Good books for learning topology

In summary, topology is highly useful for modern theoretical physics and Jon Baez's website offers some interesting resources on the topic. Some recommended books for learning topology include "Topology without Tears" by Sidney Morris, which is available for free on his website, and "Topology" by James Munkres. It may also be beneficial to consult different sources on the subject from a local university library.
  • #1
Ed Quanta
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0
How useful is topology for physics? And what are soome good books for learning topology. I find a lot of the definitions in textbooks way too abstract and not giving examples of the topological spaces they are defining. Drop some titles if you have a moment.
 
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  • #2
For modern theoretical physics it appears indispensible. Look at Jon Baez's website to see some stuff that might interest you.

www.math.ucr.edu

thence faculty > baez > home page and browse the back issues of this week's finds etc.

if you want to throw yourself in at the deep end then I can suggest other stuff but i think it would be totally inappropriate at this stage.
 
  • #3
You could take a look at Sidney Morris' "Topology without tears", you can get it for free at his website http://uob-community.ballarat.edu.au/~smorris/topology.htm [Broken].
 
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  • #4
Munkres is good. It was quite pricy, but well worth the cost, when I bought it. You might try a local university library to look at topolgy books.
 
  • #5
NateTG said:
Munkres is good. It was quite pricy, but well worth the cost, when I bought it. You might try a local university library to look at topolgy books.
^^^

munkres is very clear. other books such as royden are good but only if you do the exercises (he gives you very little...you basically learn everything from the problems). like nate said, i would recommend you go to the library and get a few different top books. the more different sources the easier it is to understand.
 

1. What is topology and why is it important to learn?

Topology is the branch of mathematics that studies the properties of spaces that are preserved under continuous deformations, such as stretching or bending. It is important to learn because it provides a framework for understanding and analyzing complex geometric structures in mathematics and other fields, such as physics and computer science.

2. What are some good introductory books for learning topology?

Some good introductory books for learning topology include "Introduction to Topology" by Bert Mendelson, "Topology" by James R. Munkres, and "Topology: A First Course" by James R. Wilcox.

3. Do I need a strong background in mathematics to understand topology?

While a strong background in mathematics can certainly be helpful, it is not necessarily required to understand topology. However, a basic understanding of set theory, calculus, and linear algebra is recommended.

4. Are there any online resources for learning topology?

Yes, there are many online resources for learning topology, such as video lectures, interactive tutorials, and online textbooks. Some popular resources include Khan Academy, MIT OpenCourseWare, and Topology Atlas.

5. How can I apply topology in real-world problems?

Topology has many applications in various fields, such as engineering, physics, and biology. Some examples include analyzing the topology of networks and understanding the behavior of fluids through porous materials. It can also be applied in data analysis and machine learning for pattern recognition and classification tasks.

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