Topology Of Numbers PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Topology Of Numbers PDF full book. Access full book title Topology Of Numbers.
Author | : Pieter Moree |
Publisher | : American Mathematical Soc. |
Total Pages | : 347 |
Release | : 2020-02-12 |
Genre | : Education |
ISBN | : 147045100X |
Download Dynamics: Topology and Numbers Book in PDF, ePub and Kindle
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.
Author | : Allen Hatcher |
Publisher | : American Mathematical Society |
Total Pages | : 351 |
Release | : 2022-10-19 |
Genre | : Mathematics |
ISBN | : 1470456117 |
Download Topology of Numbers Book in PDF, ePub and Kindle
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.
Author | : John Roe |
Publisher | : American Mathematical Soc. |
Total Pages | : 269 |
Release | : 2015-09-03 |
Genre | : Algebraic topology |
ISBN | : 1470421984 |
Download Winding Around: The Winding Number in Topology, Geometry, and Analysis Book in PDF, ePub and Kindle
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.
Author | : Allen Hatcher |
Publisher | : Cambridge University Press |
Total Pages | : 572 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780521795401 |
Download Algebraic Topology Book in PDF, ePub and Kindle
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.
Author | : Paul Alexandroff |
Publisher | : Courier Corporation |
Total Pages | : 68 |
Release | : 2012-08-13 |
Genre | : Mathematics |
ISBN | : 0486155064 |
Download Elementary Concepts of Topology Book in PDF, ePub and Kindle
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.
Author | : Stephen Barr |
Publisher | : Courier Corporation |
Total Pages | : 244 |
Release | : 2012-12-04 |
Genre | : Mathematics |
ISBN | : 048615274X |
Download Experiments in Topology Book in PDF, ePub and Kindle
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Author | : |
Publisher | : |
Total Pages | : 435 |
Release | : 2007 |
Genre | : Number theory |
ISBN | : 9787115156112 |
Download 数论导引 Book in PDF, ePub and Kindle
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。
Author | : George E. Andrews |
Publisher | : Courier Corporation |
Total Pages | : 292 |
Release | : 2012-04-30 |
Genre | : Mathematics |
ISBN | : 0486135101 |
Download Number Theory Book in PDF, ePub and Kindle
Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Author | : John D. Baum |
Publisher | : Courier Corporation |
Total Pages | : 164 |
Release | : 1991-01-01 |
Genre | : Mathematics |
ISBN | : 0486668266 |
Download Elements of Point Set Topology Book in PDF, ePub and Kindle
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.
Author | : Masanori Morishita |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2011-11-27 |
Genre | : Mathematics |
ISBN | : 1447121589 |
Download Knots and Primes Book in PDF, ePub and Kindle
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.