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by Michael Henle
Download Combinatorial Introduction to Topology (Series of Books in Mathematical Sciences) fb2
Mathematics
  • Author:
    Michael Henle
  • ISBN:
    0716700832
  • ISBN13:
    978-0716700838
  • Genre:
  • Publisher:
    W H Freeman & Co; First Edition edition (December 1, 1978)
  • Pages:
    310 pages
  • Subcategory:
    Mathematics
  • Language:
  • FB2 format
    1187 kb
  • ePUB format
    1183 kb
  • DJVU format
    1997 kb
  • Rating:
    4.7
  • Votes:
    199
  • Formats:
    mbr azw txt mobi


To facilitate understanding, Professor Henle has deliberately restricted the . A Combinatorial Introduction to Topology Dover Books on Mathematics Series Dover books on advanced mathematics Series of books in mathematical sciences.

To facilitate understanding, Professor Henle has deliberately restricted the subject matter of this volume, focusing especially on surfaces because the theorems can be easily visualized there, encouraging geometric intuition. In addition, this area presents many interesting applications arising from systems of differential equations. To illuminate the interaction of geometry and algebra, a single important algebraic tool - homology - is developed in detail.

Series: Dover Books on Mathematics. Paperback: 224 pages. I purchased this book for an introductory course in topology. As a non-specialist in applied mathematics, this book has concise contents and very readable

Series: Dover Books on Mathematics. As a non-specialist in applied mathematics, this book has concise contents and very readable. I am still on my way through this book and recommend this book to who wants to dive into an astonishing world of topology. Highly recommended for.

book by Michael Henle

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.

The list is updated on a daily basis, so, if you want to bookmark this page, use one of the buttons below. Introduction to the Galois Theory of Linear Differential Equations Michael F. Singer arXiv, Published in 2008, 83 pages.

A Combinatorial Introduction to Topology.

This book can be found in: Science, Technology & Medicine Mathematics & science Mathematics Geometry Science, Technology & Medicine Mathematics & science Mathematics Topology Science, Technology & Medicine Mathematics & science Mathematics Combinatorics & graph theory. A Combinatorial Introduction to Topology - Dover Books on Mathematics (Paperback). Michael Henle (author). Paperback 310 Pages, Published: 28/03/2003. Publisher out of stock. A Combinatorial Introduction to Topology.

A Combinatorial Introduction to Topology book. Goodreads helps you keep track of books you want to read

A Combinatorial Introduction to Topology book. Goodreads helps you keep track of books you want to read. Start by marking A Combinatorial Introduction to Topology as Want to Read: Want to Read savin. ant to Read.

Other books in this series. 33% off. Introduction to Topology.

This book is a translation of the original Zadlmia z olimpiad matematycznych, Vo. Introduction to Methods of Applied Mathematics or Advanced Mathematical Methods for Scientists.

This book is a translation of the original Zadlmia z olimpiad matematycznych, Vol. I, published. Introduction to Insurance Mathematics: Technical and Financial Features of Risk Transfers. Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Textbook + e-book. 33 MB·20,456 Downloads·New!

PDF The mathematical combinatorics is a subject that applies combinatorial notion to all mathematics and all . I even have written a book with title: A Biblical Theory of Everything based on the Johannine Prologue. Saarbrucken: LAP Lambert Academic Publishing, 2015.

PDF The mathematical combinatorics is a subject that applies combinatorial notion to all mathematics and all sciences for understanding the reality o. . Invitation to a second collective book on Neutrosophic Overset, Underset, Offset. Florentin Smarandache.

Book Title :Foundations of Combinatorial Topology. Author(s) :l pontriagin (1952)

Book Title :Foundations of Combinatorial Topology. Author(s) :l pontriagin (1952).

Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some knowledge of differential equations and multivariate calculus required. Many problems and exercises (some solutions) integrated into the text. 1979 edition. Bibliography.

