How accessible is Bott & Tu's book on algebraic topology?

In summary, the conversation discusses the book "Differential Forms in Algebraic Topology" by Bott & Tu and whether it would be too advanced for someone with knowledge at the level of Munkres' book on algebraic topology. It is suggested to read Tu's book on manifolds as a bridge between undergrad level math and Bott-Tu's book. The importance of reading books by well-known mathematicians is also emphasized.
  • #1
petergreat
267
4
Recently a professor recommended Bott & Tu's Differential Forms in Algebraic Topology to me. My knowledge of algebraic topology is at the level of Munkres' book. Would Bott & Tu's book be too advanced for me to understand at this stage?
 
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  • #2
It depends on how smart\sharp a kid you are... The only way to know is to give it a shot.

Have you been submitted to an introduction to manifolds yet? If not, Tu has written a book on that specifically to serve as a bridge between undergrad level math and an appropriate level to read Bott-Tu. It is called "An introduction to manifolds".
 
  • #3
Thanks for the advice. I know some manifold stuff from some informal introduction in physics courses but I suppose I'll read more about it before I take on Bott and Tu.
 
  • #4
open the book. it won't bite you.
 
  • #5
petergreat said:
My knowledge of algebraic topology is at the level of Munkres' book. Would Bott & Tu's book be too advanced for me to understand at this stage?
You know, Munkres has written (at least) two books on topology: 'Topology' (the most well-known one with a lot of point-set topology and a bit of algebraic topology), and 'Elements Of Algebraic Topology'. Probably you meant the first one?

I have been meaning to read Boot & Tu myself, I have heard great things about it.
 
  • #6
I am going to argue that even average students like me should read great books by stars like bott. that is really the only way we can aspire to the level of better mathematicians. Do not let the smart guys haVE A MONOPOLY ON READING THE BEST BOOKS! books by th greats can transform us into something different.
 

Related to How accessible is Bott & Tu's book on algebraic topology?

1. What is the difficulty level of Bott & Tu's book on algebraic topology?

The difficulty level of Bott & Tu's book on algebraic topology is considered to be intermediate to advanced. It assumes a basic knowledge of algebra, topology, and analysis, and gradually builds upon those concepts to introduce more advanced topics in algebraic topology.

2. Is Bott & Tu's book suitable for self-study?

Yes, Bott & Tu's book is suitable for self-study. It is well-organized and contains clear explanations and examples, making it accessible for independent learning. However, it is recommended to have a strong foundation in mathematics before attempting to study this book on your own.

3. What are the prerequisites for understanding Bott & Tu's book?

The prerequisites for understanding Bott & Tu's book on algebraic topology include a basic understanding of algebra, topology, and analysis. It is also helpful to have some knowledge of abstract algebra and category theory. Familiarity with point-set topology and basic homological algebra is also recommended.

4. Does Bott & Tu's book cover all the main topics in algebraic topology?

Yes, Bott & Tu's book covers all the main topics in algebraic topology, including fundamental concepts such as homotopy, homology, and cohomology. It also delves into more advanced topics such as spectral sequences and characteristic classes.

5. Is Bott & Tu's book a good reference for researchers in algebraic topology?

Yes, Bott & Tu's book is considered to be a standard reference for researchers in algebraic topology. It provides a comprehensive and rigorous treatment of the subject, making it a valuable resource for those working in the field.

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