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Title: First Concepts of Topology by William G. Chinn ISBN: 0-88385-618-2 Publisher: Mathematical Assn of America Pub. Date: 01 June, 1975 Format: Paperback Volumes: 1 List Price(USD): $17.50 |
Average Customer Rating: 4 (2 reviews)
Rating: 4
Summary: Good introduction to the basics of topology
Comment: This book gave me my first introduction to the basic concepts of topology and I consider that to have been a point of good fortune. Everything is explained in detail at a level that is appropriate for people who have just mastered calculus. The authors were also thoughtful enough to have included solutions to the exercises, which is something that is just not done often enough. Coverage includes compactness, connectedness, mappings and fixed points; winding numbers, dividing pancakes and sandwiches and vector fields. When students ask me to recommend a basic book on these topics, this is the one that I recommend, which is the highest praise that I can give.
Rating: 4
Summary: Great Introduction to Topology
Comment: When reading this book, I kept on wondering how good it will serve as the textbook for a semester-long high school intro to topology class! The authors placed great effort in making this book rigorous and rich in material yet at the same time very accessible (at least the first part) to the average high school junior or senior who's interested in higher math. The book builds up the fundamental concepts in general topology rather slowly to ease their digestion, and provides abundant examples along the way. Following the definitions and examples are celebrated theorems and their proofs that truly demonstrate the power and beauty of tology as well as mathematics in general. In fact, the whole book revolve around the "existence theorem" in one and two dimension (in one dimension, it's also known as the intermediate value theorem in calculus). This theorem is not only important in its own right, it is also intimately connected (not in the topological sense) with many concepts in topology. To prove the theorem for a disk in two dimension, the authors go through a thorough study of winding numbers and later on introduces vector fields, concept of homotopy, and interesting theorems like fixed-point theorem and ham-sandwich theorem. The later chapters of the book where these things are mentioned are rather obscure and difficult to understand, rather unlike the spirit of the earlier part; but by the time a high school senior gets to that point, he or she will probably be a mathematician enough to willingly dwell into these abstract wonders.
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Title: Graphs and Their Uses (New Mathematical Library; No. 34) by Oystein Ore ISBN: 0883856352 Publisher: Mathematical Assn of America Pub. Date: 01 February, 1991 List Price(USD): $24.95 |
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Title: Geometry Revisited (New Mathematical Library) by H. S. Coxeter, Geometry Revisted ISBN: 0883856190 Publisher: Mathematical Assn of America Pub. Date: 01 June, 1975 List Price(USD): $22.95 |
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Title: Groups and Their Graphs by I. Grossman, Magnus W. ISBN: 088385614X Publisher: Mathematical Association of America (MAA) Pub. Date: 01 June, 1975 List Price(USD): $18.46 |
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Title: Introduction to Inequalities (New Mathematical Library) by E. F. Backenbach, R. Bellman ISBN: 0883856034 Publisher: Mathematical Association of America (MAA) Pub. Date: 01 June, 1975 List Price(USD): $9.95 |
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Title: Understanding Infinity: The Mathematics of Infinite Processes by A. Gardiner, A. Infinite Processes, Background to Analysis Gardiner ISBN: 048642538X Publisher: Dover Publications Pub. Date: 01 February, 2003 List Price(USD): $19.95 |
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