How to Learn both Differential Geometry and Relativity?

Click For Summary

Discussion Overview

The discussion revolves around the feasibility of learning differential geometry concurrently with the study of relativity and gravitation. Participants explore the implications of this dual learning approach, considering the mathematical foundations necessary for understanding modern research in relativity.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether it is possible to learn differential geometry while studying relativity, noting that modern research relies heavily on differential geometry and algebraic topology.
  • Another participant asserts that simultaneous learning is possible, acknowledging the increased difficulty but suggesting that relativity can provide a focused context for understanding differential geometry.
  • A participant expresses concern about the potential drawbacks of reading mathematically-inclined books on relativity, citing worries about comprehension and the relationship between mathematics and physical concepts.
  • There is mention of various resources, including books by Sachs/Wu and Hawking/Ellis, which may be more mathematically rigorous.
  • One participant suggests that confusion in understanding may stem from a lack of sufficient background and encourages practice and discussion of specific problems in other threads.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of learning both subjects simultaneously, with some supporting the idea while others raise concerns about comprehension and the appropriateness of mathematically-inclined texts. The discussion remains unresolved regarding the best approach to integrate these subjects.

Contextual Notes

Participants highlight limitations in their mathematical backgrounds, including gaps in single-variable analysis and multilinear algebra, which may affect their ability to grasp the material. There is also a recognition that the relationship between mathematics and physical interpretation is complex and may vary among learners.

bacte2013
Messages
394
Reaction score
48
Dear Physics Forum personnel,

Is it possible to learn differential geometry simultaneously while learning the relativity and gravitation? I have been reading Weinberg's book (currently in Chapter 02), but I believe that modern research in relativity is heavily based on the differential geometry and algebraic topology, which I did not master yet. I would like to learn them alongside with relativity, which will help me to prepare for upcoming theoretical research in relativity. I was thinking about studying differential geometry first, but it would be inefficient in time-wise as I am not convinced that I need thorough knowledge in it, at least from my experience with Weinberg.

I have strong background in set-theoretic topology (Engelking) and algebra (Lang, Aluffi, Isaacs), but my memory of single-variable analysis and multilinear algebra are quite foggy...Also, I only have practical knowledge in vector calculus.
 
Physics news on Phys.org
bacte2013 said:
Is it possible to learn differential geometry simultaneously while learning the relativity and gravitation?
Yes. It is harder in many ways - but there is an advantage in that you can use the GR to focus the differential geometry whereas a math paper will be more general.
 
Simon Bridge said:
Yes. It is harder in many ways - but there is an advantage in that you can use the GR to focus the differential geometry whereas a math paper will be more general.

Thank you for your advice. I have a lot of time to devote myself to physics as my current medical treatment forced me to take only few official courses on this semester. I have been searching books that are more mathematically-inclined and also covering manifolds, and I found some books like Sachs/Wu, Hawking/Ellis, etc. Some people said that reading mathematically-inclined books in relativity will hurt the understanding, which makes me worry too. Weinberg is not quite heavy in mathematics, particularly in differential geometry, and I found that physical explanation is causing me a lot of confusions. Maybe I do not have a sufficient background?
 
Some people said that reading mathematically-inclined books in relativity will hurt the understanding, which makes me worry too.
To be "physics", you need to be able to relate the maths to something you can measure in Nature. It is possible to study the mathematics of relativity asa concept though and lots of theoretical physicists seem to do just that.

Weinberg is not quite heavy in mathematics, particularly in differential geometry, and I found that physical explanation is causing me a lot of confusions. Maybe I do not have a sufficient background?
It's just practise ... perhaps where you get confused you can try describing the problem in another thread?
 

Similar threads

Textbook/study plan questions
  • · Replies 9 ·
Replies
9
Views
2K
Studying Need advice for research subjects in both topological and general relativity
  • · Replies 2 ·
Replies
2
Views
2K
Is this a good self-study program?
  • · Replies 16 ·
Replies
16
Views
3K
Studying What Are the Best Steps for Self-Teaching Theoretical Physics?
  • · Replies 14 ·
Replies
14
Views
5K
Recommendations for study materials to prepare for undergrad Physics
  • · Replies 7 ·
Replies
7
Views
3K
I want to study algebraic geometry and differential geometry
  • · Replies 2 ·
Replies
2
Views
5K
Studying Seeking your suggestions on my upcoming undergraduate course workload
  • · Replies 5 ·
Replies
5
Views
2K
Studying Geometry- where to start, how far to go?
  • · Replies 23 ·
Replies
23
Views
3K
Studying Self-studying physics in preparation for learning astrophysics on my own
  • · Replies 6 ·
Replies
6
Views
4K
Functional Analysis or Differential Geometry?
  • · Replies 3 ·
Replies
3
Views
4K