How much linear algebra do you need?

[One on One]

My school has 3 linear algebra courses so I'm not sure how much I need here. The first is a freshman course that I have already taken and is required of engineers. Then, there is a linear algebra course in the 3xxx sequence which is only required by math majors I believe. This course requires proofs. Then, there is a 3rd course which is like the 2nd course part 2 so it also would require proofs. How many of these courses should I take to look good to top 50 econ phd programs?

[asquare]

Linear algebra isn't the course that's going to make you look good to adcoms -- that course is real analysis. Linear algebra is just a tool. You should know how to use it, but there's no need to spend a lot of time taking extra courses. You might want to flip through a grad metrics book like Hayashi -- if you can follow the linear algebra there, you're fine.

Also, it might not be obvious to an adcom that your higher level linear algebra course was a proof-based class. Bottom line? So long as you can do basic linear algebra, there are better classes than advanced linear algebra to take to both help you get in and to help you do better your first year.

[shootermcgavin7]

Originally Posted by asquare

Linear algebra isn't the course that's going to make you look good to adcoms -- that course is real analysis. Linear algebra is just a tool. You should know how to use it, but there's no need to spend a lot of time taking extra courses. You might want to flip through a grad metrics book like Hayashi -- if you can follow the linear algebra there, you're fine.

Linear Algebra may be just a tool, but most schools require two semesters of Linear Algebra (of some sort) as a pre-req for Real Analysis

[asquare]

Originally Posted by shootermcgavin7

Linear Algebra may be just a tool, but most schools require two semesters of Linear Algebra (of some sort) as a pre-req for Real Analysis

Really? I never actually took a course in linear algebra (had some of it in an undergrad "math for economists" class, but never a math department class) and had no problem enrolling in or doing well in real analysis. I wasn't a math major, but real analysis was actually the first course in the accelerated sequence for math majors -- no prereqs except 5 on the calc BC exam.

Still, I'd say to take the second linear algebra class only if you need it for upper division classes, you don't think your linear algebra is good enough to keep up with grad metrics, or there isn't something else you'd rather take. I don't think the course in itself will help much with admissions or your first year, above and beyond what the first semester of linear algebra does for you.

[Econ2006]

I think a course in linear algebra is usually a pre-requisite for real analysis (along with an intro. to proofs course), but I don't remember using LA at all in my analysis course. Perhaps it's just a mathematical maturity requirement. In any event, a second semester of analysis would be more beneficial with regard to admissions than another semester of LA.

[economicus]

One additional question. What do you think about the usefulness of the following course: stochastic calculus. I would take it as an additional course during my msc. So far I have a limited math background (only two classes: I'm on the level of simon&Blume). Would this course be regarded as "good" in the adcomms' eyes? Unfortunately, our programme doesn't have a real analysis...but this one seems quite a demanding course...

In this course elements of probability theory, stochastic processes and stochastic calculus are discussed, in sofar as they are relevant in the analysis of financial derivatives. The emphasis is on the mathematical concepts and techniques, and to a lesser extent on their application in pricing and hedging derivatives. The topics that are covered are:

• discrete-time methods: binomial trees, the Cox-Ross-Rubinstein model
• continuous-time stochastic processes: Brownian motion, martingales
• stochastic calculus: the Itô integral, Itô’s lemma, stochastic differential equations
• Girsanov's theorem, equivalent martingale measures, risk-neutral valuation
• the Black-Scholes-Merton model
• implementation of various numerical methods in computer programs

[shootermcgavin7]

Originally Posted by asquare

I never actually took a course in linear algebra (had some of it in an undergrad "math for economists" class, but never a math department class) and had no problem enrolling in or doing well in real analysis..

That doesn't mean many/most schools don't have it as a prereq due to whatever their sequence may be.

Most schools have these pain-in-the-*** moments at least in some curriculum.

For example, if you're in a business program, principles of accounting may be a prereq to an advanced marketing class.....even though marketing uses virtually no accounting.

I'm taking LAII right now because it is a co-requisite for Analysis I, and a pre-req for Analysis II.

Originally Posted by economicus

One additional question. What do you think about the usefulness of the following course: stochastic calculus. I would take it as an additional course during my msc. So far I have a limited math background (only two classes: I'm on the level of simon&Blume). Would this course be regarded as "good" in the adcomms' eyes? Unfortunately, our programme doesn't have a real analysis...but this one seems quite a demanding course...

In this course elements of probability theory, stochastic processes and stochastic calculus are discussed, in sofar as they are relevant in the analysis of financial derivatives. The emphasis is on the mathematical concepts and techniques, and to a lesser extent on their application in pricing and hedging derivatives. The topics that are covered are:

• discrete-time methods: binomial trees, the Cox-Ross-Rubinstein model
• continuous-time stochastic processes: Brownian motion, martingales
• stochastic calculus: the Itô integral, Itô’s lemma, stochastic differential equations
• Girsanov's theorem, equivalent martingale measures, risk-neutral valuation
• the Black-Scholes-Merton model
• implementation of various numerical methods in computer programs

That seems more along the line of a course geared toward finance majors. If it is your only option, though, more math is always better.

[asquare]

Originally Posted by shootermcgavin7

That doesn't mean many/most schools don't have it as a prereq due to whatever their sequence may be.

Most schools have these pain-in-the-*** moments at least in some curriculum.

For example, if you're in a business program, principles of accounting may be a prereq to an advanced marketing class.....even though marketing uses virtually no accounting.

I'm taking LAII right now because it is a co-requisite for Analysis I, and a pre-req for Analysis II.

Sure -- I guess my point is that it's hard for us to generalize beyond our own experiences. I only know the requirements at the schools I've attended (and a bit about the requirements at schools my friends attended.) I was curious, though, so I looked up the prereqs for Principals of Analysis in the math department here at Michigan. The prereq is calc 3 (which at Michigan is multivariable calc, using Stewart), and ONE linear algebra course (which can be waived at the discretion of the instructor). The advanced undergrad real analysis course at Michigan is intended as a substitute for Principals of Analysis for those so inclined, and it doesn't have any linear algebra prereqs, though it does have more advanced calculus prereqs.

All I'm getting at is that if additional linear algebra courses aren't required for analysis, then I don't think they are the most helpful courses the OP could take.

[One on One]

At my school, Advanced Calc (ie. Calc IV) is the prereq for real analysis. Of course you would have had to have taken the first linear algebra course to get that far, but the 2nd linear algebra course is not a prereq for anything unless you want to take more linear algebra.

[asquare]

Originally Posted by One on One

At my school, Advanced Calc (ie. Calc IV) is the prereq for real analysis. Of course you would have had to have taken the first linear algebra course to get that far, but the 2nd linear algebra course is not a prereq for anything unless you want to take more linear algebra.

Have you taken Advanced Calc and real analysis? If not, I'd take those instead of more linear algebra. They'll help you a lot more with the first year, and will be more important to admissions committees.