First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.
An easily accessible introduction to over threecenturies of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalizedtreatments bound to the old thinking. This clearly written,well-illustrated book supplies sufficient background to beself-contained.” —CHOICE This fully revised new edition offers the most comprehensivecoverage of modern geometry currently available at an introductorylevel. The book strikes a welcome balance between academic rigorand accessibility, providing a complete and cohesive picture of thescience with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction toTopology and Geometry, Second Edition discusses introductorytopology, algebraic topology, knot theory, the geometry ofsurfaces, Riemann geometries, fundamental groups, and differentialgeometry, which opens the doors to a wealth of applications. Withits logical, yet flexible, organization, the SecondEdition: • Explores historical notes interspersed throughout theexposition to provide readers with a feel for how the mathematicaldisciplines and theorems came into being • Provides exercises ranging from routine to challenging,allowing readers at varying levels of study to master the conceptsand methods • Bridges seemingly disparate topics by creating thoughtfuland logical connections • Contains coverage on the elements of polytope theory, whichacquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is anexcellent introductory text for topology and geometry courses atthe upper-undergraduate level. In addition, the book serves as anideal reference for professionals interested in gaining a deeperunderstanding of the topic.
Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.
This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses. The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.
Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.
Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.
This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.