some minor corrections,
In actuarial, You will probably have to deal with all sorts of math a statistician will have to deal with,
common calculus & limiting distributions. Financial math for premium pricing, Generalised linear models &
mathematical statistics most of the time, sometimes Geometry & trigo, when you are fitting models
with (sin, cos, characteristics) or using certain algorithm when running simulations.
But dont worry, you dont do those everyday, Calculus? yes.
The building blocks of Actuarial Science, is reasonable, logical and fluent, with introductory economics,
some understanding of mechanism in finance. Although the statistics part is rather abstract at first, but ease up as you go on.
Insurance math stuff, is not abstract, just you know where you start, where to end, but there's a huge drama in between
the calculation to get there.
Math degree (I am assuming pure math, which is also whats special bout math anyway) mostly
give you deeper understanding on "stuff you dont really directly need in applied math" (if you are gonna work in some
boring corporation someday). You go deeper into fundamental principles of everything, learn techniques of proof,
bunch and bunch of abstract concept (not really tedious, but if you dont know it, you probably dont even know how to start).
I am not sure bout others, as I just do probability & measure theory. But can expect similar structure for all other pure math courses.
Well it also depends on the University, how theoretical or applied they want most math courses to be.
PS: Pre-U and high school math hardly tell anything. I have bunch of friends with 3A's struggle in 1st year pure math course.
And some of my 3rd yr math classmates hardly reach a TER of 82.
If you like to deal with numbers, stick with Actuarial, finance, stat, engineering. Or math will make your life miserable.
here's a small example of how both are different:
Actuarial Sci.
Here's f(x) a probability density function that describes
automobile claim, X. While here's f(y) another Prob. density function
to describe the similar automobile claim, X.
Provided is 120 claim size data that are assumed to be independent.
Run a suitable test to decide which model fits the claim distribution more adequate. Explain.
Math
Using similar argument in Axiom of Choice,
Prove or disprove that there exist a probability measure Q(x), from Powerset(Real) -> [0,1] such that
F(x) := Q((-inf,x]) is a continous function.