Differential geometry or number theory (which to take)

In summary, the person is entering their 3rd year of a PMAT degree and is trying to choose between taking a course in differential geometry or number theory. They are looking for suggestions from people who have taken either course, and mention that they enjoyed abstract algebra but have not taken analysis. The other person advises that the choice depends on the person's interests and future direction in grad school, and notes that differential geometry may be difficult without prior knowledge of analysis. They also mention that if the number theory course is elementary, it may not be necessary to take it as the textbook by Burton's is sufficient for self-study. However, if the differential geometry course includes manifolds, they recommend taking it as it is important for modern mathematic
  • #1
ocohen
24
0
hi,
I'm entering my 3rd year of PMAT degree and need to make a choice between differential geometry and number theory. These are both undergrad courses. I am trying to decide which would be more interesting/useful to take. I am planning on going into grad school, so it would be nice to choose a course that would help with that.

I enjoyed the abstract algebra courses, and I haven't done analysis but it seems pretty interesting.

Any suggestions from people who have taken either or both would be appreciated

Thanks
 
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  • #2
Weird question. You're asking us which course is more interesting? That depends on your interests! You're asking which would help more regarding grad school? That depends on which direction you go to in grad school!

Anyway, if you haven't done any analysis, I don't think Differential Geometry is doable. The whole idea is that you can locally do analysis, on manifolds. Things like the implicit function theorem are important.

Unless it is some kind of course about curves and surfaces without the manifolds machinery...
 
  • #3
What is a PMAT degree?
I googled it and all I found was "Pharmaceutical Microbiology Advanced Training".
 
  • #4
If the NT course is elementary NT, then I don't see any need to take a course in it, the textbook by Burton's is all one needs to learn elementary NT, it's ideal for self study.

If the DG course includes manifolds, then take it without hesitation, nowdays every modern mathematician ought to know what's a manifold.
 
  • #5
MathematicalPhysicist said:
If the NT course is elementary NT, then I don't see any need to take a course in it, the textbook by Burton's is all one needs to learn elementary NT, it's ideal for self study.

If the DG course includes manifolds, then take it without hesitation, nowdays every modern mathematician ought to know what's a manifold.

thanks that helps
 

1. What is the difference between differential geometry and number theory?

Differential geometry is a branch of mathematics that studies the properties of curves and surfaces using tools from calculus and linear algebra. It is often used to describe the geometry of physical spaces. On the other hand, number theory is a branch of mathematics that studies the properties of numbers, including prime numbers, divisibility, and arithmetic operations. It has applications in cryptography and coding theory.

2. Which field is more applicable in real-world scenarios?

Both differential geometry and number theory have many real-world applications. Differential geometry is used in physics, engineering, and computer graphics to model and understand physical spaces. Number theory has applications in cryptography, coding theory, and the study of prime numbers, which are important in many areas of mathematics and computer science.

3. Which field is more challenging to study?

Both differential geometry and number theory require a strong foundation in mathematics and can be challenging to study. Differential geometry involves abstract concepts and requires knowledge of calculus and linear algebra. Number theory involves intricate proofs and requires a deep understanding of number theory concepts and techniques.

4. Can I study both differential geometry and number theory?

Yes, it is possible to study both differential geometry and number theory. Many mathematicians specialize in both fields and use techniques from one to solve problems in the other. However, it is important to have a strong foundation in mathematics and to prioritize which field to focus on in your studies.

5. Which field has more job opportunities?

Both differential geometry and number theory have job opportunities in academia, research, and industry. However, the demand for mathematicians in each field may vary depending on current trends and economic factors. It is important to choose a field that interests you and in which you have a strong skill set.

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