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Applied Math (Computational Science Emphasis vs Statistics Emphasis) for undergrad.

UrbanSkydiver

UrbanSkydiver

Joined
4/9/23
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Points
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I am a freshman majoring in applied math at texas a&m for my undergrad, trying to decide which path within my major would be the best option, Computational Science Emphasis / Statistics Emphasis / math emphasis or just a pure math major.

The curriculi is linked here, the foundational coursework is the same, but the comp sci. emphasis has upper level cs classes and the statistics one has stats classes, and math one has math respectively

Computational : Data Structures and Algorithms, Programming Languages, Design and Analysis of Algorithms, Formal Languages and Automata.

Stats: Statistical Computing, Introduction to Linear Models, Operations Research I or Operations Research II, Mathematical Probability or Mathematical Statistics I

math emphasis:
Advanced Calculus II or Principles of Analysis I,
Modern Algebra I or Applied Algebra,
Operations Research I / Operations Research II / The Mathematics of Interest
(select 2)Theory of Partial Differential Equations ,Fourier Series and Wavelets ,Probability and Computing ,Mathematical Modeling


Appreciate any input.
 
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I’m sure there are people here (including me) that would love to give you advice, but (imho) it’s a bit too much to ask to go through the offered curricula, especially since different schools offer different courses/concentrations. But maybe there’s someone here who has the time? If you could summarize the 3rd-4th year courses offered for each concentration, that could help. Also, Im assuming you posted this here because you are interested in quant finance, so I would go with a few sample MFE curricula to your appm undergrad advisor and ask which concentration would best prepare you for these programs/quant finance career.
 
I don't know, both look decent. I'm assuming your 'best option' is to increase your odds at admission to a top MFE. You might want to take the statistics route for the calculus based probability and statistical computing. You get numerical methods in both, but more operations research in the stat role as well. All things considered, the stat route matches the profile of MFE courses/pre-reqs more than the computational science emphasis (I think). You could take that route and then take the C++ courses offered through this site.
 
GWeitz said:
I’m sure there are people here (including me) that would love to give you advice, but (imho) it’s a bit too much to ask to go through the offered curricula, especially since different schools offer different courses/concentrations. But maybe there’s someone here who has the time? If you could summarize the 3rd-4th year courses offered for each concentration, that could help. Also, Im assuming you posted this here because you are interested in quant finance, so I would go with a few sample MFE curricula to your appm undergrad advisor and ask which concentration would best prepare you for these programs/quant finance career.
Click to expand...
It only took ten minutes of my time. Maybe.
 
GWeitz said:
I’m sure there are people here (including me) that would love to give you advice, but (imho) it’s a bit too much to ask to go through the offered curricula, especially since different schools offer different courses/concentrations. But maybe there’s someone here who has the time? If you could summarize the 3rd-4th year courses offered for each concentration, that could help. Also, Im assuming you posted this here because you are interested in quant finance, so I would go with a few sample MFE curricula to your appm undergrad advisor and ask which concentration would best prepare you for these programs/quant finance career.
Click to expand...
Sure, here's the required ones in each. Computational : Data Structures and Algorithms, Programming Languages, Design and Analysis of Algorithms, Formal Languages and Automata. Stats: Statistical Computing, Introduction to Linear Models, Operations Research I or Operations Research II, Mathematical Probability or Mathematical Statistics I
 
UrbanSkydiver said:
Sure, here's the required ones in each. Computational : Data Structures and Algorithms, Programming Languages, Design and Analysis of Algorithms, Formal Languages and Automata. Stats: Statistical Computing, Introduction to Linear Models, Operations Research I or Operations Research II, Mathematical Probability or Mathematical Statistics I
Click to expand...
Awesome - 100% take the Stat concentration but if you have free electives, take data structures and algos (the earlier the better for internship interviewing).
Not sure what the courses you mentioned specifically teach, but make sure they include stochastic calculus and Markov chains. Between these two they will cover the probability you need, so take math stats over math prob.
Maybe not related to your question but make sure you take PDEs (theory + analytical solutions, if numerical is offered - even better) and as many econ classes as you can per your social science electives (if you are required to take them).

