Simmons' Topology and Modern Analysis

In summary: I think Topology by Munkres is a good book. I would recommend it if you are looking for clearness. I would not recommend it if you are looking for motivation.
  • #1
mattmns
1,128
6
I am looking at an independent study next semester and I want to do something with point-set topology and analysis, so I have been looking at the book Introduction to Topology and Modern Analysis by Simmons, which I have heard good things about. For a little background I am currently taking Advanced Calculus and we are using Terrence Tao's Analysis I book, so I know a little analysis, but we are doing everything in the real line, nothing in metric/topological spaces. The question I must ask is how much should I try to cover in a 16-week semester? I am thinking the first 7 chapters [Sets and Functions, Metric Spaces, Topological Spaces, Compactness, Separation, Connectedness, Approximation] (the entire section on Topology) would be plenty (I could probably cover the first chapter before the semester begins since it will be nearly all review). For those who have gone through the book, or know of it, does this seem like a good amount for a 16-week course? Either way, what would you suggest? Thanks.
 
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  • #2
i suggest having as much fun as possible, and going at an any pace you find suitable. this si not a race, and it is very lengthy. so even if you start slowly, if you enjoy yourself you may well outlast others who start more quickly.

simmons is a good, readable, intro to basic topology used in analysis. i recommend it. i liked it myaelf when i found other books like rudin too dry and repellant. if you plan to be a topologist you might like a book with less dry, more fun topology, like artin and braun.
 
  • #3
i never understood the point of topology. volume of this=volume of that?

at least it has more applications than fractal geometry
 
  • #4
geez. get on the train. you have a great adventure ahead of you.
 
  • #5
I'm really liking Topology by Munkres. Not sure where that ranks though.
 
  • #6
If you want clearness, i suggest Munkres.
If you want motivation, I suggest Janich, but this book does not define many things. Please be ware.
 

Related to Simmons' Topology and Modern Analysis

1. What is the main focus of Simmons' Topology and Modern Analysis?

The main focus of Simmons' Topology and Modern Analysis is to provide a comprehensive introduction to topology and its applications in modern analysis. It covers topics such as metric spaces, topological spaces, continuity, connectedness, compactness, and more.

2. Is Simmons' Topology and Modern Analysis suitable for beginners?

While some prior knowledge of calculus and linear algebra is helpful, Simmons' Topology and Modern Analysis is written in a clear and accessible style that makes it suitable for beginners. It also includes numerous examples and exercises to aid in understanding the concepts.

3. How is this book different from other topology textbooks?

Simmons' Topology and Modern Analysis stands out for its emphasis on modern applications of topology in analysis, such as differential equations and functional analysis. It also includes a chapter on algebraic topology, which is not typically found in introductory topology texts.

4. Can this book be used as a reference for graduate level courses?

Yes, Simmons' Topology and Modern Analysis is often used as a textbook for graduate level courses in topology and analysis. It covers advanced topics such as Banach and Hilbert spaces, and provides a solid foundation for further study in these areas.

5. Are there any online resources available for this book?

Yes, the publisher's website offers supplementary materials for this book, including additional exercises and solutions, as well as a study guide for instructors. There are also many online resources available for topology and modern analysis, such as lecture notes and video lectures, that can be used in conjunction with this book.

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