zonk said:
My current circumstances do not permit me to get an undergraduate major in either of those three, though in grad school I'll probably take up one of those three. I would like a list of mathematical topics I should be well acquainted with to do any of those three in graduate school. I'm planning to do it in Europe though, and I heard they cover advanced mathematics in undergrad there. Here's what I think I should know:
Calculus
Multivariable Calculus
Linear Algebra
Ordinary differential equations
Probability and Statistics
Abstract Algebra
Discrete Math
Topology
Real and Complex Analysis
Partial Differential Equations
Differential Geometry
Calculus of Variations
Hi zonk and welcome to the forums.
I can't speak for physics, but I can speak for mathematics and computer science.
It really depends on what you want to do. With statistics, you need the full calculus sequence as well as introductory A-level year of statistics and then you take specialist courses in probability, experimental design, linear models, and statistical inference. On top of that you will probably want a course in analysis, and then maybe some courses that are either highly specific to a subject area (like say biostatistics, financial math), or you do some more coursework and a thesis/project of some sort.
Most computer science courses (at least in my country) require you do some calculus, discrete math, an intro stats (not like the A-level stuff I mentioned above), and then computer science specific courses. The courses encapsulate all the required math, so if its cryptography: all the number theory and so on is taught within the course. It's the same for stuff like automata, machine learning and so on.
I love math, both applied, pure and statistics so I take as much as I can, but I'm lucky that I can take all math courses and I don't have the so called gen-ed requirements here (thank god).
With regards to "math" degrees, no matter what your sub-major (stats, applied, pure, math+comp sci) you will need to take all Calculus (I,II,II,IV), Linear Algebra, some discrete subject, some applied math subject, some stats, analysis, group theory, and then specific courses for sub-major (at least in my uni and other unis in my country), so you will get a taste of what's out there on which you can use to choose where you will go with it.
Also if I were you, I would choose somewhere that has a recognized degree in math and covers more or less the basics that I said above. If its a reasonably large uni, it probably will be alright, but if in doubt, get some feedback from a good source.
If your pursue this field of study, I wish you all the best, and hope you enjoy your coursework and learning as much as I have.