Which of the following are the most important courses :

[roni]

1) Stochastic Processes - I am taking Intro to MFin, and we cover a little of Geometric Brownian Motion. But I understand that the most important part of the course is Markov Chain...

2) PDEs - I am taking a Differential Equations class and we are going to do some elementary PDEs, should I also take a PDE class ?

3) Real Analysis- it's mostly offered in grad schools, so I don't know if I'll be able to get into one of them in NYC.

4) Mathematical Modeling I - Optimization

5) Numerical Analysis


How would you order them if the first is the most important ?

I wanted to take Numerical Analysis during the summer. But, since the only school that is offering this, is going to use Mathematica and not C++ or MatLab, I decided to take an Advanced C++ course instead. But, really want to take it in addition to another 1 or two of these.

So, I will be able to take 2 courses or maybe 3(which I' really doubt) in fall 2010. And, I will be applying for MFE programs in Oct 2010. So, there's no point for me to take courses in spring 2011, because the schools are not going to know about it...

Roni.

 

[Connor]

I would say for your 2 courses, stochastic processes and PDEs

 

[roni]

PDEs is really more important than Numerical Analysis ?

I thought Numerical Analysis was 1 of the most important prereq.

 

[DanM]

3) Real Analysis- it's mostly offered in grad schools, so I don't know if I'll be able to get into one of them in NYC.

That's not true at all. Intro courses in analysis are offered at the undergrad level, and even more advanced courses that deal with measure theory & Lebesgue integration are offered for undergrads.

 

[goodstudent]

1. Numerical Analysis
2. Stochastic Processes
3. PDE
4. Real Analysis
5. Mathematical Modeling I - Optimization

I put PDE 3rd assuming you already have ODE. If not, PDE should be number one.

Just my opinion =]. But I'm also an undergrad, so you don't really have to listen to me.

 

[bob]

1) Stochastic Processes - I am taking Intro to MFin, and we cover a little of Geometric Brownian Motion. But I understand that the most important part of the course is Markov Chain...

2) PDEs - I am taking a Differential Equations class and we are going to do some elementary PDEs, should I also take a PDE class ?

3) Real Analysis- it's mostly offered in grad schools, so I don't know if I'll be able to get into one of them in NYC.

4) Mathematical Modeling I - Optimization

5) Numerical Analysis


How would you order them if the first is the most important ?

I wanted to take Numerical Analysis during the summer. But, since the only school that is offering this, is going to use Mathematica and not C++ or MatLab, I decided to take an Advanced C++ course instead. But, really want to take it in addition to another 1 or two of these.

So, I will be able to take 2 courses or maybe 3(which I' really doubt) in fall 2010. And, I will be applying for MFE programs in Oct 2010. So, there's no point for me to take courses in spring 2011, because the schools are not going to know about it...

Roni.

Not exactly an answer to your question, but here are two undergrad courses that are more important for this area than those listed above:

mathematical statistics
linear algebra
...both at a pretty rigorous level

Actually, if you've never taken a good OR intro (linear/integer programming, graph theory, perhaps a bit of game theory), that would probably also serve you well. My take on this is that there's no real reason to take MFE courses as an undergrad if you're going to be taking MFE courses as a grad student. Providing you're decent at math, you'll be far better served both in your graduate program and in your eventual career by having a solid, broad foundation rather than by overspecializing as an undergrad. Just my opinion, of course.

 

[quantstart]

I find it difficult to see how one could attempt courses on Stochastic Processes or PDEs without a basic grasp of Real Analysis.

For example, Ito's Lemma is analogous to the Chain Rule for functions and would require the knowledge of Taylor Series. These concepts would only be taught in a Real Analysis course.

 

[roni]

1. Numerical Analysis
2. Stochastic Processes
3. PDE
4. Real Analysis
5. Mathematical Modeling I - Optimization

I put PDE 3rd assuming you already have ODE. If not, PDE should be number one.

Just my opinion =]. But I'm also an undergrad, so you don't really have to listen to me.

The first two were the classes I thought I'd take. However, I realized that the last three are also very important.
Will need to hear a few more opinions :\

thanks

---------- Post added at 01:09 AM ---------- Previous post was at 01:06 AM ----------

Not exactly an answer to your question, but here are two undergrad courses that are more important for this area than those listed above:

mathematical statistics
linear algebra
...both at a pretty rigorous level

Actually, if you've never taken a good OR intro (linear/integer programming, graph theory, perhaps a bit of game theory), that would probably also serve you well. My take on this is that there's no real reason to take MFE courses as an undergrad if you're going to be taking MFE courses as a grad student. Providing you're decent at math, you'll be far better served both in your graduate program and in your eventual career by having a solid, broad foundation rather than by overspecializing as an undergrad. Just my opinion, of course.

