Papers on Topology

Analysis Situs and Its Five Supplements
Author: Henri Poincaré
Publisher: American Mathematical Soc.
ISBN: 0821852345
Category: Mathematics
Page: 228
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The papers in this book chronicle Henri Poincare's Journey in algebraic topology between 1892 and 1904, from his discovery of the fundamental group to his formulation of the Poincare conjecture. For the first time in English translation, one can follow every step (and occasional stumble) along the way, with the help of translator John Stillwell's introduction and editorial comments. Now that the Poincare conjecture has finally been proved, by Grigory perelman, it seems timely to collect the papers that from the background to this famous conjecture. Poincare's papers are in fact the first draft of algebraic topology, introducing its main subject matter (manifolds) and basic concepts (homotopy and homology). All mathematicians interested in topology and its history will enjoy this book. These famous papers, with their characteristic mixture of deep insight and inevitable confusion, are here presented complete and in English for the first time, with a commentary by their translator, John Stillwell, that guides the reader into the beart of the subject. One of the finest works of one of the great mathematicians is now available anew for students and experts alike.---Jeremy Gray The AMS and John Stillwell have made an important contribution to the mathematics literature in this translation of Poincare. For many of us, these great papers on the foundations of topology are given greater clarity in English. Moreover, reading Poincare here illustrates the ultimate in research by successive approximations (akin to my own way of mathematical thinking)---Stephen Smale I am a proud owner of the original complete works in green leather in French bought for a princely sum in Paris around 1975. I have read in them exten-sively, and often during topology lectures I refer to parts of these works. I am happy that there is now the option for my students to read them in English---Dennis Sullivan

Basic Algebraic Topology and its Applications


Author: Mahima Ranjan Adhikari
Publisher: Springer
ISBN: 813222843X
Category: Mathematics
Page: 615
View: 4997
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This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Advances in Applied and Computational Topology

American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana
Author: American Mathematical Society. Short Course on Computational Topology
Publisher: American Mathematical Soc.
ISBN: 0821853279
Category: Mathematics
Page: 232
View: 4982
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What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.

Elements of Mathematics

From Euclid to Gödel
Author: John Stillwell
Publisher: Princeton University Press
ISBN: 1400880564
Category: Mathematics
Page: 440
View: 5633
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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

The Foundations of Chaos Revisited: From Poincaré to Recent Advancements


Author: Christos Skiadas
Publisher: Springer
ISBN: 3319297015
Category: Science
Page: 261
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With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.

An Investigation of the Laws of Thought

On which are Founded the Mathematical Theories of Logic and Probabilities
Author: George Boole
Publisher: N.A
ISBN: N.A
Category: Algebra, Boolean
Page: 424
View: 4351
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Ebene algebraische Kurven


Author: Egbert Brieskorn,Horst Knörrer
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 964
View: 2909
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Hermann Weyl und die Mathematik an der ETH Zürich, 1913–1930


Author: G. Frei,U. Stammbach
Publisher: Springer-Verlag
ISBN: 303488608X
Category: Mathematics
Page: 182
View: 9324
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Theory of Finite and Infinite Graphs


Author: Denes König
Publisher: Springer Science & Business Media
ISBN: 1468489712
Category: Mathematics
Page: 426
View: 5016
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To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in 1936. "From Konigsberg to Konig's book" sings the poetess, "So runs the graphic tale . . . " 10]. There were earlier books that took note of graph theory. Veb len's Analysis Situs, published in 1931, is about general combinato rial topology. But its first two chapters, on "Linear graphs" and "Two-Dimensional Complexes," are almost exclusively concerned with the territory still explored by graph theorists. Rouse Ball's Mathematical Recreations and Essays told, usually without proofs, of the major graph-theoretical advances ofthe nineteenth century, of the Five Colour Theorem, of Petersen's Theorem on I-factors, and of Cayley's enumerations of trees. It was Rouse Ball's book that kindled my own graph-theoretical enthusiasm. The graph-theoretical papers of Hassler Whitney, published in 1931-1933, would have made an excellent textbook in English had they been collected and published as such. But the honour of presenting Graph Theory to the mathe matical world as a subject in its own right, with its own textbook, belongs to Denes Konig. Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amuse ment, how one mathematician scorned it as "The slums of Topol ogy.""

The study of the history of mathematics and the study of the history of science


Author: George Sarton
Publisher: N.A
ISBN: N.A
Category: Mathematicians
Page: 113
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Poincarés Vermutung

die Geschichte eines mathematischen Abenteuers
Author: Donal O'Shea
Publisher: N.A
ISBN: 9783596176632
Category:
Page: 376
View: 1355
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An Elementary Treatise on Fourier's Series

And Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics
Author: William Elwood Byerly
Publisher: Courier Dover Publications
ISBN: N.A
Category: Mathematics
Page: 287
View: 2966
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This classic text is one of the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. Includes 190 problems, approximately half with answers. 1893 edition.

The Discovery of Radioactivity and Transmutation


Author: Alfred Romer
Publisher: N.A
ISBN: N.A
Category: Radioactivity
Page: 233
View: 708
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Statics and the dynamics of a particle


Author: William Duncan MacMillan
Publisher: N.A
ISBN: N.A
Category: Dynamics of a particle
Page: 430
View: 5413
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Isis Cumulative Bibliography 1965 to 1974

A Bibliography of the History of Science Formed from Isis Critical Bibliographies 91-100 Indexing Literature Published from 1965 Through 1974. Subjects, periods and civilitations
Author: History of Science Society
Publisher: London : Mansell in conjunction with the History of Science Society
ISBN: 9780720115161
Category: Science
Page: 720
View: 1417
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The Thermodynamics of Electrical Phenomena in Metals, and A Condensed Collection of Thermodynamic Formulas


Author: Percy Williams Bridgman
Publisher: N.A
ISBN: N.A
Category: Metals
Page: 244
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Elementary mathematics from an advanced standpoint


Author: Felix Klein
Publisher: N.A
ISBN: N.A
Category: Algebra
Page: N.A
View: 4083
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Grundzüge der Mengenlehre


Author: Felix Hausdorff
Publisher: American Mathematical Soc.
ISBN: 9780828400619
Category: Mathematics
Page: 476
View: 9520
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This reprint of the original 1914 edition of this famous work contains many topics that had to be omitted from later editions, notably, Symmetric Sets, Principle of Duality, most of the ``Algebra'' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, the Special Methods Applicable in the Euclidean Plane, Jordan's Separation Theorem, the Theory of Content and Measure, the Theory of the Lebesgue Integral. The text is in German.

Masterpieces of the Russian drama


Author: George Rapall Noyes
Publisher: N.A
ISBN: N.A
Category: English drama
Page: 902
View: 6627
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The thirteen books of Euclid's Elements


Author: Euclid,Thomas L. Heath
Publisher: Dover Pubns
ISBN: N.A
Category: Mathematics
Page: 443
View: 8327
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Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate, and proposition in great detail. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 1 includes Introduction, Books 1-2: Triangles, rectangles.