# Compare these two Linear Algebra courses

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1. Nov 3, 2016

### themli

Hi!

First off, I am actually a math / econ major. I hope I'm still welcome here

I am trying to figure out if it's worth it to take both of these courses or just one of them. I have not taken LA before.

Course 1:
• Addition, subtraction and scalar multiplication of vectors, length of vector, distance between vectors and the inner product between vectors, lines and planes in space, hyperplane, parametric and normal equations for lines and planes in space and linearly dependent and independent vectors.
• Apply addition and multiplication of matrices, identity, inverse matrix and linear system of equations in matrix form. Apply Gauss-Jordan elimination to solve linear equations.
• Determine the rank of a matrix and explain how the range can be used to classify linear system of equations.
• You will also be able to calculate determinants and could use Cramer's rules for solving linear system of equations.
• Text: Simon & Blume, Math for econ
Course 2:
• Solving homogeneous and inhomogeneous linear equations
• Understand and apply the rules of matrix algebra
• Calculating determinants in specific cases
• Reproduce definitions and concepts related to vector spaces and their dimensions.
• Using the theory of eigenvalues and eigenvectors to answer questions about linear equations.
• Applying the theory of orthogonality on least squares method.
• Using the theory of eigenvalues and eigenvectors to studying quadratic forms.
• Text: David C. Lay,Linear Algebra and Its Applications
I will be taking course 1, because I need it for credit (it counts towards my econ-credits, as it is taught by the econ department). If I don't take course 2 (by math department) (would take two semesters after), I will be able to take Measure theory - which I would like to take.

I guess my main question is, would course 1 provide me with adequate LA skills to handle later courses (I am taking real analysis the semesters after, then measure theory). Is course 1 rigorous enough (for mentioned courses)? I am also taking LA to handle graduate Econometrics and time series.

Last edited: Nov 3, 2016
2. Nov 3, 2016

### Staff: Mentor

Course 1 seems to be an introductory course in Linear Algebra, while Course 2 seems to be much more in depth, with more exposure to vector spaces, eigenvalues and eigenvectors, and other topics. Course 1 seems to be considerably more elementary than Course 2. I don't believe that Course 1 would give you the skills you need in subsequent analysis courses.

3. Nov 3, 2016

### FactChecker

I am not an economist, but I am familiar with optimization problems and feedback systems that I think are often central to theoretical economics. With that said, I think that the second course of LA would be more beneficial than measure theory.

4. Nov 3, 2016

### themli

Thank you both of you. I definitly agree in terms of application. LA seems crucial for grad school econometrics. I was considering Measure theory for a pure signalling effect (admissions) - and maybe some more mathematical maturity. So I guess I would be better off in the long run if I take more LA.

I won't actually be able to take LA course 2 before Analysis, but I think I'll be fine. (I will have taken all the prereq's, including vector calculus).

Of course, a second option could be to take both next semester. I might consider that, if there is sufficient overlap.

Last edited: Nov 3, 2016
5. Nov 3, 2016

### micromass

You can never know too much linear algebra. The contents in the second linear algebra course are very important and fundamental. Any math and economics major will want to be very acquainted with them. I would definitely want to know it well, more so than measure theory.

6. Nov 3, 2016

### Krylov

Obviously you are.
This was my first text on linear algebra. In another topic I recommended it to someone looking for an example from economics. The text as a whole is very well-written, clear and applicable.

It struck me that in the second course there are the topics of eigenvalues and eigenvectors as well as least squares. These topics seem missing in the first course, but they are crucial for understanding statistical applications, such as regression analysis.

My advice would be to buy Lay's book and take both courses, possibly in parallel, basing yourself mainly on his text and using the other book for examples specific to economics and additional exercises. Have fun!

P.S. Measure theory is the foundation for probability, hence for stochastic processes and advanced statistics. Depending on your interests, you could certainly consider taking it at some point, but for now LA should have priority.

7. Nov 3, 2016

### Crass_Oscillator

Measure theory may only be relevant to mathematical economists/statisticians too, meaning that if you wind up doing more applied work you may only need familiarity rather than mastery of the subject, but I'm no expert here.

8. Nov 4, 2016

### themli

Thank you! This is great stuff, you made things clearer. I will definitely take the second course. Since I'll take it next semester I'll be able to take measure theory as well - after real analysis. I am interested in theoretical work (micro) - so I think measure theory will be helpful.

9. Nov 4, 2016

### Krylov

Yes, it will. Theoretical micro-economics can be delightfully mathematical. It also makes use of certain subjects that are usually at most merely touched upon in the standard (applied) mathematics curriculum, such as set-valued analysis.

Once you have a good basis in real analysis, you may find "Theory of Value: An Axiomatic Analysis of Economic Equilibrium" by Debreu (1959) and "Core and Equilibria of a Large Economy" by Hildenbrand (1974) inspiring. (Maybe you already knew this for long yourself, sorry in that case. Also, probably since then a lot has developed beyond general equilibrium theory.) At some point I found these titles useful in a non-economic context.

Anyway, I think you reached the correct conclusions about your curriculum. Good luck and enjoy

10. Nov 4, 2016

### themli

Thank you sir! I am familiar with Debreu, but have not read any of his work or Hildenbrand's.

My interest in theory might change, but I'll still take the Measure theory class, as I find it very interesting. The texts used are "Papa Rudin" (Real and Complex analysis) and stochastic calculus (Klebaner).

11. Nov 4, 2016

### micromass

Oh... You might want to think of self-studying measure theory then. Rudin is an awful book.

12. Nov 4, 2016

### themli

Really? I tought all Rudin's books were classics. What do you think about his Real analysis book? That's what I'll use in the RA class. I suppose I could look for a supplementary book as well (for measure). But it's not gonna be for another year so we'll see.

13. Nov 4, 2016

### micromass

Yes, they are classics. And they're also horrible to read and to learn from. But I think we'll soon get people in here who disagree with me.

14. Nov 4, 2016

### themli

I always try to use multiple sources (and usually need to when I'm stuck), but thank you for the heads up!

15. Nov 4, 2016

### Crass_Oscillator

Sometimes a book is classic because experienced practitioners find it to be a useful reference, not because it is suitable for beginners.

16. Nov 4, 2016

### FactChecker

Yes. If you might go into pure math, measure theory and real analysis are necessary. I am surprised with the choice of text books for measure theory, since those books cover much more. I guess that stochastic calculus is important in economics and finance and that the other subjects are certainly necessary for understanding stochastic calculus. So they are good subjects to study. I think that the second LA class is probably a prerequisite for stochastic calculus.

17. Nov 4, 2016

### themli

That course is actually taught by the math department - the professor told me they never really see any econ students taking it (semi-small uni), it's set up for math majors. But I take your point, it is useful for econ and finance for sure! And you're right about the second LA course - which was the reason for my question, I wasn't sure if it would be enough. But now I know better :)

Last edited: Nov 4, 2016