# Must Take Undergraduate Math Courses ?

#### Princeton Man

I was just wondering as to what undergraduate courses a potential masters candidate in financial engineering or finance take before graduation. I have been browsing most of the top program websites and it seems like partial differential equations is a must. I am also planning to take stochastic processes and Monte Carlo simulation. Thanks

#### goodstudent

The three courses you mentioned are important but they are not must-takes. The must takes are calculus, ODE, linear algebra, probability, statistics, and programming.

I really don't think PDE is a must take. In an undergrad PDE class, you just learn to solve heat, wave, and Lapace equations over and over again. And maybe with some numerical and non-linear stuff. It definitely helps and you should only take it if you have the time. But it's not a priority.

#### Connor

in addition numerical analysis could be useful

#### ngts

I m studying a BSc econ degree and I am only allowed to take one outside option in my second and third year, which needs to be a mathematical modules, considering that I want to pursue a master degree of mathematical finance. I have already taken calculas linear algebra and stats in year 1.

I am now struggling in choosing my outside option for my second year. I can choose between calculas & linear algebra (these 2 are considered as 1 course), statistics, or analysis? Which one of these are the most important?

The followings are the course content:
For Calculas & Linear Alegbra:
i will be learning how integrals may be calculated, or transformed by a variety of manipulations, and how they may be applied to the solution of differential equations. This aim is achieved by studying such topics as: Limiting processes. Riemann integral, Multiple integration, Improper integrals, Manipulation of integrals, Laplace transforms, the Riemann-Stieltjes integral (permitting application of the Laplace transform to discrete and continuous probability distributions) is studied in some detail, depending on the time constraints............Vector spaces and dimension. Linear transformations, kernel and image. Real inner products, orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. An application to popular dynamics. Singular values, and the singular values decomposition matrix. Direct sums, orthogonal projections, least square proximations, Fourier series. Right and left inverses and generalized inverses.

For stats:
Events and their probabilities. Random variables. Discrete and continuous distributions. Moments, moment generating functions and cumulant generating functions. Joint distributions and joint moments. Marginal and conditional densities. Independence, covariance and correlation. Sums of random variables and compounding. Multinomial and bivariate normal distributions. Law of large numbers and central limit theorem. Poisson processes, Functions of random variables. Sampling distributions. Criteria of estimation: consistency, unbiasedness, efficiency, minimum variance. Sufficiency. Maximum likelihood estimation. Confidence intervals. Tests of simple hypotheses. Likelihood ratio tests. Wald tests, score tests.

For analysis,
Logic, integers, sets and functions, prime numbers, relations, real and complex numbers, greatest common divisor and modular arithmetic, infimum and supremum, sequences, limits, continuity, groups and vector spaces.

Plz help me to decide which one I should take, ( i m only allowed to choose one)

#### goodstudent

Plz help me to decide which one I should take, ( i m only allowed to choose one)

Calculus should be a prereq for stats and analysis... So take the first one

#### QuantNeeds

Hello, I noticed that to begin an MFE program only those basic math courses are needed. But then I came across the “Reading List Before You Start an MFE Program” on this site and became a little overwhelmed. I am thinking about taking Stochastic Calculus next semester. I am not sure if I should wait a little longer to go through some of those books before starting the program.

#### Connor

You don't need to go through all of them and it isn't necessarily required that you go through any of them beforehand. But what you do look at before a MFE should help you and hopefully make the actual MFE less stressful.

#### Andy Nguyen

Re: Reading List Before You Start an MFE Program

In the past, you may not heard about Shreve or Hull until your first semester in an MFE program.
Now, since more people know about MFE programs, many applicants have went through Hull, Neftci, Shreve, Stefanica, etc before they apply. And thanks to websites like quantnet and the popularity of our master reading list, people are increasingly aware of what books these programs use, what books most people read, etc.

Also, think about it, if those books are too complex for you, maybe you can take your time, read more supplement texts. And if they don't deter you, then go ahead and apply.

