebraic Surgery in Codimension 2 (Springer Monographs in Mathematics)
by Andrew Ranicki
36. Fibrewise Homotopy Theory (Springer Monographs in Mathematics)
by I. M. James, Michael C. Crabb
37. Topological Field Theory, Primitive Forms and Related Topics (Progress in Mathematics, Vol 160)
by Masaki Kashiwara(Editor), et al
38. Notes on Crystalline Cohomology
by Pierre Berthelot, Arthur Ogus
39. Algebraic Topology Based on Knots
by Jozef H. Przytycki
40. Multi-Hamiltonian Theory of Dynamical Systems (Texts and Monographs in Physics)
by MacIej Blaszak(Editor), et al
41. Riemann, Topology and Physics
by Mikhail Ilich Monastyrskii, et al
42. Casson's Invariant for Oriented Homology 3-Spheres : An Exposition (Mathematical Notes, No 36)
by Selman Akbulut, et al
43. Commensurabilities Among Lattices in Pu (1,N)
by Pierre Deligne, G. Daniel Mostow
44. The Topology of Fibre Bundles
by Norman Steenrod
45. Foundations of Combinational Topology
by L .S. Pontryagin, L. S. Pontriagin
46. Introduction to Topology
by Theodore W. Gamelin, Robert Everist Greene
47. Analysis of Structures : An Integration of Classical and Modern Methods
by Harry H. West
48. Introduction to Topology
by Dennis Roseman
... if you want to satisfy your gray cells .. here are a few GOOD BOOKS THAT REALLY BELONG IN YOUR PERSONAL LIBRARY ....
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The Age of Spiritual Machines : When Computers Exceed Human Intelligence
- if Ray Kurzweil is right, we've only got until about 2020 before computers outpace the human brain in computational power. Kurzweil, artificial intelligence expert and author of The Age of Intelligent Machines, shows that technological evolution moves at an exponential pace. Further, he asserts, in a sort of swirling postulate, time speeds up as order increases, and vice versa. He calls this the "Law of Time and Chaos," and it means that although entropy is slowing the stream of time down for the universe overall, and thus vastly increasing the amount of time between major events, in the eddy of technological evolution the exact opposite is happening, and events will soon be coming faster and more furiously. This means that we'd better figure out how to deal with conscious machines as soon as possible--they'll soon not only be able to beat us at chess, they'll likely demand civil rights, and they may at last realize the very human dream of immortality. -- an oustanding must get book!
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The Century
- A LAND MARK BOOK FOR THIS ERA ... coauthored by PETER JENNINGS - - - the news anchor ... "We have sought," write Peter Jennings and Todd Brewster, "to distinguish our story from other histories by holding each chapter up to a litmus test: Have we looked at this time from the perspective of someone who lived through it? And in doing so, have we captured a sense not only of the events of a particular era, but of the mood, the prevailing attitudes?" Thus, the experiences of ordinary men and women come to life in sidebars that appear throughout The Century. Sharpe James, the mayor of Newark, New Jersey, recalls the sense of excitement and possibility he felt when Jackie Robinson became the first black ballplayer in the major leagues. Gilles Ryan remembers what it was like to be a high-school student in Dayton, Tennessee, during the Scopes Trial. Connie Chang talks about emigrating to the United States from Korea and establishing a liquor store in Los Angeles, only to have it destroyed in the civil unrest. --- what this boils down to is ... GET THIS BOOK OR RISK BEING LEFT BEHIND IN THE HISTORICAL DUST ...
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Microsoft Secrets : How the World's Most Powerful Software Company Creates Technology, Shapes Markets, and Manages People
- DO YOU WANT TO KNOW HOW BILL GATES REALLY MADE HIS BILLIONS -- AND HOW HE WILL CONTINUE TO? Read this book ... The description says: Today, Microsoft commands the high ground of the information superhighway by owning the operating systems and basic applications programs that run on the world's 170 million computers. Beyond the unquestioned genius and vision of Bill Gates, what accounts for Microsofts astounding success?
Drawing on almost two years of on-site observation at Microsoft headquarters, eminent scientists Michael A. Cusumano and Richard W. Selby reveal many of Microsoft's innermost secrets. This inside report, based on forty in-depth interviews by authors who had access to confidential documents and project data, outlines the seven complementary strategies that characterize exactly how Microsoft competes and operates, including the "Brain Trust" of talented employees and exceptional management; "bang for the buck" competitive strategies and clear organizational goals that produce self-critiquing, learning, and improving; a flexible, incremental approach to product development; and a relentless pursuit of future markets.
Cusumano and Selby's masterful analysis successfully uncovers the distinctive way in which Microsoft has combined all of the elements necessary to get to the top of an enormously important industry -- and stay there.
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and ...
GEORGE SOROS - Billionaire Philanthropist & NEXTGEN MAN -- if you don't know who SOROS is, you don't need to.
Retirement Planning Here it doesn't matter if you don't know Soros. All you need to know is that you are in charge of your destiny. Do you ever think about YOUR future? Are you working? Do you know how you'll support your retirement? If you haven't started, staart her. If you have started, fine tune your portfolio and learn new tricks (well not tricks but serious advice). ANYHOW from alpha to zulu through Romeo, check these out and sleep easy later on.
DAVID BRIN - Visionary! Listen David has moved on ... to talk about more than science fiction and the postman. If you at all want a glimpse of a very possible future - do it here. (Yes we have his scifi award winning books listed here as well).
RUMI - they mystic poet. IF you understand romantic mysticism -- you'll know we can't really say more on this page. But click on the link and who knows where you'll end up. Maybe in lover's heaven? ...
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