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How important are higher level math courses?

HI everyone. I know some basic math courses such as linear algebra, probability, and PDE, ODE are fundamental to quant. But I heard that if I really want to do well in these stuffs, or go even further like SDE and stochastic control, real analysis, functional analysis and a little bit of complex variables are necessary. To land an intern or a job(master's level, not PHD level), should I self-learn all of these stuffs during master's degree or learn part of them like real analysis and the rest depends on the needs of the jobs?
 
Do you have a study plan or reading plan to learn all these stuffs?
Yes. I am now reviewing math analysis, and the following step is real analysis. But I am not sure what should go next, there are many choices like measure theory and functional analysis. I have no idea about what can better help me understand quant stuffs. Any comment and advice is appreciated.
 

YankeesR

Active Member
C++
As far as books, I've heard Visual complex analysis is a great book for self teaching complex. My class we used Ahlfors. Would not recommend for self teaching. A great book for self teaching real analysis is "Elementary Analysis" by Kenneth Ross. Easy read, goes in detail on topics, but the downside of the Ross book is it only deals with one variable. Without knowing anything about your quant curriculum, learning real analysis will probably be helpful. Not because of what it will do for your quant career, but because for me at least, it truly changed how I approach math and made courses I took later on seem much easier whereas if I didn't take real analysis before hand I don't think I would say said course was as easy. I didn't speak on SDE or functional analysis because well, I haven't taken them yet, but I do know functional analysis requires some pre reqs that you didn't mention, such as topology to truly understand.
 

quantsmodelsbottles

Well-Known Member
if you have the spare time to study stuff besides the core basics, it’s a great idea to develop quantitative problem-solving skills. there’s a reason quant firms hire abstract algebra phd’s
 

Daniel Duffy

C++ author, trainer
HI everyone. I know some basic math courses such as linear algebra, probability, and PDE, ODE are fundamental to quant. But I heard that if I really want to do well in these stuffs, or go even further like SDE and stochastic control, real analysis, functional analysis and a little bit of complex variables are necessary. To land an intern or a job(master's level, not PHD level), should I self-learn all of these stuffs during master's degree or learn part of them like real analysis and the rest depends on the needs of the jobs?
The maths you mention here cannot be learned alone.
 

YankeesR

Active Member
C++
See my courses where all these topics are worked out.


What's 'abstract algebra'??
A first semester course in abstract algebra in the U.S will be something such as "Theory of groups, including cyclic and permutation groups, homomorphisms, normal and factor groups. Theory of rings, integral domains, field of quotients, maximal and prime ideals, rings of polynomials, field extensions."
A common first semester book is "Contemporary Abstract Algebra" by Joseph Gallian
 
Last edited:

Daniel Duffy

C++ author, trainer
A first semester course in abstract algebra in the U.S will be something such as "Theory of groups, including cyclic and permutation groups, homomorphisms, normal and factor groups. Theory of rings, integral domains, field of quotients, maximal and prime ideals, rings of polynomials, field extensions."
A common first semester book is "Contemporary Abstract Algebra" by Joseph Gallian
Ah, OK.
Over here in Europe we call it 'Algebra'.

My school teacher was PhD and I Iearned group theory at 17. It does not have may applications in finance AFAIK.
 
As far as books, I've heard Visual complex analysis is a great book for self teaching complex. My class we used Ahlfors. Would not recommend for self teaching. A great book for self teaching real analysis is "Elementary Analysis" by Kenneth Ross. Easy read, goes in detail on topics, but the downside of the Ross book is it only deals with one variable. Without knowing anything about your quant curriculum, learning real analysis will probably be helpful. Not because of what it will do for your quant career, but because for me at least, it truly changed how I approach math and made courses I took later on seem much easier whereas if I didn't take real analysis before hand I don't think I would say said course was as easy. I didn't speak on SDE or functional analysis because well, I haven't taken them yet, but I do know functional analysis requires some pre reqs that you didn't mention, such as topology to truly understand.
Thanks for book recommendation. You are right. Functional analysis is like the last course for math student to learn in undergraduate level. I have a long way to go. My quant program is math-oriented so it is not totally self-teaching. I am not sure that should I go further in bizarre love triangle of functional analysis, topology and other stuffs or stop at real analysis because of limited time. Maybe horning my programming skills is more realistic.
 
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