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Topology Of Numbers
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Book Synopsis Dynamics: Topology and Numbers by : Pieter Moree
Download or read book Dynamics: Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Book Synopsis Winding Around: The Winding Number in Topology, Geometry, and Analysis by : John Roe
Download or read book Winding Around: The Winding Number in Topology, Geometry, and Analysis written by John Roe and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra),guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem),explain why every simple closed curve has an inside and an outside (the Jordan curve theorem),relate calculus to curvature and the singularities of vector fields (the Hopf index theorem),allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators),generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem). All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses.
Book Synopsis Topology of Numbers by : Allen Hatcher
Download or read book Topology of Numbers written by Allen Hatcher and published by American Mathematical Society. This book was released on 2022-10-19 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the classical topic of quadratic forms with integer coefficients, a central topic of the book. Quadratic forms of this type in two variables have a very rich theory, developed mostly by Euler, Lagrange, Legendre, and Gauss during the period 1750–1800. In this book their approach is modernized by using the splendid visualization tool introduced by John Conway in the 1990s called the topograph of a quadratic form. Besides the intrinsic interest of quadratic forms, this theory has also served as a stepping stone for many later developments in algebra and number theory. The book is accessible to students with a basic knowledge of linear algebra and arithmetic modulo $n$. Some exposure to mathematical proofs will also be helpful. The early chapters focus on examples rather than general theorems, but theorems and their proofs play a larger role as the book progresses.
Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff
Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Topology by : Allen Hatcher
Download or read book Algebraic Topology written by Allen Hatcher and published by Cambridge University Press. This book was released on 2002 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.
Book Synopsis Elements of Point Set Topology by : John D. Baum
Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book 数论导引 written by and published by . This book was released on 2007 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
Book Synopsis General Topology by : Stephen Willard
Download or read book General Topology written by Stephen Willard and published by Courier Corporation. This book was released on 2004-01-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.
Book Synopsis Knots and Primes by : Masanori Morishita
Download or read book Knots and Primes written by Masanori Morishita and published by Springer Science & Business Media. This book was released on 2011-11-27 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
Author :O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Publisher :American Mathematical Soc. ISBN 13 :9780821886250 Total Pages :432 pages Book Rating :4.8/5 (862 download)
Book Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Download or read book Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and published by American Mathematical Soc.. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
Book Synopsis A First Course in Topology by : Robert A Conover
Download or read book A First Course in Topology written by Robert A Conover and published by Courier Corporation. This book was released on 2014-05-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com
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 Essentials of Topology with Applications by : Steven G. Krantz
Download or read book Essentials of Topology with Applications written by Steven G. Krantz and published by CRC Press. This book was released on 2009-07-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings Readers Up to Speed in This Important and Rapidly Growing AreaSupported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological
Book Synopsis American Mathematical Society Translations by : S. P. Demuškin
Download or read book American Mathematical Society Translations written by S. P. Demuškin and published by American Mathematical Soc.. This book was released on 1966 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Eulerian Numbers by : T. Kyle Petersen
Download or read book Eulerian Numbers written by T. Kyle Petersen and published by Birkhäuser. This book was released on 2015-10-12 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.
Book Synopsis Math Without Numbers by : Milo Beckman
Download or read book Math Without Numbers written by Milo Beckman and published by Penguin. This book was released on 2022-01-11 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
