Math Sequence Undergraduate

[joseclar]

I have seen a few threads listing prereqs for mfe subjects. I would like to see people's opinion on math with suggested books and the sequence in which to study them. So starting from Calculus 1 to be able to get graduate mfe stochastic calc say at the level of Steele. Thank you in advance.

So as an example

1 Calc 1 book
2 Calc 2 book
3 Linear Algebra Book
4 ect ect

If there has already been a detailed post about this please provide the link.

 

[Pavlos Sakoglou]

I have seen a few threads listing prereqs for mfe subjects. I would like to see people's opinion on math with suggested books and the sequence in which to study them. So starting from Calculus 1 to be able to get graduate mfe stochastic calc say at the level of Steele. Thank you in advance.

So as an example

1 Calc 1 book
2 Calc 2 book
3 Linear Algebra Book
4 ect ect

If there has already been a detailed post about this please provide the link.

These elementary math are certainly the basis, but you will need a bit more for stochastic processes and calculus: probability theory and multivariate calculus, mainly.

There are some free resources from my university on calc 1,2,3 and some other courses:
Department of Mathematics, CCNY --- Courses
(see "Video lessons")
And then navigate back for calc 2 and 3 for the same.

If your level of math is calc 1, depending on your commitment, I would say you are looking into at least 2-3 years in the future to understand stochastic calculus.

 

[Connor Whelan]

All these courses with their respective books can be found on MIT OCW. Also, many of these courses may be broken up into sequences (i.e. Real Analysis I and Real Analysis II).

1. Calculus Sequence (Calc 1 through Multivariable and Diff Eq)
2. Introductory Stats and Probability
3. Linear Algebra
4. Numerical Methods
5. Probability Theory
6. Mathematical Statistics
7. Applied Statistics
8. PDE or Applied Math Course
9. Real Analysis
10. Complex Analysis
11. Stochastic Processes
12. Statistical Learning
13. Stochastic Calculus

Helpful courses but not necessarily required
1. Convex Analysis and Optimization
2. Data Structures and Algorithms
3. Time Series Analysis (may be covered in Applied Stats)
4. Econometrics
5. Discrete Mathematics
6. Game Theory
7. Combinatorics
8. Anything related to Data Science

 

[joseclar]

These elementary math are certainly the basis, but you will need a bit more for stochastic processes and calculus: probability theory and multivariate calculus, mainly.

There are some free resources from my university on calc 1,2,3 and some other courses:
Department of Mathematics, CCNY --- Courses
(see "Video lessons")
And then navigate back for calc 2 and 3 for the same.

If your level of math is calc 1, depending on your commitment, I would say you are looking into at least 2-3 years in the future to understand stochastic calculus.

Thank you for the reply. I was asking this to create a reference of courses and the sequence people think best. I was listing calc 1 as the starting point not saying it was sufficient.

 

[Drew L]

Ok, to understand higher-level stuff like stochastic processes you don't just need the Cal1-3 and Linear Algebra sequence!
Topics that Connor mentioned (like game theory) are good, but they're not offered at every university and it's most important to get a background in mathematical theory. With a knowledge of theory, you'll see new topics and quickly understand how they work (under the hood). It takes out the hard work!

So it's most important to take courses in Analysis which is like the theory of calculus. And take all that you can. Walter Rudin's Principles of Mathematical Analysis is the best place to start your education on calculus and all forms of math really.

Once you've gone through Cal 1 start linear algebra.
You don't need graduate linear algebra tbph. The relevant stuff will probably be covered in Analysis courses. There is something called the Spectral Theorem you need to know.

For my undergrad I did a math major with a Finance minor and I really think that helped me understand the finance world much better than anything else because you want to know what's on these financial statements and how the stock markets work. On the other hand a CS minor would have been really useful too but programming's fun so I ended up teaching that myself.

For Calculus use Stewart's book! Good balance of theory and practice.
There was a Russian mathematician named Kolmogorov who wrote some really good books as well. His book on Functional Analysis is really easy to understand and teaches you the important parts of Probability.

To actually understand all the math notation used in stochastic processes, you will need some familiarity with Topology.

Eventually you'll work your way up to Real Analysis and it's only after you've had Real Analysis that you'll actually understand the Ito integral. Real Analysis starts off with "measure theory" which is the heart of all probability.