Math prerequisites for quantitative finance

[Government]

Hi everybody, this October I will be starting math undergraduate studies, after witch will try to join some MFE in US (i live in Europe). Anyway, after reading these and other forums i found out that to understand quant finance, one needs understanding of:

1. Single and multivariable calculus
2. Linear algebra
3. Differential equation
4. Probability and Statistics
5. Stochastic Calculus

So i went over my math undergraduate syllabubs and found out that i will be learning differential equations in my third year and about probability and statistics in my fourth. And no stochastic calculus.I have no intention of waiting that another two-three years so i could understand math behind quant finance. Considering i am finishing last year of high school and that my university starts in October i have 9 months of good amount of free time, i wanted to invest that time in higher mathematics. So here are my questions:

1. Are the courses above enough for me to start learning about quant finance, i am planning to start with Paul Willmot on Quantitative Finance 2nd Edition ?
2. Are courses on MIT Open CourseWare sufficient:
Single Calculus: link
Multi Calculus: link
Linear Algebra: link
Differential equations: link
3. Please suggest me good books on Probability and Statistics and Stochastic Calculus that are sufficient for quant finance. (Is stochastic calculus I and II from Steven Shreve enough)

Thank you

 

[Daniel Duffy]

A lot of QF involves Numerical Analysis.

In the computer all mathematics becomes discrete (e.g. a derivative is approximated by divided differences and integrals by sums of rectangles etc. etc.)

Exact becomes approximate as you get closer to the bits and the bytes.

 

[Government]

So i should add numerical analysis to my courses?

 

[Daniel Duffy]

So i should add numerical analysis to my courses?

I personally would advise it, for sure.

 

[BaconPudding]

I would also take some kind of programming course. I've taken MATLAB and Java. For my numerical methods class, programming skills were essential for projects and having a deeper understanding of the concepts.

 

[markhobbus]

My god, I did not even know about finance at your age. Don't forget to have fun in college.

 

[BaconPudding]

Finance is fun! :D

 

[PatelK]

Hello,
Instead of posting a new thread I figured continuing this thread is the best way. I just finished PDE and Probs&Stats as part of Math Finance prerequisite requirement last semester. One last class I need to complete is Linear Algebra but I'm not sure how much LA is required for study in FE/Math Finance. In my PDE course we actually did 3 weeks(6 lectures) of linear algebra and specfically following topics:

1. Systems of Linear Diff Equations2. Vector Space3. Matrix Algebra4. Systems of Linear Equations5. Rank of Matrix6. Determinants7. Properties of Determinants8. Inverse of a Matrix9. Cramer’s Rule10.Eigenvalue Problems11. Orthogonal Matrices12. Diagonalization of Matrices
Should I take a course in Linear Algebra or does the above cover the required knowledge for higher level Math Finance classes and the Industry? I'm debating to whether spend the $1500 on Linear Algebra or save it for the Masters program.

I need your recommendation and suggestions.
Thanks so much for your time.

Ps: I'm taking intro to comp finance on Coursera where the professor is covering LA implemntation in R language.

 

[BaconPudding]

What are the prereqs for the linear algebra course you are thinking about taking? If it's only calc I and II, don't bother spending money on it. Grab a book and study the material, as you've covered most introductory concepts in your PDE class. If the department insists that you have taken linear algebra for credit, taking it at a community college might save you money. You can spend the money you were going to spend on introductory lin alg on more useful classes, like stochastic calculus.

If it's the upper level linear algebra, you should probably take it.

I don't know much about how much math is required for higher level math finance classes, as I'm only a sophomore right now.

 

[PatelK]

Prereq for LA is Calc 2, which I completed back in 2002 time frame. Since I haven't applied for any MS programs yet, I don't know what departments think yet but the director of the program is recommending I take it. As I read more posts here and on the internet it makes me want to take the class to understand the deep details of LA. It seems to be important in finance and in math fields.

Thanks for your reply BaconPudding.

V/r,
PatelK

 

[Daniel Duffy]

Have you seen the MIT video lectures by Gilbert Strang on Numerical Linea Algebra?

The blue chip.

 

[PatelK]

I did more searches on Quantnet and came across a thread that linked me to pre-MFE program website at Baruch. The syllabus provided good amount of application info. I'm putting together my resume and statement for this pre-MFE class, hopefully they accept me into their seminar.

Daniel,
I need to do more internet research before I ask questions. I wasn't aware of the MIT lectures on Numerical Linear Algebra. I will use this if Pre-MFE seminar is denied...Thank you sir.

V/r,
PatelK