Probability Theory or Mathematical Statistics?

[Macromatica]

Advice and expertise on which two classes to take for this fall semester would be very helpful and appreciated. These are my choice of courses for the fall, this would somewhat be a relatively easy decision but the similarities between prob theory and math stats is what poses a problem in my decision making. This will be the last of my courses to appear on my transcript before I apply to PhD programs. Pick your favorite two. (My other course that I'm in is Intro to Real Analysis.)

*Advanced Linear Algebra
*Probability Theory
*Mathematical Statistics I

STAT 4203*
Mathematical Statistics I
Prerequisite(s): MATH 2163 (Calculus III). Introduction to probability theory for students who are not graduate majors in statistics or mathematics. Probability, dependence and independence, random variables, univariate distributions, multivariate distributions, moments, functions of random variables, moment generating functions.

and

STAT 5123*
Probability Theory
Prerequisite(s): MATH 2163 (Calc III) and one other course in MATH that has either 2144 (Calc I) or 2153 (Calc II) as a prerequisite. Basic probability theory, random events, dependence and independence, random variables, moments, distributions of functions of random variables, weak laws of large numbers, central limit theorems.

and

Advanced Linear Algebra: A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and hermitian forms, and dual spaces.

Thanks for your time!

[C152dude]

I vote math stats. My stats i and prob theory classes looked just like that. I found math stats to be more difficult, more informative, and more rewarding.

Although, what did you do in l.a.?

[Macromatica]

I took l.a. about a year ago, and was one of my favorite mathematics courses. Majority was computations and the rest was formal definitions.

MATH 3013*
Linear Algebra
Prerequisite(s): 2153 (Calc II). Algebra and geometry of finite-dimensional linear spaces, linear transformations, algebra of matrices, eigenvalues and eigenvectors.

[C152dude]

Go stats.

[Macromatica]

Cool, thanks for your insight. Intro to RA, math stats, and which other one:

Advanced linear or prob theory?

[C152dude]

Sorry, I cannot read. From my personal experience, those classes overlapped a bunch. There was basically nothing in prob theory that we did not do in stats; well, besides the proof of CLT and the various inequalities around the weak law. That makes me inclined to say linear algebra. I, as well, loved linear algebra. Of course, "advanced" might look nice as well.

Other suggestions: What about an econ grad course? Diff eq? Programming?

(Someone with more knowledge will give you more concrete advice.)

[treblekicker]

Originally Posted by Macromatica

Advice and expertise on which two classes to take for this fall semester would be very helpful and appreciated. These are my choice of courses for the fall, this would somewhat be a relatively easy decision but the similarities between prob theory and math stats is what poses a problem in my decision making. This will be the last of my courses to appear on my transcript before I apply to PhD programs. Pick your favorite two. (My other course that I'm in is Intro to Real Analysis.)

*Advanced Linear Algebra
*Probability Theory
*Mathematical Statistics I

STAT 4203*
Mathematical Statistics I
Prerequisite(s): MATH 2163 (Calculus III). Introduction to probability theory for students who are not graduate majors in statistics or mathematics. Probability, dependence and independence, random variables, univariate distributions, multivariate distributions, moments, functions of random variables, moment generating functions.

and

STAT 5123*
Probability Theory
Prerequisite(s): MATH 2163 (Calc III) and one other course in MATH that has either 2144 (Calc I) or 2153 (Calc II) as a prerequisite. Basic probability theory, random events, dependence and independence, random variables, moments, distributions of functions of random variables, weak laws of large numbers, central limit theorems.

and

Advanced Linear Algebra: A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and hermitian forms, and dual spaces.

Thanks for your time!

I think I mentioned this in another thread by you. There really isn't a huge difference between the probability theory course and the math stats course you listed. When I think math stats, I think likelihood, estimation, and hypothesis testing. The only major differences I see between those two course descriptions:

Stats covers multivariate distributions

Prob covers limit theorems

Both are very useful, but I think it would be hard to get through more advanced statistics courses without decent coverage of the limit theorems. And, since you're taking Advanced LA, multivariate distributions should be too hard to pick up down the road for you.

So I guess my advice is Prob + Adv. LA