Topology of Surfaces
By addebook • Oct 3rd, 2008 • Category: Mathematics •
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Topology of Surfaces (Undergraduate Texts in Mathematics)
Topology of Surfaces (Undergraduate Texts in Mathematics)
By L.Christine Kinsey
Publisher: Springer
Number Of Pages: 296
Publication Date: 1997-09-26
ISBN-10 / ASIN: 0387941029
ISBN-13 / EAN: 9780387941028
Binding: Hardcover
This book aims to provide undergraduates with an understanding of geometric topology. Topics covered include a sampling from point-set, geometric, and algebraic topology. The presentation is pragmatic, avoiding the famous pedagogical method “whereby one begins with the general and proceeds to the particular only after the student is too confused to understand it.” Exercises are an integral part of the text. Students taking the course should have some knowledge of linear algebra. An appendix provides a brief survey of the necessary background of group theory.
Summary: Not great but good
Rating: 4
Let me begin by saying that I only got through the chapter on triangulations. I used this book in an undergraduate topology course where the instructor was not the best at teaching topology. So, I had to self-study with this book.
The first three chapters of the book are very well written. The theorems are proven in an intuitive manner that makes sense with some analysis background. Also, the exercises encourage, and at times force, the reader to really understand the topologies of the reals. The reader then is introduced to general topological spaces, including quotient and product topologies. This material is also very well written and relatively easy to understand, with some work by the reader.
The chapter on triangulations and surfaces is very difficult to understand. In the first few chapters, I could tell that the casual language chosen by the author would eventually lead to trouble. The careful word choices necessary in a math book were missing in this chapter. Little details like “relative to” and “in” are left out, sometimes requiring hours of careful reading of definitions trying to figure out exactly what the author means. This, to me, in unacceptable. The book reads more like lecture notes and less like a text book. Fortunately, I also purchased Munkres’ topology book and referred to that whenever I didn’t understand the author’s explanation, which was a lot in the last chapter I studied.
Taking into account all the deficiencies with this book, I would still recommend it just for the first 3 chapters. These chapters are an excelent introduction to topology. I give this book 4 stars because it offers a good introduction to general topology. I also liked how the author put the exercises in the sections. This made it easy to see exactly what you should try to use in your proofs. I would also getting another, more theoretical, book to use as a reference if(when?) you get stuck by the author’s poor choice of words.
Summary: The best undergrad topology text
Rating: 5
Considering several other undergrad topology texts, e.g. Munkres, Armstrong, etc. this is the easiest to work with. Certainly the best text for self-study. The problems are not too difficult yet they help you grasp concepts as well. They are also laid out as you go; so every so often while you read the text you encounter a problem and you do it as you go. It is much better than putting them in the back of the chapters, as most text do. It is better to lay the problems in the text so you are encouraged to do them as you learn the material. The material in the text is very well explained and contrary to the previous review, is very well-suited, and with sufficient rigor, for mathematics students. The fact that this book “can be grasped at the sophomore level” as the previous revewer claims (and I agree with) lends credence to the simplicity of presentation of the material. Some reviewers I suppose aren’t satisfied unless they see a hyperdense conglomeration of gobbledygook which characterizes so many mathematics texts. I don’t fall into that camp and if you don’t either and at the same want to begin study in topology then I highly recommend this book.
Summary: great Topology text
Rating: 5
I must say that this is by far the best topology text that I have seen. Very readable, easy to follow. The anecdotal comments are also amusing. I’m particularly fond of the Ham and Cheese Sandwich Theorem! Highly recommend.
Summary: A very readable introduction to homology.
Rating: 5
This is a very readable introduction to homology theory, replete with good illustrations and lucid writing. Kinsey does a great job of motivating and explaining her material. I only wish I could have had a text this readable when I was a student.
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