It's cheaper to spend a few hundred dollars on books than spending 100K to learn that you are not cut out for it.

#### MFwhartonite

Hi guys, i have had similar questions for the past few months and can't get a good response. My situation is very similar.

my undergrad program is finance and statistics at Wharton with a math minor in the college of arts and sciences. I want to get a MFE or MFIN later in life. I've considered getting a math major in addition to my Bachelor of science in econ from wharton, but that is a ton of work and will impact my gpa. The only difference between taking the math minor and taking the major is taking 2 semesters of advanced abstract algebra and 2 smesters of real analysis. These courses are known for being terribly difficult and with no application in the world of finance which is where i plan to work(trading).

Most of the upper level quant finance degrees say real analysis is recommended. So my question is if i don't get the math major and don't take real analysis and abstract algebra(really advanced calculus) will i not be able to do well and get accepted to a MFE program?

thanks

#### goodstudent

Hi guys, i have had similar questions for the past few months and can't get a good response. My situation is very similar.

my undergrad program is finance and statistics at Wharton with a math minor in the college of arts and sciences. I want to get a MFE or MFIN later in life. I've considered getting a math major in addition to my Bachelor of science in econ from wharton, but that is a ton of work and will impact my gpa. The only difference between taking the math minor and taking the major is taking 2 semesters of advanced abstract algebra and 2 smesters of real analysis. These courses are known for being terribly difficult and with no application in the world of finance which is where i plan to work(trading).

Most of the upper level quant finance degrees say real analysis is recommended. So my question is if i don't get the math major and don't take real analysis and abstract algebra(really advanced calculus) will i not be able to do well and get accepted to a MFE program?

thanks

If it requires 2 semesters of abstract algebra... I would forget about it... I think stats major plus math minor is more than enough. BTW, abstract algebra is not advanced calculus (that's real analysis). Algebra is about doing things like proving that you can't trisect an angle with straightedge and compass...

#### Yike Lu

##### Finder of biased coins.
Algebra is about doing things like proving that you can't trisect an angle with straightedge and compass...
What?

No, abstract algebra is Group Theory, Rings, etc. It has nothing to do with straightedges and compasses. That would be geometry.

#### koupparis

##### Carpe noctum
Actually those types of problems are often recast into abstract algebra problems. So while abs. algebra doesn't deal exclusively with these "geometry" problems, it is used to solve them, rather nicely.

MFwhartonite, if your real analysis course touches open measure theory, then I'd say go for it. It'll help some when you start stochastic calc. Also the real analysis sequence will give you a more theoretical theorem-proof style background, which does come in handy.

#### MFwhartonite

I am really hesitant to take the abstract algebra and real analysis sequence of 4 classes. I just don't understand how proofs can be applicable to a trading career. My friend at harvard told me that his real analysis class was the hardest class he's ever taken, and my friends who have taken the sequence at penn have told me it has very very little application to anything. Can you guys tell me what applications in finance these courses have if any? I feel like sure it is good to have, but would i b e better off doing some computer science and padding my gpa than struggling through the math major.
thanks

What?

No, abstract algebra is Group Theory, Rings, etc. It has nothing to do with straightedges and compasses. That would be geometry.

In field and Galois theory, among other things, the results that a general angle can't be trisected, a cube can't be doubled, and the circle can't be squared (i.e., using straightedge and compass) are proved. Pick up any respectable undergrad text in abstract algebra to see these standard results (e.g., Herstein, section 5.4)

---------- Post added at 12:17 PM ---------- Previous post was at 12:08 PM ----------

I am really hesitant to take the abstract algebra and real analysis sequence of 4 classes. I just don't understand how proofs can be applicable to a trading career.

