Even though I'll never be a true mathematical economist, dabbling in mathy magic is one of my economic indulgences. There's something to be said for having a bag of tricks up your sleeve, and these are mine. (There's also something to be said for not mixing your metaphors.) The more tricks you know, the more problems you can model and solve. There's this premium on developing math skills as a grad student, which is why my job got invented. I'm supposed to teach you guys mathematics for use in economic theory -- basically, the math you'll need before you start the program, and then how to do the math tricks you'll need in grad school and beyond.
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This page starts with lecture notes that were disseminated during the
summer 2000 and summer 2001 math review classes for the department's
incoming grad students. I have revised them to correct some of the more
embarassing typos, and to include some materials I covered in class but
that hadn't been in the notes. Additionally, this site contains
references to sections of textbooks for more information on a number of
that hadn't been in the notes. Additionally, this site contains
references to sections of textbooks for more information on a number of
levels -- for those needing more review, as well as for those budding
theorists.
Next are notes on some micro and macro topics for the fall semester (currently under development). Those will start appearing late in August and throughout September. Finally, there are also some notes on a few bonus topics that I have not been allowed to release in the wild. Those are mostly just posted because I was bored. This website is intended to provide something like an online manual for first-year (and even more advanced) economics students. |
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Grad Math Review (Summer 2001)
The math prep class contained fourteen lectures, each of which corresponded (more or less) to the fourteen math classes you were expected to take before starting grad school. Under each of these should be my lecture notes, a list of references, and a list of recommended problems. The textbooks to which I make references are all listed at the bottom of this page.
This is an introduction to the course and an outline of the topics covered.
A calculus refresher
1. Calculus: Univariate 2. Calculus: Multivariate 3. Calculus: Integration 4. Calculus: Special Topics for Economists
Optimization and an introduction to the language
5. Optimization: Unconstrained and Equality Constrained 6. Optimization: Inequality Constrained 7. Logic, set notation, and proofs 8. Analysis: basics of real analysis 9. Analysis: basics of convex analysisMathematical tools
10a. Linear algebra: the basics (part one) 10b. Linear algebra: the basics part two) 11. Linear algebra: matrices of derivatives and derivatives of matrices 12. Linear algebra: systems of linear equations 13. Difference and Differential Equations: some basics 14. Probability: some basicsHere is the exam.
Here are select solutions.
Grad Math for Economic Theory (Fall 2001)
During the fall semester, I am teaching mathematical tool and techniques to complement the core grad Micro and Macro classes. This class will consist of approximately nine units. It will meet twice a week in the afternoon -- tentatively scheduled for Mondays and Wednesdays, 5-6pm, in BRB 2.136.
Here is the syllabus.
1. Relations and orderings 2. Implicit function theorem 3. Matrix algebra 4. Optimization 5. Dynamic programming 6. Optimal control 7. Optimization II 8. Probability theory 9. Matrix algebra IISome of my own indulgences
These are notes which I created (or might create) just for funzies.
1. Calculus of variationsOn the pages listed above, I made references to some books. Follow this link to see some useful mathematical textbooks, some of which I've actually read.
Fine print: All materials on this page and those linked from here are the intellectual property of somebody, probably Stephen Lich-Tyler. Do not distribute without my permission and paying large royalties, etc., etc. Copyrights are enforced by a large, kinda dumb guy named Otto. You don't want to mess with him, trust me. Questions? Comments? Offended by my jokes about sociologists? Sock it to me! lichtyler@itam.mx