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Author: Steve Warner
Publisher:
Published: 2019-11-13
Total Pages: 142
ISBN-13: 9781951619039
DOWNLOAD EBOOKTopology for Beginners - Solution GuideThis book contains complete solutions to the problems in the 16 Problem Sets in Topology for Beginners. Note that this book references examples and theorems from Topology for Beginners. Therefore, it is strongly suggested that you purchase a copy of that book before purchasing this one.
Author: Steve Warner
Publisher:
Published: 2019-04-25
Total Pages: 282
ISBN-13: 9780999811771
DOWNLOAD EBOOKTopology for Beginners consists of a series of basic to intermediate lessons in topology. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Topology for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in topology. high school teachers working with advanced math students. students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and topology. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Topology Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets and Subsets Lesson 2 - Operations on Sets Lesson 3 - Relations Lesson 4 - Functions and Equinumerosity Lesson 5 - Number Systems and Induction Lesson 6 - Algebraic Structures and Completeness Lesson 7 - Basic Topology of R and C Lesson 8 - Continuity in R and C Lesson 9 - Topological Spaces Lesson 10 - Separation and Countability Lesson 11 - Metrizable Spaces Lesson 12 - Compactness Lesson 13 - Continuity and Homeomorphisms Lesson 14 - Connectedness Lesson 15 - Function Spaces Lesson 16 - Algebraic Topology
Author:
Publisher: Research & Education Assoc.
Published:
Total Pages: 750
ISBN-13: 9780738670683
DOWNLOAD EBOOKAuthor: Hajime Satō
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 144
ISBN-13: 9780821810460
DOWNLOAD EBOOKThe single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.
Author: Steve Y. Oudot
Publisher: American Mathematical Soc.
Published: 2017-05-17
Total Pages: 229
ISBN-13: 1470434431
DOWNLOAD EBOOKPersistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.
Author: James F. Davis
Publisher: American Mathematical Society
Published: 2023-05-22
Total Pages: 385
ISBN-13: 1470473682
DOWNLOAD EBOOKThe amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 395
ISBN-13: 038722727X
DOWNLOAD EBOOKManifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Author: Tai-Danae Bradley
Publisher: MIT Press
Published: 2020-08-18
Total Pages: 167
ISBN-13: 0262359626
DOWNLOAD EBOOKA graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Author: J. P. May
Publisher: University of Chicago Press
Published: 1999-09
Total Pages: 262
ISBN-13: 9780226511832
DOWNLOAD EBOOKAlgebraic 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.
Author: Matthew Skelton
Publisher: IT Revolution
Published: 2019-09-17
Total Pages: 210
ISBN-13: 1942788827
DOWNLOAD EBOOKEffective software teams are essential for any organization to deliver value continuously and sustainably. But how do you build the best team organization for your specific goals, culture, and needs? Team Topologies is a practical, step-by-step, adaptive model for organizational design and team interaction based on four fundamental team types and three team interaction patterns. It is a model that treats teams as the fundamental means of delivery, where team structures and communication pathways are able to evolve with technological and organizational maturity. In Team Topologies, IT consultants Matthew Skelton and Manuel Pais share secrets of successful team patterns and interactions to help readers choose and evolve the right team patterns for their organization, making sure to keep the software healthy and optimize value streams. Team Topologies is a major step forward in organizational design for software, presenting a well-defined way for teams to interact and interrelate that helps make the resulting software architecture clearer and more sustainable, turning inter-team problems into valuable signals for the self-steering organization.
