Topology Of Numbers
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Topology Of Numbers
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Author : Allen Hatcher
language : en
Publisher: American Mathematical Society
Release Date : 2022-10-19
Topology Of Numbers written by Allen Hatcher and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-19 with Mathematics categories.
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.
Dynamics Topology And Numbers
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Author : Pieter Moree
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-12
Dynamics Topology And Numbers written by Pieter Moree and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-12 with Education categories.
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.
American Mathematical Society Translations
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Author : S. P. Demuškin
language : en
Publisher: American Mathematical Soc.
Release Date : 1966
American Mathematical Society Translations written by S. P. Demuškin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Mathematics categories.
Knots And Primes
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Author : Masanori Morishita
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-27
Knots And Primes written by Masanori Morishita and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-27 with Mathematics categories.
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.
General Topology
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Author : Waclaw Sierpinski
language : en
Publisher: Courier Dover Publications
Release Date : 2020-04-15
General Topology written by Waclaw Sierpinski and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-15 with Mathematics categories.
Critically acclaimed text by distinguished mathematician presents detailed theory of Fréchet (V) spaces and comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. 1956 edition.
Winding Around The Winding Number In Topology Geometry And Analysis
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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-03
Winding Around The Winding Number In Topology Geometry And Analysis written by John Roe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Algebraic topology categories.
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.
Mathematics
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Author : Britannica Educational Publishing
language : en
Publisher: Britannica Educational Publishing
Release Date : 2015-01-01
Mathematics written by Britannica Educational Publishing and has been published by Britannica Educational Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-01 with Juvenile Nonfiction categories.
This insightful guide to the history and basic concepts of mathematics reveals how math concepts helped to shape society--from the basic counting and units of measurement that facilitated commerce to the kind of surveying techniques and geometry that helped build the Egyptian pyramids. A chronological account of advancements in mathematics ranges Aristotle and al-Khwarizmi (who first used the term "algebra") to high-speed computers and their impact upon the teaching and understanding of mathematics. Readers will also find out how much of ancient arithmetic--like the 60 minute hour--is still part of our everyday life.
Algebraic Groups And Number Theory
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Author : Vladimir Platonov
language : en
Publisher: Academic Press
Release Date : 1993-12-07
Algebraic Groups And Number Theory written by Vladimir Platonov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-07 with Mathematics categories.
This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
The Real Numbers In Pointfree Topology
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Author : Bernhard Banaschewski
language : en
Publisher:
Release Date : 1997
The Real Numbers In Pointfree Topology written by Bernhard Banaschewski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Frames (Combinatorial analysis) categories.
Introduction To Set Theory And Topology
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Author : Kazimierz Kuratowski
language : en
Publisher: Elsevier
Release Date : 2014-07-10
Introduction To Set Theory And Topology written by Kazimierz Kuratowski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.