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A Geometric Introduction to Topology

1993-01-01 Mathematics
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Release : 1993-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 504/5 ( reviews)

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Book Synopsis A Geometric Introduction to Topology by : Charles Terence Clegg Wall

Download or read book A Geometric Introduction to Topology written by Charles Terence Clegg Wall. This book was released on 1993-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Combinatorial Introduction to Topology

1994-01-01 Mathematics
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Release : 1994-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 662/5 ( reviews)

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Book Synopsis A Combinatorial Introduction to Topology by : Michael Henle

Download or read book A Combinatorial Introduction to Topology written by Michael Henle. This book was released on 1994-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Geometry and Topology

2018-07-18 Mathematics
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Release : 2018-07-18
Genre : Mathematics
Kind : eBook
Book Rating : 832/5 ( reviews)

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Book Synopsis Introduction to Geometry and Topology by : Werner Ballmann

Download or read book Introduction to Geometry and Topology written by Werner Ballmann. This book was released on 2018-07-18. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.

Introduction to Topology

2012-04-26 Mathematics
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Release : 2012-04-26
Genre : Mathematics
Kind : eBook
Book Rating : 098/5 ( reviews)

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Book Synopsis Introduction to Topology by : Bert Mendelson

Download or read book Introduction to Topology written by Bert Mendelson. This book was released on 2012-04-26. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Knots, Molecules, and the Universe

2015-12-22 Mathematics
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Release : 2015-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 351/5 ( reviews)

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Book Synopsis Knots, Molecules, and the Universe by : Erica Flapan

Download or read book Knots, Molecules, and the Universe written by Erica Flapan. This book was released on 2015-12-22. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

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