Opinion seems to be divided here. I'm a math major myself but I wouldn't push the advantages of the definition-lemma-theorem-corollary style. It seems to me that engineers and physicists who gravitate towards quant finance do just fine without the rigors of pure math. In fact I would argue that the pure math style can often work against a heuristic style of thinking and feeling, which is probably much more important in applied areas like physics and finance than sterile rigor. Sometimes I think the sterile rigor of modern pure math is akin to the sterile theoretical arguments of scholastic philosophers a thousand years ago.

You definitely do not need abstract algebra. For analysis, at least work through a simple text by yourself -- say something like "Real Analysis" by Howie. This will come in handy if you look at stochastic theory. More important than this, however, is to learn to construct individual heuristic arguments by yourself. This is a valuable applied math and physics skill.

#### Mr Doe

Can you guys tell me what applications in finance these courses have if any?

There are plenty of applications of the material learned in these courses, but I doubt you will find any (direct) application to trading. Basically, things work or make sense for some reason, like Central Limit Theorem or Black-Scholes formula, but it should be your least concern (as a trader) why they work.
My list of courses you should avoid at all cost is the following (as I had them all):
Toplogy, Abstract Algebra, Functional Analysis, Complex Analyis, Convex Analysis, Measure Theory and (graduate level) PDE.
Some posters will try to convince you that measure theory is really important and that you will be hitting a brick wall (in courses like Stochastic Processes and Ito Calculus) unless you know of Caratheodorys theorem (a measure exists), Lebesgue integral (something like "plain" integral) and convergence theorems (basically, you can switch (\lim \int) with (\int \lim )). The highlight of these things will be, when one of your professors mentions some of it during a proof of a theorem (guys from the math department will nod their heads with great satisfaction when the prof does so).

Goodstudent made a good list of things needed later on. You should also be on a lookout for courses that require interdisciplinary, say, statistics and programming. They usually have a fancy name like; numerical methods in finance, probability models with applications and so on.

My 2 cents.

#### MFwhartonite

Oh wow these posts are what i've been looking for hopping around finance forums the past few months. Thanks Soo much for these insights.

From traders i've talked to from wharton, they've told me that the concentration in statistics here is much more important than any math major. The math minor that i'm taking has 3 semesters of calculus(through DiffEQ) and a semester of linear algebra(there's some overlap with my stat and finance concentrations hence the light courseload). The finance profs i've talked to have told me that that's the extent of pure math needed. Now the statistics concentration i've chosen consists of probability(goes into brownian motion and a few other topics, i've already taken intro probability and statistics as well as a course on multiple regression that i liked), Financial and economic time series, Stochastic processes, and finally i'm planning to take a graduate math course entitled math of finance. From all of the information i've gathered, this is the most useful sequence of math and statistics courses for an undergraduate education(this is in addition to my finance major). Doing a math major in my opinion might be over-doing it, and not doing the math major gives me opportunity to take a few comp sci classes(i've taken basic and visual basic in high school, but i'd like to learn C++)

I read about the interview process of jane street and other highly quantitative firms on another forum. This was the only thing that really scared me in that apparently they ask about proofs. Now i'm beginning to think that those questions might be only asked to math majors applying, but I would hate to make it to a fourth round interview and get tripped up on a stupid proofs question.

My ultimate goal is to work in trading for a little while and then perhaps go to columbia for their MA in quantitative finance and/or their masters of financial engineering. They both look amazing.

If you guys have any comments on my chosen courses above, definitely let me know, but i thank you guys so much for the insights. Sorry for the long post.

#### Mr Doe

MFwhartonite, I don't know if you are aware of it, but a guy who teaches Financial Time Series class (J. Michael Steel) at Wharton, has a great(!!!) web page that covers most of the material learned in class (at least that is my impression), here's the link: Financial Time Series Wharton Statistics 434 J. Michael Steele . That might give you an idea what is done in "serious" FE courses.

#### MFwhartonite

thanks a lot. OH YES i can't wait for prof steele's time series class, and i plan to take the graduate version of stochastic processes that he teaches in the spring. I haven't met him or sat in on one of his classes, but from what i hear and from his ratings, he's wonderful.

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