I have already sought some very useful opinions. I just prefer polling

I do not know what research areas I'll wish to do.

- Thread starter hedgie
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I have already sought some very useful opinions. I just prefer polling

I do not know what research areas I'll wish to do.

Stochastic Processes:

Introduction to the basic concepts and applications of stochastic processes. Markov chains, continuous-time Markov processes, Poisson and renewal processes, and Brownian motion. Applications of stochastic processes including queueing theory and probabilistic analysis of computational algorithms.

Numerical Linear Algebra:

Further study of matrix theory, emphasizing computational aspects. Topics include direct solution of linear systems, analysis of errors in numerical methods for solving linear systems, least-squares problems, orthogonal and unitary transformations, eigenvalues and eigenvectors, and singular value decomposition. Usually offered in the spring semester.

The syllabus I have access to are old so the material covered may have evolved more now.

Stochastic from syllabus:

DESCRIPTION: This course is an introduction of the basic concepts and applications of stochastic processes. Stochastic processes studied are Markov chains, continuous-time Markov processes, Poisson and renewal processes, and Brownian motion. Applications of stochastic processes include queueing theory, communication networks, finance, and others.

Book: Intro To Stochastic Modeling, Pinsky

OUTLINE

TOPICS # OF 75 MINUTE LECTURES

PRELIMINARIES 4

POISSON PROCESS 5

RENEWAL PROCESS 2

MARKOV CHAINS 5

CONTINUOUS-TIME MARKOV CHAINS 5

BROWNIAN MOTION 5

Numerical Linear Algebra from the Syllabus:

Book: Fundamentals Of Matrix Computation, Watkins

This course is a continuation of Intro to LA on a less abstract level than an "algebraic" graduate course in linear algebra. The course will be accessible to engineers and physical science students though duplication of introductory material given in intro to numerical analysis will be avoided. The motivation of the course is to emphasize some important computational aspects of matrix theory which are often neglected by linear algebra courses at all levels, and yet which (in the real world) comprise the essence of the subject. This course covers the solution of linear systems, least square problems, eigenvalue problems, and the singular value decomposition. Lectures in the text book will be followed, but Part IV, the interative methods, will not be covered. This topic is regarded as fundamental to applied math and hence furnishes required knowledge for ensuing professional careers. The outline of the topics on this course is the following:

1. Review Linear Algebra Basic Concepts.

a. Vector spaces, subspaces, and bases

b. Vectors and matrices and their norms

c. Linear transformations and their matrix representations.

2. Conditioning and Stability

a. Condition numbers

b. Floating point arithmetic

c. Stability of various algorithms

3. Linear Equation Solving

a. Gaussian Elimination

b. Pivoting

c. Stability of Gaussian Elimination

d. Cholesky Factorization

4. Least Square Problems

a. Orthogonal Matrices

b. QR Factorization

c. Gram-Schmidt Process

d. Householder Transformation

5. Eigenvalue Problems

a. Canonical Forms

b. Algorithms for eigen problems

c. Generalized eigen-problems

6. Singular Value Problems

a. Singular value decomposition (SVD)

b. Computing the SVD

Would it be advisable to pick up the topics on my own?

Thanks again, ...any recommendations on a numerical analysis - numerical linear algebra book? And what language is best to learn in? The book at my University I uses matlab.

The book I used in my class, which isn't special, is

Stochastic processes you can do on your own if you like learning statistical theory on your own. I, personally, do not. I'm lazy and won't do homework lol I've never had the class, though. I heard it is good, and can be tough. At the graduate level, I would just assume it will be tough! haha

Dason what do you think the value of either or both courses is (given I do not know my research interests, though I am interested in all stats and probability subjects)? I may take the stochastic processes course in person then.

I know a little python a little. Is it advisable to pick up more python and potentially C or just stick with R. I guess I am asking what you guys are using in grad school and the real world on a regular basis.

Also Dason stochastic or the numerical LA course do you see a lot of value I taking them or waiting till I narrow down research interests ?

Thanks for all your time and advice. Its greatly appreciated!

Also Dason stochastic or the numerical LA course do you see a lot of value I taking them or waiting till I narrow down research interests ?

Dason so in your position youd want to take both courses? I'd love to except for funding!!

Is stochastic too much to learn on ones own...I assumed because it was more an applies. course it wouldnt be as bad. Also I assumed for certain I'd be repeating it in grad school.

I was going to take the semester to work on SAS, R, and python but is it advisable to take courses beyond the first programming course? I assumed that was definitely self teachable.

Thanks so much to everyone!

Programming is self teachable but you can definitely learn a lot from taking courses. There are certain things that you might not get from books when it comes to programming whereas if you have a teacher they'll correct you or tell you why it's a bad idea to do the seemingly not-so-bad thing in your code.

Thanks again, ...any recommendations on a numerical analysis - numerical linear algebra book? And what language is best to learn in? The book at my University I uses matlab.