Will these courses will be good enough preparation for a pure math PhD program?

In summary, the speaker is currently a freshman and plans on taking a variety of math courses in their four years of undergrad, including Calculus II, Calculus III, Linear Algebra, Real Analysis, Differential Equations, Abstract Algebra, Complex Variables, and more. They also plan on taking several graduate level courses, such as Algebraic Topology and Complex Analysis. The speaker also suggests taking courses that one enjoys and mentions the importance of understanding advanced calculus concepts. They also recommend taking theoretical computer science courses and mention a lack of knowledge about physics courses.
  • #1
inknit
58
0
I'm currently a freshman and these are all the math courses I plan on taking in 4 years.

Undergrad:
- Calc II (taken), Calc III, Linear Algebra I, Linear Algebra II, Real Analysis I, Real Analysis II, Ordinary Differential Equations, Intro to Abstract Algebra, Complex Variables, Survey of Algebra, Number Theory, General Topology, Differential Geometry, Advanced Multivariate Calculus

Graduate:
-Algebraic Topology I, Complex Analysis I, Homological Algebra, Measure Theory, Algebraic Topology II, Complex Analysis II...3-6 more graduate math classes

Also, do you think it's necessary to take some physics, computer science classes? I already took programming.
 
Physics news on Phys.org
  • #2
My first advice for you would be "take courses that you think you will enjoy", because in the long term perspective how much you have learned will matter very less as opposed to how much you have enjoyed. Also, learning and enjoying what you learn have very good correlation, one can easily affect the other. Sorry for this boring advice, just my 2 cents!

The simple answer to your question is yes. I would add Functional Analysis to your list of "courses to take". Regarding Physics & Computer Science, if you can take courses from theoretical computer science that will be so cool, both the subject and the math you apply to them. I don't know much about Physics courses.
 
  • #3
More important than how many courses you take, is what you understand well. I would say especially important is advanced calculus (multivariable), i.e. roughly the content of spivak's little book, calculus on manifolds, although it might be better to read that after having a more traditional course on the material.

E.g absolutely basic results include Green's theorem and the implicit function theorem of two variables, and yet it is rare (in some places) to find even an advanced graduate class in which most students know these theorems well.
 

1. What are the required courses for a pure math PhD program?

The specific required courses for a pure math PhD program may vary between universities, but typically they include advanced courses in calculus, linear algebra, abstract algebra, real analysis, and topology. It is also recommended to have a strong foundation in computer science and programming.

2. Will these courses cover all the necessary topics for a pure math PhD program?

It depends on the specific courses you take and the requirements of the PhD program you are interested in. It is best to consult with an academic advisor or the program director to ensure that you are covering all the necessary topics.

3. Are there any additional courses or topics I should study to prepare for a pure math PhD program?

In addition to the required courses, it is beneficial to have a broad understanding of other areas of mathematics such as number theory, differential equations, and mathematical logic. It is also recommended to have experience with writing mathematical proofs.

4. Is it necessary to have a strong background in physics or other sciences for a pure math PhD program?

No, a strong background in pure mathematics is the most important factor for success in a pure math PhD program. While some interdisciplinary research may involve knowledge of other sciences, it is not a requirement for the program.

5. Can I still be accepted into a pure math PhD program if I have not taken all of the required courses?

It is possible, but it may be more difficult to be accepted without the necessary coursework. Admissions committees typically look at a combination of factors, including coursework, research experience, letters of recommendation, and GRE scores. It is best to have a well-rounded application to increase your chances of acceptance.

Similar threads

  • STEM Academic Advising
Replies
5
Views
1K
  • STEM Academic Advising
Replies
11
Views
612
  • STEM Academic Advising
Replies
19
Views
2K
  • STEM Academic Advising
Replies
5
Views
1K
  • STEM Academic Advising
Replies
21
Views
2K
  • STEM Academic Advising
Replies
11
Views
369
  • STEM Academic Advising
Replies
23
Views
3K
  • STEM Academic Advising
Replies
11
Views
1K
  • STEM Academic Advising
Replies
6
Views
1K
  • STEM Academic Advising
Replies
13
Views
1K
Back
Top