Topology Of Numbers PDF Download
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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 | : 287 |
Release | : 2015-09-03 |
Genre | : Mathematics |
ISBN | : 1470421984 |
Download Winding Around 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 | : 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 | : 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 | : 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 | : Masanori Morishita |
Publisher | : Springer Nature |
Total Pages | : 268 |
Release | : |
Genre | : |
ISBN | : 9819992559 |
Download Knots and Primes Book in PDF, ePub and Kindle
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 | : Robert A Conover |
Publisher | : Courier Corporation |
Total Pages | : 276 |
Release | : 2014-05-21 |
Genre | : Mathematics |
ISBN | : 0486780015 |
Download A First Course in Topology Book in PDF, ePub and Kindle
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
Author | : T. Kyle Petersen |
Publisher | : Birkhäuser |
Total Pages | : 463 |
Release | : 2015-10-12 |
Genre | : Mathematics |
ISBN | : 1493930915 |
Download Eulerian Numbers Book in PDF, ePub and Kindle
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.