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Using The Borsuk Ulam Theorem
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Book Synopsis Using the Borsuk-Ulam Theorem by : Jiri Matousek
Download or read book Using the Borsuk-Ulam Theorem written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2008-01-12 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.
Book Synopsis Using the Borsuk-Ulam Theorem by : Jiri Matousek
Download or read book Using the Borsuk-Ulam Theorem written by Jiri Matousek and published by . This book was released on 2014-09-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Topology and Related Topics by : Mahender Singh
Download or read book Algebraic Topology and Related Topics written by Mahender Singh and published by Springer. This book was released on 2019-02-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.
Book Synopsis A Journey Through Discrete Mathematics by : Martin Loebl
Download or read book A Journey Through Discrete Mathematics written by Martin Loebl and published by Springer. This book was released on 2017-10-11 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.
Book Synopsis Elements of Differential Topology by : Anant R. Shastri
Download or read book Elements of Differential Topology written by Anant R. Shastri and published by CRC Press. This book was released on 2011-03-04 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol
Book Synopsis Topological Methods for Variational Problems with Symmetries by : Thomas Bartsch
Download or read book Topological Methods for Variational Problems with Symmetries written by Thomas Bartsch and published by Springer. This book was released on 2006-11-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.
Book Synopsis Topology Through Inquiry by : Michael Starbird
Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2020-09-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.
Book Synopsis Representation Theory by : Zongzhu Lin
Download or read book Representation Theory written by Zongzhu Lin and published by American Mathematical Soc.. This book was released on 2009-01-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided
Book Synopsis Thirty-three Miniatures by : Jiří Matoušek
Download or read book Thirty-three Miniatures written by Jiří Matoušek and published by American Mathematical Soc.. This book was released on 2010 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)
Book Synopsis Infinite-Dimensional Topology by : J. van Mill
Download or read book Infinite-Dimensional Topology written by J. van Mill and published by Elsevier. This book was released on 1988-12-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed. One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.
Book Synopsis Simplicial Complexes of Graphs by : Jakob Jonsson
Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Book Synopsis A Concise Course in Algebraic Topology by : J. P. May
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Book Synopsis Differential Topology by : Victor Guillemin
Download or read book Differential Topology written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.
Download or read book Algebraic Topology written by Satya Deo and published by Springer. This book was released on 2003-12-01 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topology for Computing by : Afra J. Zomorodian
Download or read book Topology for Computing written by Afra J. Zomorodian and published by Cambridge University Press. This book was released on 2005-01-10 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Book Synopsis Introduction to Differential Topology by : Theodor Bröcker
Download or read book Introduction to Differential Topology written by Theodor Bröcker and published by Cambridge University Press. This book was released on 1982-09-16 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally supplied with exercises and will be welcomed by students with some basic knowledge of analysis and topology.
Book Synopsis Elements of Mathematics by : John Stillwell
Download or read book Elements of Mathematics written by John Stillwell and published by Princeton University Press. This book was released on 2017-11-07 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exciting look at the world of elementary mathematics 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.