Hello,

I am taking the math courses you mentioned.
I listed only the ones I haven't taken.

And, a good OR into course would be Optimization ? or should I take a linear programming in a CS department instead ?

---------- Post added at 01:13 AM ---------- Previous post was at 01:09 AM ----------

I find it difficult to see how one could attempt courses on Stochastic Processes or PDEs without a basic grasp of Real Analysis.

For example, Ito's Lemma is analogous to the Chain Rule for functions and would require the knowledge of Taylor Series. These concepts would only be taught in a Real Analysis course.

I think the basic real analysis is started in the calculus courses (like Taylor Series)

And a Real Analysis course is not a prerequisite for Stochastic Processes or PDEs ( at least not in the different NYC schools I checked)

 

[quantstart]

Roni,

I guess that would work if the student had the Calculus basics grasped before SC or PDEs. I'm London based so am not sure what level a student in NYC would have at that stage. Over here, people rarely use the term "Calculus" and instead focus on "Analysis" at undergraduate mathematics. That's been my experience at least.

At the end of the day, people really just mean Differentiation and Integration

Mike.

 

[goodstudent]

Roni,

I guess that would work if the student had the Calculus basics grasped before SC or PDEs. I'm London based so am not sure what level a student in NYC would have at that stage. Over here, people rarely use the term "Calculus" and instead focus on "Analysis" at undergraduate mathematics. That's been my experience at least.

At the end of the day, people really just mean Differentiation and Integration

Mike.

Oh ok, at my school, people generally take Advanced Calculus before taking real analysis. I assumed roni had a good background in calculus so I but Real Analysis 4th.

 

[quantstart]

That would make sense. What is generally included in an Advanced Calculus course over in the states?

 

[goodstudent]

That would make sense. What is generally included in an Advanced Calculus course over in the states?

I don't think every school in the US has advanced calculus. Some probably just include it with multi-variable calc. But for our school, it is basically an introduction to analysis, or something between lower-division calculus and real analysis. We covered limits and continuity, differentiability, chain rule for several variables, relative extrema, improper integral, vector calcululs, etc.

 

[roni]

I just got an email from Berkeley and it says that even though the Differential Equations class that I'm taking right now covers a little PDEs, I should take a course devoted for PDEs only.

So, I guess I'll take these three classes:
1. Numerical Analysis
2. Stochastic Processes
3. PDE

But I'll need to give up on 1 course (advanced programming in C++) which I wanted to take. I think I'll be able to do it on my own. What do you guys think ? is it possible to learn the second programming course on my own ?

here is a description of such a course:

"A second course in programming. Advanced programming techniques emphasizing reliability, maintainability, and reusability. Module design and multifile programs. Abstract data types. Objects, classes, and object-oriented design. Storage class and scope. Addresses, pointers, and dynamic storage allocation. Test suites, test drivers, and testing strategies; debugging and assertions. An introduction to formal techniques. Recursion and function parameters."

 

[Stefan Zota]

I just got an email from Berkeley and it says that even though the Differential Equations class that I'm taking right now covers a little PDEs, I should take a course devoted for PDEs only.

So, I guess I'll take these three classes:
1. Numerical Analysis
2. Stochastic Processes
3. PDE

But I'll need to give up on 1 course (advanced programming in C++) which I wanted to take. I think I'll be able to do it on my own. What do you guys think ? is it possible to learn the second programming course on my own ?

here is a description of such a course:

"A second course in programming. Advanced programming techniques emphasizing reliability, maintainability, and reusability. Module design and multifile programs. Abstract data types. Objects, classes, and object-oriented design. Storage class and scope. Addresses, pointers, and dynamic storage allocation. Test suites, test drivers, and testing strategies; debugging and assertions. An introduction to formal techniques. Recursion and function parameters."

I am surprised that Berkeley would consider PDE as a prerequisite. ODE I can understand, but PDE is a deep subject, graduate level. To my knowledge, never heard of "elementary PDE". Even the simplest of them require numerical methods, transforms, spaces etc.
Something elementary would find a closed form solution in half a page ...
Anyway, maybe that's just me

 

[roni]

I am surprised that Berkeley would consider PDE as a prerequisite. ODE I can understand, but PDE is a deep subject, graduate level. To my knowledge, never heard of "elementary PDE". Even the simplest of them require numerical methods, transforms, spaces etc.
Something elementary would find a closed form solution in half a page ...
Anyway, maybe that's just me

I understand what you are saying.
I guess that's exactly the reason why it's not offered very ofter at the different campuses around NYC (undergrad level).

