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Advice for a Novice



I am an incoming junior at a top 15 US university. I am currently majoring in Finance and Accounting. While im very good at accounting i find it boring and I have recently become fascinated with quantitative finance. Im thinking of dropping Acct and picking up a Maj in Applied Math and a minor in CS. Unfortunately i would have to stay an extra year (Im not considering $ in this discussion)
Ive always liked math and been good at math and have never really been challenged but I admit ive only been exposed to rudimentary math (Calc III)
My concerns are that I'll hit a wall in advanced math classes and tank my GPA (at a 3.8 rt now) but Im leaning towards taking that risk
I would be taking: A more advanced Multivariate Calc, Intro to proofs, Matrix Algebra, Calc based Probability, Stochastic process, DE & PDE, 2 Numerical Applied Math Courses.
I’d be taking CS classes in Algorithms, Java, C/C++, and MATLAB

My questions are: I can take Linear Algebra but I’d prefer not to (Just bases on scheduling) so would Matrix Algebra and my other set of classes be sufficient for MFE/MSMF
Any other suggested math classes (or classes for MFE programs)
And how difficult are the math classes I listed. Yes I know that every school/class/person is different but I’d like to get a sense of these classes before I commit.

Thanks

 
I was in a similar case where I was always good at math but afraid of bombing the upper level math classes and went with an econ major. Like you, I was very bored and went with a math/econ major to spice up my junior/senior years. I found that if you really like the math and have the drive, you will do fine. However, it can get a little overbearing so don't get to confident as you load up on 3 math and 2 cs courses each semester. Ease into the math major with a few lower level classes and continue with it as long as you are doing well in the classes. Just be sure you are able to fulfill the minimum requirements for MFE admissions (calc III, lin algebra, probability, C++).
 
Hi, I have a B.S. in Math, so I can offer some sound advice.

I don't know much about you, but based on your post I'm willing to assume that you have the ability to succeed in the aforementioned courses. Real analysis, topology, measure theory, etc., are courses where you might "hit a wall".

Matrix algebra is very useful in various facets of applied mathematics, therefore you are better off taking matrix algebra, as opposed to linear algebra. There is a fair amount of overlap between the two courses, but verify with the MFE programs you are interested in to ensure matrix algebra can be taken in place of linear algebra.

I hope this helps.
 
If you're going to take ODEs and PDEs then the more abstract linear algebra will be needed rather than the more computational matrix algebra. Also, as the previous poster indicated, there's a chasm between computational math and the more conceptual and proof-oriented real analysis, measure theory, and set topology. I think most worthwhile MFE programs will want to see at least one course in real analysis (without it stochastic theory can't be developed unless it's at the low and heuristic level of Ross's "Stochastic Processes").
 
Is linear algebra very proof based? I find it curious that the only pre-req for Linear Algebra at my school is a proofs class (matrix algebra is only suggested)

bigbadwolf linear algebra is not a pre-req for PDE at my school so maybe my PDE class is lacking or the matrix class is more broad

Thanks for all the responses
 

mfegrad

CMU MSCF Alum
i don't remember many proofs at all from linear. it's mostly cool ways to solve matrices and some pca, eigenvalues, eigenvectors, etc. it can be a lot of writing (reducing matrices by hand), but it's fun.
 
From what I understand linear algebra can be taught using various approaches. I am taking it currently and it is quite proof-intensive with less of a computational component.
 
From what I understand linear algebra can be taught using various approaches. I am taking it currently and it is quite proof-intensive with less of a computational component.

That's right -- sometimes it's just a fancy title for matrix algebra. Done right, it begins with the formal definition of a vector space (essentially a module over a field). Matrices are merely used for computational purposes in the framework of a rigorous theoretical development. Is the abstract approach necessary? Absolutely. Take the simplest 2nd order ODE such as y" + y = 0. You need to know that two particular solutions -- sin x and cos x -- are a basis for the vector space of solutions. Linear algebra in both its finite and infinite aspects is at the core of ODEs and PDEs. I'm amazed there can be a course in ODEs that doesn't insist on a prior rigorous course in linear algebra.
 
At my undergrad institution Linear Algebra precedes Advanced Matrix Theory. Perhaps I was wrong for associating Matrix Algebra with Advanced Matrix Theory, they seem to be completely different courses. My greatest apologies, chuckhouse.

Anyway, Ken Abbott brings up a really good point. Most MFE programs require Linear Algebra, you should choose courses accordingly.
 
Is linear algebra very proof based? I find it curious that the only pre-req for Linear Algebra at my school is a proofs class (matrix algebra is only suggested)

Linear algebra is foundational in that students learn for the first time how to move back and forth between conceptualising and proving on the one hand and calculating on the other. If an area of math only has the first, it's likely it's already sterile and in its senescence; if it has only the latter, it's likely to be just a grab bag of tricks and without the skeleton of careful definitions and theorems that both give it structure and sense of direction.
 

Ken Abbott

Managing Director
Linear algebra is foundational in that students learn for the first time how to move back and forth between conceptualising and proving on the one hand and calculating on the other. If an area of math only has the first, it's likely it's already sterile and in its senescence; if it has only the latter, it's likely to be just a grab bag of tricks and without the skeleton of careful definitions and theorems that both give it structure and sense of direction.

Well said. I agree.

I often use it to summarize quickly and efficiently a system of equations.
 
Many courses can have similar names but quite different content.

It would be very helpful to examine the syllabus, or at a minimum, to find out the name of the textbook that the instructor is going to use for each course you are considering.

If you do an MFE, you are going to be bombarded with Stochastic Calculus (also known as "Ito Calculus", after its inventor, Kiyoshi Ito.)

To pursue this topic, you need a theoretical understanding of real analysis/measure theory.

Many people entering such a graduate program may not have seen this material before (especially if their undergraduate major was something other than Math), so they will have to struggle to understand it.

These topics are very abstract, and are quite a departure from the computational/calculation-based approach that you have likely seen in your lower-level math courses.

This material can be quite confusing the first time that you see it, but with repeated interaction, it can eventually begin to make sense.

This is why if you have the opportunity to encounter this material now, you will be in a much better position than your future MFE classmates, many of whom would be seeing it for the first time.
 
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