What should I study after Calculus 3?

In summary, the conversation discusses the speaker's academic background in physics and math, their plans for self-study during a winter break, and their interest in pursuing a theoretical physics PhD. They ask for suggestions on what to study and receive recommendations such as real analysis, abstract algebra, differential geometry, and discrete mathematics. The conversation also mentions the book "Spivak's Calculus on Manifolds" as a potential resource for further study.
  • #1
Genericcoder
131
0
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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  • #2
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.
 
  • #3
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 ?
 
  • #4
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.
 
  • #5
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?
 
  • #6
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.
 
  • #7
Differential topology/geometry and tensor calculus.
 
  • #8
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).
 

Related to What should I study after Calculus 3?

What is the purpose of learning calculus 3?

Calculus 3 builds upon the concepts learned in previous calculus courses and introduces new topics such as vector calculus, multivariable functions, and partial derivatives. It is important for understanding advanced math and science courses, as well as applications in engineering, physics, and economics.

What are the career opportunities for someone who has taken calculus 3?

Individuals who have taken calculus 3 may pursue careers in fields such as engineering, physics, economics, data analysis, and computer science. Calculus 3 is also a prerequisite for many graduate programs in these fields.

Do I need to take calculus 3 if I am not majoring in a STEM field?

While calculus 3 may not be required for all majors, it is a valuable course that helps develop critical thinking and problem-solving skills. It can also be useful in fields such as business, medicine, and psychology.

Is calculus 3 difficult?

Calculus 3 can be challenging, as it introduces new concepts and requires a strong foundation in algebra and trigonometry. However, with dedication and practice, it can be mastered by most students.

What should I do after completing calculus 3?

After completing calculus 3, students can continue their study of math with courses such as linear algebra, differential equations, and advanced calculus. They may also explore applications of calculus in their field of interest or prepare for graduate studies.

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