I also majored in appm, best major out there 🤙
 
GWeitz said:
Awesome - 100% take the Stat concentration but if you have free electives, take data structures and algos (the earlier the better for internship interviewing).
Not sure what the courses you mentioned specifically teach, but make sure they include stochastic calculus and Markov chains. Between these two they will cover the probability you need, so take math stats over math prob.
Maybe not related to your question but make sure you take PDEs (theory + analytical solutions, if numerical is offered - even better) and as many econ classes as you can per your social science electives (if you are required to take them).

I also majored in appm, best major out there 🤙
Click to expand...
there's a math emphasis as well that consists of :
Advanced Calculus II or Principles of Analysis I,
Modern Algebra I or Applied Algebra,
(select 2)Theory of Partial Differential Equations ,Fourier Series and Wavelets ,Probability and Computing ,Mathematical Modeling

Stochalistic seems to be a grad level class that can only be taken in undergrad senior year as pure math major. That'll also come with the addition of
Advanced Calculus II or Principles of Analysis I.

Because there exists commonality between the stats emphasis, math emphasis, and just a normal math major, i'm confused and cant figure out which one might be best suited.
 
PDEs are mentioned a few times ... Fourier series and stuff like that are not on the critical path. Edu courses in general are lacking what is needed in industry.

Before PDE, learn ODE theory + NUMERICS is a must. I can't emphasise enough.

Online Courses :: Datasim

www.datasim.nl www.datasim.nl

And ODE/PDE is a prerequisite for FDM. So the critical path is

Calculus->ODE->PDE->FDM->Black Scholes PDE

Any short-circuiting leads to disappointment and/or sub-optimal results.

 
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GWeitz said:
Awesome - 100% take the Stat concentration but if you have free electives, take data structures and algos (the earlier the better for internship interviewing).
Not sure what the courses you mentioned specifically teach, but make sure they include stochastic calculus and Markov chains. Between these two they will cover the probability you need, so take math stats over math prob.
Maybe not related to your question but make sure you take PDEs (theory + analytical solutions, if numerical is offered - even better) and as many econ classes as you can per your social science electives (if you are required to take them).

I also majored in appm, best major out there 🤙
Click to expand...
^^ I agree with this.

Numerical Linear algebra is probably offered and comes recommended by others, I haven't taken it yet though. Matrix calculus and other advances linear algebra topics are good too.
UrbanSkydiver said:
Stochalistic seems to be a grad level class that can only be taken in undergrad senior year as pure math major. That'll also come with the addition of
Advanced Calculus II or Principles of Analysis I.

Because there exists commonality between the stats emphasis, math emphasis, and just a normal math major, i'm confused and cant figure out which one might be best suited.
Click to expand...
Coincidentally, all you need for some stochastic calculus textbooks is calculus based probability, which you will get in the stats route. But Real analysis (probably advanced calc I, that's what it is called at my school) and then measure theory are said to be needed before a truly advanced study in the subject. But my and @Quasar Chunawala might be switching from Neftci's book to Arguin's intro to stochastic calc so by the time you get through calculus based statistics (the math stat courses) I could probably help you through Arguin's book. Quasar is starting his masters in the fall and wants something he can finish beforehand (also something a little more sharp with a more obvious payoff) not sure if the switch will actually happen though. If he switches I will too, since I just want the benefits of partner studying. We will update the discord if it does happen. If we don't make the switch, I'll still probably be down to go through Arguin's book when you get there. It has key numerical components as well.
I also might be doing a more advanced study after I do some real analysis, if the professor is still available (He offered verbally but that is some time in the future), so if you wanted to go that route there's a shot I'd still be of some use.
 
The stat concentration requirements seems pretty solid to me. If my school labelled the courses I took, it would pretty much be a stats concentration too. If what you listed are only the required courses, you should still have room for major electives, right? If so, just make sure you take courses that include the topics that I mentioned and you should be gucci.
Maybe as a point of reference, use this to make sure you cover these topics in your courses (ignore the finance part):
 

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