 

[Barny]

I am surprised that Berkeley would consider PDE as a prerequisite. ODE I can understand, but PDE is a deep subject, graduate level. To my knowledge, never heard of "elementary PDE". Even the simplest of them require numerical methods, transforms, spaces etc.
Something elementary would find a closed form solution in half a page ...
Anyway, maybe that's just me

Elementary PDE's are the linear heat, wave and laplace's equations.

 

[Stefan Zota]

Elementary PDE's are the linear heat, wave and laplace's equations.

Each of these "elementary PDE" require at least 10 pages. They use Fourier/Laplace transforms, Banach spaces, numerical methods. It depends what is perceived as "elementary"

In my opinion, it would be more useful to focus on ODE in undergrad instead of PDE. There is material for advanced ODE courses. With PDE, after several lectures, the content morphs into a PhD course.
In the end, in finance, you need to look only at a small subset of PDE. They are solved numerically in many cases, so the content fits better in a "Numerical Methods" course.

 

[DanM]

This is what the PDE course (undergrad) at my school covers:

Partial differential equations of mathematical physics (Heat Equation, Laplace Equation, Wave Equation) and their solutions in various coordinates, separation of variables in Cartesian coordinates, application of boundary conditions; Fourier series and eigenfunction expansions; generalized curvilinear coordinates; separation of variables in spherical and polar coordinates.

 

[Barny]

Each of these "elementary PDE" require at least 10 pages. They use Fourier/Laplace transforms, Banach spaces, numerical methods. It depends what is perceived as "elementary"

In my opinion, it would be more useful to focus on ODE in undergrad instead of PDE. There is material for advanced ODE courses. With PDE, after several lectures, the content morphs into a PhD course.
In the end, in finance, you need to look only at a small subset of PDE. They are solved numerically in many cases, so the content fits better in a "Numerical Methods" course.

Banach spaces and numerical methods? Solving the Heat/Wave/Laplace equation can be done by separation of variables and using simple boundary conditions can be solved fairly easily. We also learnt how to solve them using fourier transforms/laplace transforms, again this was pretty easy, I don't consider this advanced, I did it in my second year of University with only linear algebra, calculus and analysis as pre-requisites. Of course PDE's can and do get much more advanced, that is when you need functional analysis and numerical methods, but in the beginning it's pretty straightforward.

 

[Stefan Zota]

This is what the PDE course (undergrad) at my school covers:

Partial differential equations of mathematical physics (Heat Equation, Laplace Equation, Wave Equation) and their solutions in various coordinates, separation of variables in Cartesian coordinates, application of boundary conditions; Fourier series and eigenfunction expansions; generalized curvilinear coordinates; separation of variables in spherical and polar coordinates.

Interesting. In Romania, in my undergrad, most of this curriculum is covered in different classes: all series & polar coordinates are in advanced calculus, eigenfunction expansions&coordinate transformations in linear algebra, separation of variables in ODE (same concept).
Even more interesting is that most of the content seems to be a basis for future PDE classes. In other words, the bulk of the course is not spent solving PDE, it's understanding the tools.

Banach spaces and numerical methods? Solving the Heat/Wave/Laplace equation can be done by separation of variables and using simple boundary conditions can be solved fairly easily. We also learnt how to solve them using fourier transforms/laplace transforms, again this was pretty easy, I don't consider this advanced, I did it in my second year of University with only linear algebra, calculus and analysis as pre-requisites. Of course PDE's can and do get much more advanced, that is when you need functional analysis and numerical methods, but in the beginning it's pretty straightforward.

I still keep my opinion that is advanced. The reason is that you are applying 1, 2 methods in a space that is widely unknown. In other words, you need much more to understand if you find one solution or all of them, if they are unique, if they work for any starting conditions.
I can understand using a separation of variables and Fourier transform to find a solution for above PDE, in last 2 sessions of an ODE class. Unless you add the material Dan mentioned, I still find it difficult to build an undergrad PDE class ...

However we have gone through different undergrad systems. For instance, in my case, the weight was on Calculus & Systems Theory, Probability & Statistics were neglected. ODE were explored in-depth but PDE were done primarily for Physics orientation ...