What should I study after Calculus 3?

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Discussion Overview

The discussion revolves around recommendations for advanced study topics following completion of Calculus III, particularly for a student majoring in physics and mathematics. Participants explore various subjects that could enhance the student's understanding and preparation for a theoretical physics PhD.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests considering Spivak's calculus if the student's previous calculus course was not rigorous enough.
  • Another participant proposes studying real analysis, abstract algebra, differential geometry, or discrete mathematics, emphasizing the importance of personal interest in the choice.
  • A participant confirms the rigor of their calculus course and reflects on a professor's comment that calculus is a subset of real analysis, questioning whether to pursue real analysis next.
  • One suggestion is to take Linear Algebra and Differential Equations as reasonable next steps for a physics major.
  • Another participant recommends real analysis as a beneficial next step and mentions that Spivak's book serves as an introduction to real analysis.
  • One participant inquires about the student's comfort with proofs, indicating that this is relevant for studying real analysis.
  • Another participant introduces the idea of studying differential topology/geometry and tensor calculus.
  • A suggestion is made to explore Spivak's Calculus on Manifolds, distinguishing it from other works by Spivak.

Areas of Agreement / Disagreement

Participants express various recommendations for advanced study topics, with no consensus on a single path forward. Multiple competing views on what subjects to pursue remain evident.

Contextual Notes

Participants reference the rigor of previous coursework and the relevance of personal interest in selecting study topics. There is also mention of the importance of proof comprehension for certain subjects.

Who May Find This Useful

Students in physics or mathematics looking for guidance on advanced topics to study after completing Calculus III, particularly those interested in theoretical physics or self-study opportunities.

Genericcoder
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Hey guys,

So I am a physics and math major so far I am took Calculus I,II,III linear algebra and statistics
I did really good in them almost acing all of them and aced vector calculus.

I am taking complex analysis and introduction to probability in fall. I have holiday in the winter break for about 1 month and I want to self study some high level material, so what would you suggest studying ?

I am planning to go into theortical physics PHD besides I really like math and started to like it even more than physics,so I want to improve myself even more than university so I need some suggestions.

I don't know if this is the right section to post this but it seems like it.
 
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Was your calculus course very rigorous? If not, you might want to go through Spivak's calculus.

There's really a lot you can do now: real analysis, abstract algebra, differential geometry, discrete mathematics, etc. Pick something you're really interested in.
 
Yeh it was very rigorous course but I might also check Spivak . Our Professor for vector calculus said that calculus is a subset of real analysis so I think should I go into real analysis ? What do you think ?
 
For a physics major, Linear Algebra and Differential Equations would be reasonable next courses. But why ask us? Your college catalog surely has a list of required courses and probably some "recommended" courses for physics majors. And your best possible source are your major professors.
 
Genericcoder said:
Yeh it was very rigorous course but I might also check Spivak . Our Professor for vector calculus said that calculus is a subset of real analysis so I think should I go into real analysis ? What do you think ?

Yes, doing real analysis is a great thing to do next. Spivak actually is an intro to real analysis, so do take a look at that book.

Are you comfortable with proofs?
 
Yes I am comfortable with proofs @ micromass. @hallsYeh I am already taking DE and also I am asking here because I want to get ahead of university and do more self study.
 
Differential topology/geometry and tensor calculus.
 
If you are really keen, you might want to look on Spivaks Calculus on Manifolds book (not the same as the other Spivak titles that may be referenced).
 

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