SadLendy
Usually books on algebraic topology, even with the title "introduction" or something, are extremely difficult. This book is an exception. And it is a exceptional book since the author tried his best to explain abstract concepts in charts. You know, most of the modern "geometry" books do not really use illustrations! (They only cares about group theory)
Mbon
This is an excellent book on topology. It is perfect for the researcher or student who wants to get the hands dirty. It is very clear with great examples. I wish all of my books were as useful and delightful to read.A Combinatorial Introduction to Topology (Dover Books on Mathematics)
Malarad
Historically, combinatorial topology was a precursor to what is now the field of algebraic topology, and this book gives an elementary introduction to the subject, directed towards the beginning student of topology or geometry. Due to its importance in applications, the physicist reader who is intending eventually to specialize in elementary particle physics will gain much in the perusal of this book.
Combinatorial topology can be viewed first as an attempt to study the properties of polyhedra and how they fit together to form more complicated objects. Conversely, one can view it as a way of studying complicated objects by breaking them up into elementary polyhedral pieces. The author takes the former view in this book, and he restricts his attention to the study of objects that are built up from polygons, with the proviso that vertices are joined to vertices and (whole) edges are joined to (whole) edges.
He begins the book with a consideration of the Euler formula, and as one example considers the Euler number of the Platonic solids, resulting in a Diophantine equation. This equation only has five solutions, the Platonic solids. The author then motivates the concept of a homeomorphism (he calls them "topological equivalences") by considering topological transformations in the plane. Using the notion of topological equivalence he defines the notions of cell, path, and Jordan curve. Compactness and connectedness are then defined, along with the general notion of a topological space.
Elementary notions from differential topology are then considered in chapter 2, with the reader encountering for the first time the connections between analysis and topology, via the consideration of the phase portraits of differential equations. Brouwer's fixed point theorem is proved via Sperner's lemma, the latter being a combinatorial result which deals with the labeling of vertices in a triangulation of the cell. Gradient vector fields, the Poincare index theorem, and dual vector fields, which are some elementary notions in Morse theory, are treated here briefly.
An excellent introduction to some elementary notions from algebraic topology is done in chapter 3. The author treats the case of plane homology (mod 2), which is discussed via the use of polygonal chains on a grating in the plane. Beginning students will find the presentation very understandable, and the formalism that is developed is used to give a proof of the Jordan curve theorem. Then in chapter 4, the author proves the classification theorem for surfaces, using a combinatorial definition of a surface.
The author raises the level of complication in chapter 5, wherein he studies the (mod 2) homology of complexes. A complex is defined somewhat loosely as a topological space that is constructed out of vertices, edges, and polygons via topological identification. He proves the invariance theorem for triangulations of surfaces by showing that the homology groups of the triangulation are same as the homology groups of the plane model of the surface. This is an example of the invariance principle, and the author briefly details some of the history of invariance principles, such as the Hauptvermutung, its counterexample due to the mathematician John Milnor, and Heawood's conjecture, the latter of which deals with the minimum number of colors needed to color all maps on a surface with a given Euler characteristic. Integral homology is also introduced by the author, and he shows the origin of torsion in the consideration of the "twist" in a surface.
In the last part of the book, the author returns to the consideration of continuous transformations, tackling first the idea of a universal covering space. Algebraic topology again makes its appearance via the consideration of transformations of triangulated topological spaces, i.e. simplicial transformations. He shows how these transformations induce transformations in the homology groups, thus introducing the reader to some notions from category theory. The elaboration of the invariance theorem for homology leads the author to studying the properties of the group homomorphisms via matrix algebra, and then to a proof of the Lefschetz fixed point theorem. The book ends with a brief discussion of homotopy, topological dynamics, and alternative homology theories.
The beginning student of topology will thus be well prepared to move on to more rigorous and advanced treatments of differential, algebraic, and geometric topology after the reading of this book. There are still many unsolved problems in these areas, and each one of these will require a deep understanding and intuition of the underlying concepts in topology. This book is a good start.
Rgia
This covers the basics of algebraic topology with simplexes, covering in essence the fundamental ideas behind of the work of Poincare, Brouwer, and Alexander. He proves the Jordan curve theorem, classifies all compact surfaces, and the relationship with vector fields. The homology groups are defined and used.
There are excellent examples, clear writing, and humour. An outstanding introduction.
One nice feature is that he bases his notions of continuity on "nearness" not epsilon-delta.
Hellmaster
This is the second time I have bought this book since I offered

the first one to my son. An excellent introduction to the topic!