Advanced Linear for Stat/Actuarial

[StatlyDude]

I just took an elementary Linear Algebra class using the Anton textbook.

Next semester I may take an Advanced Linear Algebra class using Friedberg, et. al. (proof-based LA). I may take this course because I heard that Linear Algebra is used extensively in Stat, and I would like to be prepared for grad program in stat. On the other hand, I could take Probabilily (calc-based) to prepare for the actuarial exam P.

I think I could study the Probability on my own, but having a class might be better. Anyway, how important really is Linear Algebra for stat? Is it important just for the ph.d., or master's programs also? What if I just want to be an actuary and forget stat grad school, would I still need advanced linear algebra for actuarial work?

[PompousPilots]

I would recommend a probability course over a second proof-based linear algebra course for both grad stat and for the actuarial exam.

You definitely use a lot of Linear Algebra in stat, but you really just have to be good at using the results of linear algebra rather than having a deep understanding of all the proofs. For example, would likely be much more useful for you to learn to use the R programming language to manipulate matrices, etc. than to take a theoretical linear algebra course.

Probability, on the other hand, is absolutely essential for every aspect of Statistics, applied and pure, master's and phd. I would recommend as much probability as you can get.

[StatlyDude]

I would recommend a probability course over a second proof-based linear algebra course for both grad stat and for the actuarial exam.

You definitely use a lot of Linear Algebra in stat, but you really just have to be good at using the results of linear algebra rather than having a deep understanding of all the proofs. For example, would likely be much more useful for you to learn to use the R programming language to manipulate matrices, etc. than to take a theoretical linear algebra course.

Probability, on the other hand, is absolutely essential for every aspect of Statistics, applied and pure, master's and phd. I would recommend as much probability as you can get.

So you think that, an elementary, computational LA class using Anton is enough for Stat? We actually did some proofs and I got an A, but I may forget even that basic stuff if I don't do further study of LA.

Again, I don't need to bother with Hoffman-Kunze, Halmos, Shilov and/or Friedberg stuff? Besides, I heard that LA is important in quantum mechanics, and I have some side interested in physics.

In a sense, I feel like I could learn the calc-based probability on my own even though it won't be easy. I'm a post-bacc and I pay $1000 for every university-level course I take. I might set aside that $1000 for measured-based probability course after I take the first-semetser Measure Theory course.

What you've told me is very different from what I've heard so far, I want to make sure. What I may do is take the calc-based probability and study the advaced linear algebra on my own. What do you think?

[PompousPilots]

So you think that, an elementary, computational LA class using Anton is enough for Stat? We actually did some proofs and I got an A, but I may forget even that basic stuff if I don't do further study of LA.

You definitely want to have a very good basic understanding of LA. Beyond that, your time would be better spent learning probability than rigorously developing LA. Maybe watch the MIT open courseware video series on LA on Youtube to review everything. Just search for "MIT Linear Algebra" and watch the whole series. The lecturer is great.

And, here's a pop quiz:

Given some vector of data, y

and some matrix of data, X

Find the vector b such that

the distance from y to X*b is minimized

In other words find the linear combination of the columns of X that has the smallest Euclidean distance from y.

You don't actually have to answer it right now. The answer is b = inv( transpose(X) * X) * transpose(X) * y

So that's a basic question in Linear Regression. Did that basically make sense? You need to know how matrix arithmetic works, column spaces, etc.

If that question made sense to you, then you probably understand LA well enough. But you should still review to stay sharp. Watch the MIT videos.

Again, I don't need to bother with Hoffman-Kunze, Halmos, Shilov and/or Friedberg stuff? Besides, I heard that LA is important in quantum mechanics, and I have some side interested in physics.

Probability is important in quantum too.

In a sense, I feel like I could learn the calc-based probability on my own even though it won't be easy. I'm a post-bacc and I pay $1000 for every university-level course I take. I might set aside that $1000 for measured-based probability course after I take the first-semetser Measure Theory course.

It definitely won't hurt to take an undergrad-level calc-based probability course now, then measure theory at some point, then a measure-based probability course.

What you've told me is very different from what I've heard so far, I want to make sure. What I may do is take the calc-based probability and study the advaced linear algebra on my own. What do you think?

I think that would be better.

You really want probability to become second nature - become intimately familiar with all the common distributions, etc. That just takes a lot of time and repetition.

[hubris]

Echoing the Prob recommendation esp since you are paying for these courses.

A non-engineering LA course is likely to not be useful to you.