Pure Math vs Applied Math curriculum

[tdot]

Hello everyone,

I am considering a degree in math and statistics, and I have 2 options: Honours Math and Statistics Degree and Applied Math Degree and Statistics. These two degrees have similar requirement for the first 2-3 years such as Calculus 1-3, Linear Algebra 1-2, Numerical Method 1, Discrete Math, Intro to Analysis, Real Analysis 1-2, Complex Analysis, ODE, and PDE 1. However, there are some requirements that are not the same, such as:

For Math classes:

Honours Math and Statistics: Algebra, Algebra 2, Algebra 3 (structure theory of groups, ring theory, integral domains, fields and field extensions, and Galois theory), Number Theory 1 (Prime numbers, unique factorization, linear congruences, multiplicative functions, primitive roots and quadratic reciprocity), Combinatorics 1 (basic counting, permutations and combinations, enumeration, inclusion-exclusion, pigeonhole principle, solving basic recursions, relations, and derangements), Real Analysis 3 (Fourier series and Fourier transforms; orthogonal systems, convergence and approximation. General chain rule and general notion of derivative, implicit function and inverse function theorems.).

Applied Math and Statistics: Numerical Methods 2.

Applied Math and Statistics degree requires 3 more elective math courses, which I intend to take Real Analysis 3, Fundamentals of Approximation Theory (density, existence, uniqueness; direct and inverse theorems for polynomial approximation), Linear Algebra and Matrix Analysis (Vector and matrix norms, matrix factorizations, eigenvalues and eigenvectors, theory of non-negative matrices), or PDE 2

Honours Math and Statistics requires 4 more elective math courses. However, it is hard to schedule classes because of time overlap. As far as I see, I cannot complete the degree within 4 years if I intend to take Numerical Methods 2 + Fundamentals of Approximation Theory + Linear Algebra and Matrix Analysis + PDE 2. Therefore, I would likely take 2 of them and 2 more pure math classes.

For Statistics, both degrees have the same requirement for the first 2-3 years: Intro Statistics 1-2, Probability 1-2, Mathematical Statistics, Probability Theory, Statistic Method 1-2. The differences are:

Honours Math and Statistics: Inference 1 (methods of estimation, including asymptotic and Bayesian methods), Sampling Theory 1 (development of sampling theory for use in sample survey problems, in regression estimates, in systematic sampling, sources of errors in surveys), and Design of Experiment 1 (Objectives in designing experiments; designs commonly used in research including analysis and an introduction to the construction of designs)

Applied Math and Statistics: Time Series, plus 1 more elective in statistics which I intend to take Inference 1.

If I pursue the Honours Math and Statistics degree, I have 4-5 more electives for some arts and a couple of intro to computer classes. If I pursue the Applied Math and Statistics degree, I have about 10-12 more electives which I can use to take whatever I want (in addition to aforementioned 3 math electives and 1 stat elective). I intend to take some computer science classes which will lead to a minor in computer science minor (2 intro computer classes, intro algorithm and data structure, oo ( inheritance, polymorphism, data abstraction and encapsulation).

I talked to the Math department, however, there is no expert in the math/quant finance. A prof put me in contact with another prof from other university but I am still waiting to hear back. In the meantime, I thought I could consult the quantnet experts! If my goal is become a quant analyst/trader, which degree should I pursue? It seems that there are several similar threads on quantnet and the answers tend to lean to the applied degree. However, would I be at any disadvantages because I do not build up the math maturity by taking pure math classes?

*Goal*: Just want to add some more info about what I want to do: I want to become someone who can model/price different asset classes quantitatively and combine that with qualitative analyses to put in good trades. I don't mind programming but I prefer not to be a full time coder. I do believe in HFT successes but I prefer to work in a low to medium frequency environment (may be like GMO/Bridgewater/AQR type of funds!?).

Thanks everyone.

 

[Daniel Duffy]

Combinatorics, Galois Theory and Number Theory - although you should learn them IMO if you claim to be a mathematician - are not directly applicable in the current context.

"I talked to the Math department, however, there is no expert in the math/quant finance.'
That's not the business they are in.

I would concentrate on Applied and Numerical Maths while time series and even statistics are _applications_ of applied maths and can be learned at a later stage.