Thoughts on Advanced Linear Algebra

[Macromatica]

So I am enrolled in Advanced Linear for the fall semester. I took linear algebra about a year ago. I am wondering if this would be a good move subject to an adcom's point of view, and futhermore, for useful knowledge in general. This would fufill a requirement for my graduate minor in math. I will be applying to phd programs for the fall '09 semester. Thanks.

[jeeves0923]

I would say Real Analysis, Measure theory, probability theory, or stochastics would be better choices. If you've already done all of those, Advanced Linear probably gives you some good knowledge, esp if you want to be an econometrician. I have no clue what adcoms will think besides more math is better.

I'm in a similar situation with math classes. I've taken all of the "signal" classes, and now it is a bit of a challenge to nail down exactly which ones will be the most useful. Overall, I'd say don't stress out so much about it, especially if you already have the other courses i listed above.

[unitroot]

An advanced course in linear algebra can mean two things. Either it's a very "computational" course where a lot emphasis is put on deriving and applying computational techniques like factoring matrices, solving equations, and such or it could be a relatively abstract course very much like a course in abstract algebra, where the primary goal is to understand how the operators work on abstract vector spaces. Matrices are still studied there but primarily to study the properties of operators on vector spaces. A good example of the text used in the later category is Axler's Linear Algebra text.

I would say that the former type of course is very useful for people who will eventually start doing lots of computational stuff in macroeconomics or say econometrics. At the same time the later course basically a pure math course that will emphasize rigorous thinking about abstract vector spaces. The former kind of course is more useful from practical standpoint. However, in the end, what kind of advanced linear course it is depends entirely on the professor.

I would say having real analysis on your transcript is more important than advanced linear algebra. At the same time, once you already have RA on the transcript, I think advanced linear algebra will send a very good signal and it's a useful, practical knowledge to boot. I would think that it's about as useful is no more useful than measure theory. No one uses measure theory except for certain kinds theorists and econometricians.

[asianeconomist]

Originally Posted by Macromatica

So I am enrolled in Advanced Linear for the fall semester. I took linear algebra about a year ago. I am wondering if this would be a good move subject to an adcom's point of view, and futhermore, for useful knowledge in general. This would fufill a requirement for my graduate minor in math. I will be applying to phd programs for the fall '09 semester. Thanks.

What topics do the course cover ?

[asianeconomist]

Originally Posted by Macromatica

So I am enrolled in Advanced Linear for the fall semester. I took linear algebra about a year ago. I am wondering if this would be a good move subject to an adcom's point of view, and futhermore, for useful knowledge in general. This would fufill a requirement for my graduate minor in math. I will be applying to phd programs for the fall '09 semester. Thanks.

What topics does the course cover ?

[Macromatica]

Thank you for the responses. My schedule for the fall currently looks like this:

Intro to Modern Analysis (intro to real analysis)
Mathematical Statistics I
Advanced Linear Algebra

And to the previous response this advanced linear course is a rigorous, pure math course. My only other options to replace advanced linear if I wanted to would be mathematical modeling, or probability theory, but prob theory is currently all filled up, dang it! Im thinking I should stick with this schedule unless prob theory opens up?

[Macromatica]

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.

[jeeves0923]

Definitely do probability theory if you can.

[unitroot]

Originally Posted by Macromatica

Thank you for the responses. My schedule for the fall currently looks like this:

Intro to Modern Analysis (intro to real analysis)
Mathematical Statistics I
Advanced Linear Algebra

And to the previous response this advanced linear course is a rigorous, pure math course. My only other options to replace advanced linear if I wanted to would be mathematical modeling, or probability theory, but prob theory is currently all filled up, dang it! Im thinking I should stick with this schedule unless prob theory opens up?

What's the Mathematical Statistics I about? It is strange that you can take a mathematical statistics class before taking a decent probability theory first. Either this mathematical statistics course is not that "mathematical" or it must devote most of its time on probability theory.

[Macromatica]

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.

These descriptions are directly out of our course catalog. They sound similar to me. What are thoughts on this, and my current fall schedule (above). I appreciate your time.