Functional Analysis or Differential Geometry?

In summary, the person is in their last semester of their undergraduate degree and is deciding between a functional analysis course and a differential geometry course. They have already taken a functional analysis course and are leaning towards taking the differential geometry course due to better presentation and their interest in the subject. They are considering their future courses and seeking advice on which course to take. They have ultimately decided to stick with the differential geometry course after speaking to lecturers.
  • #1
AXidenT
26
2
I'm in my last semester of my undergraduate majoring in mathematics (focusing on mathematical physics I guess - I'm one subject short of having a physics major) and am wondering, largely from a physics perspective if it would be better to do a functional analysis course or a differential geometry course?

I took the first functional analysis course last semester, though the majority of this was topology, metric spaces and a little on Banach and other more structured spaces at the end. This semesters functional analysis cours eis a 4th year course that continues from the previous one and does more actual functional analysis (Hilbert Spaces etc...).

Alternatively there is the 3rd year differential geometry course which mainly sounds like it is contained in R^n. I've been going to lectures for both and the DG lectures are better presented for me and I also have a comprehensive functional analysis book I was given a year ago as a present - my worry is I don't get the same experience with self study as I do doing assessment.

I probably can't take whichever course I don't do now next year in honours. To give some context courses I'm looking at next year include advanced quantum (introduces relativistic and field theory), general relativity, measure theory and algebraic topology.

Any suggestions on which course I should take? I feel functional analysis is really important, but I haven't really been exposed to much geometry before either...

Thanks for any help!
 
Physics news on Phys.org
  • #2
It depends on what your goals and aspirations are. Explain those to some local profs who can give you better advice than we probably can.
 
  • #3
I feel differential geometry is more important than functional analysis. Differential geometry is important in GR, and even in stuff like classical mechanics and others. Functional analysis is mainly important in rigorous quantum stuff.
 
  • #4
After speaking to a few lecturers and what not I think I will keep DG - thanks for the advice!
 

FAQ: Functional Analysis or Differential Geometry?

What is functional analysis?

Functional analysis is a branch of mathematics that studies vector spaces and functions. It involves the use of various mathematical tools and techniques to understand the behavior and properties of functions, especially those that map one vector space to another.

What are some applications of functional analysis?

Functional analysis has applications in many fields, including physics, economics, engineering, and computer science. It is used to solve problems related to optimization, differential equations, and signal processing, among others.

What is differential geometry?

Differential geometry is a branch of mathematics that combines concepts from both differential calculus and geometry. It studies smooth manifolds and their geometric properties, such as curvature and distance.

What are some practical applications of differential geometry?

Differential geometry has numerous applications, such as in physics, robotics, computer graphics, and computer vision. It is used to model the motion of objects, understand the shape of surfaces, and develop algorithms for image and data analysis.

What is the difference between Euclidean geometry and differential geometry?

Euclidean geometry deals with the properties of flat, two-dimensional surfaces, while differential geometry studies curved, multidimensional surfaces. Additionally, Euclidean geometry uses the concepts of points, lines, and angles, while differential geometry uses the concepts of curves, tangent spaces, and metrics.

Similar threads

Courses Math Course Advice -- Harvard freshman planning to double major in physics and mathematics
2
Replies
40
Views
1K
Courses Deciding What Math Courses to Take Next
Replies
21
Views
2K
Admissions I Need some advice about my physics undergraduate options
Replies
11
Views
2K
Courses Are mathematicians and physicists obsessed with index notation?
Replies
12
Views
1K
Recommended mathematical courses for a Physics major
Replies
9
Views
2K
Courses Which math course should I take (as a physics major)?
Replies
6
Views
2K
Courses Undergraduate Math Course Selection Question
Replies
11
Views
1K
PhD in Applied Mathematics - Finite Element Analysis
Replies
2
Views
2K
Help with deciding electives: Differential Geometry or Quantum Info
Replies
5
Views
917
Functional Analysis exchange year at Imperial
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top