SMA_01 said:
I really enjoy math (when I understand it), and am now going towards a Bachelor's degree in mathematics. I've read up on possible career options, but I was hoping to get more insight on here. So, what are the types of careers that a math major can get with a bachelors, masters, and Phd?
Also, in your opinion what is the hardest math course?
Thanks.
Hey SMA_01 and welcome to the forums.
In maths you typically have three different types: applied, pure, and statistics. You could say that statistics is a form of applied math, but what separates it is the kind of thinking involved: it has a unique kind of thinking and the framework for analyzing things is different from things found in conventional pure and applied areas of mathematics.
I live in Australia, so I can only comment on that, but I feel the progression is at least somewhat similar to other places.
Typically what happens is you choose a science or math degree and then major in that. You have core classes in your first two years and then you choose a specialization.
You could choose pure mathematics which contains subjects like topology, differential geometry, analysis, functional analysis, and similar subjects. Note these subjects are graduate or upper undergraduate subjects that you would encounter in a tough pure math stream.
If you did applied some subjects might include things like fluid modelling, partial differential equations, numerical analysis, financial modelling, insurance mathematics (stuff that actuaries do), mathematics in meteorology (weather forecasting), or things you might find in a standard engineering curriculum.
If you did statistics you would do your first intro year that contains a probability course and a "statistics" course and then take upper level courses on probability, statistical inference, experimental design, and some kind of upper level course on linear models (GLMs, GLMMs, etc). You might also take course on things like time series analysis, and more advanced courses on markov modelling in a more "rigorous" formalism (Markov and martingale approaches using measure theory).
In my degree you have to do the prerequisites of a typical calculus sequence (Calc I, II, III, IV), Linear algebra, some complex variable calculus, group theory, a course each in applied math, statistics, discrete math, and then on top of that all the other courses that form a major in an area of statistics, applied math, or pure math. You can get a double major in math if you want to.
With regards to "hard", I have mixed feelings: if you do enough of a subject then over time it gets easier. As time goes on, the amount of new material, or at least the "differential" of new concepts reduces. So in some circumstances, you might find the upper level courses easier than the 2nd year ones, because it may have been harder to learn the initial concepts from scratch than learn the extensions which build on stuff you already know from the previous year.
In terms of careers have a look at the AMS website:
http://www.ams.org/profession/data/other-sources/what-mathdegree.pdf
Good luck!