Real analysis 2 or Linear algebra 2

[YankeesR]

Next semester is my last semester and an opinion on what courses would be best suited to prepare me for a MFE would be appreciated. The available courses I can take are Numerical analysis, Real analysis 2, Linear algebra 2, OOP C++ , PDEs, and Complex analysis. The ideal situation would be for me to take Real 2, Linear 2, C++, and PDEs, but Linear and Real conflict with times so I can only take one of them. Which one would best advance my profile? I'll post the description of the courses below.

"A second course in linear algebra. Topics include a continuation of matrices and linear transformations, canonical forms, invariants, equivalence relations, similarity of matrices, eigenvalues and eigenvectors, orthogonal transformations and rigid motions, quadratic forms, bilinear maps, symmetric matrices, reduction of a real quadratic form and applications to conic sections and quadric surfaces." "Provides a foundation for a further study in mathematical analysis, topics include, basic topology in metric spaces, continuity, uniform convergence and equicontinuity, and intro to Lebesgue integration." I am concerned the real analysis 2 course will be more of the same of my real analysis 1 course and not add much benefit. The only difference I see is more of an emphasis on metric spaces and the intro to Lebesgue integration which could prove useful. Any input would be appreciated. Thank you for your time.​

 

[longgamma]

Why dont you write to head of a department (Dan Stefanica is here) or a professor at some school and ask them? I am re-learning Linear Algebra these days, its quite handy in deep learning.

 

[Aber]

Tough choice but I would have gone with Linear Algebra 2 if the choice should be purely strategically and not based on personal preferences.

From the top of my head, I will say linear algebra 2 will be more useful for your advanced stats courses than real analysis 2 will be for stochastic calculus courses. I am not quite sure but I don’t think MFE programs are too theoretical and I think that you will be able to do fine without knowledge of sigma algebra and Lebesgue integration even in stochastic calculus classes.

On the other hand Linear Algebra 2 (based on the subject list you provided) will be very useful for advanced Statistics and (even Machine Learning) classes. Subjects like linear transformations, eigenvalues and eigenvectors and orthogonal transformations is be useful indeed.

However I have only recently graduated from an applied math graduate program and I don't have deep industry knowledge. So be carefull taking advice from me

 

[YankeesR]

Thank you for the advice, much appreciated. I think I will take Linear 2, Numerical analysis, PDEs, C++, and possibly do Complex. I don't think complex is really relevant but I want to add it as it will increase mathematical maturity which I find important. As for long gamma, to be honest I never thought of that as a possibility. Reaching out directly to the departments, it seems as something that could get out of hand if they allowed people to do that, but I will ask around and see what the norm is. Since this forum was stated education advice it seemed appropriate to post here.

 

[Michsund]

I’d go with Linear algebra. As a mfe student rn you definitely need a lot more then you think, especially in topics like machine learning

 

[YankeesR]

Thanks for the advice, I also have one more question if you have the time to answer. It has come to my attention that my school is offering a "Data science/Machine learning" course this upcoming semester. Unfortunately it conflicts in time with PDEs course. I understand the importance of understanding PDEs in finance, but with the way the trend is going, would the data science course be a better choice? I know the data science course is going to be in R and it is going to be a detailed course from my understanding, as its 6 hours a week. 3 classes per week.

 

[Michsund]

PDE’s are nice but I haven’t meet anyone whose been asked about them on interviews. Last week a MD came to cmu emphasis here the importance of data analytics to the field of finance and how it’s one of the most important thing to be proficient in. So I would definitely go for the ds course

 

[Daniel Duffy]

Now that you mention PDEs, let's try to put them into context:

//
PDEs are mostly for pricing libraries in C++. I suppose an area traditionally associated with rocket scientists. Depends on the department I suppose.

Maybe Crank Nicolson??

https://wwwf.imperial.ac.uk/~ajacquie/IC_Num_Methods/IC_Num_Methods_Docs/Literature/DuffyCN.pdf

Data Analytics is Computer Science and not maths. Just saying.

 

[Daniel Duffy]

Section 5 in this paper discusses how PDEs for computational finance developed down the last years. ADE and Soviet Splitting were first introduced in finance in 2001 and 2009, respectively by yours truly.

 

[AppliedMath]

Thanks for the advice, I also have one more question if you have the time to answer. It has come to my attention that my school is offering a "Data science/Machine learning" course this upcoming semester. Unfortunately it conflicts in time with PDEs course. I understand the importance of understanding PDEs in finance, but with the way the trend is going, would the data science course be a better choice? I know the data science course is going to be in R and it is going to be a detailed course from my understanding, as its 6 hours a week. 3 classes per week.

Honestly, between Data Science and PDEs which do you have a better chance of learning on your own?
Therefore, take the PDE course!

The trend is to know math. The pen, pencil, or programming language you do math in, is secondary. Expand your mathematical mind while you can. DataSci will be simple afterward. Also, very biased, but forget learning R.

 

[Daniel Duffy]

Data Science is a kind of applied linear algebra. Put crudely, it's more or less matrix manipulation. Not necessarily bad.
PDE demands more mathematical maturity, It demands a certain background.

 

[longgamma]

Also, I think if you are in the US, you can always enroll in community college for night classes in case you are missing training in a certain topic. I asked Dan Stefanica on how to complete some pre-requisites for the MFE program and he recommended Hunter college in Manhattan.