Mathematics for EconomistsEconomics 205, Fall 2009General InformationInstructor: Joel SobelOffice: 311 EconomicsOffice Hours: After classPhone: (858) 534-4367Email: [email protected] (with link to handouts for course):http://www.econ.ucsd.edu/%7Ejsob el/205f09/205f09home.htmTeaching Assistant: Matthew NiedzwieckiOrganizationThe class meets from 8:30 to (approximately) 11:00 every weekday from Wednesday, August 24through Monday, September 14, with the following exception: There is no class on September 7. Iwill also use time between 11:00 and 11:30 if necessary for quizzes or to stay on schedule.In addition, the classroom will be available from 1:00-4:00 for study sessions on most days. Onsome days there will be organized problem sessions led by the TA. On other days, students can usethe room to work together on class material.DescriptionThis course is a rapid overview of topics in calculus, advanced calculus, optimization, and linearalgebra that are relevant to economic theory. I hope that it provides the necessary mathematicalbackground to begin the core graduate sequence. The course covers a large amount of material at arelatively high level of rigor.If you have mastered the material in standard upper-division analysis and linear algebra classes,then this class should contain little that is new. If it has been a long time since you have usedcalculus, then the course will be difficult. If you have never used calculus, then the course m ay beimpossible.To avoid misunderstandings, let me emphasize that the class is not simply a review of lower-division calculus. Nor does it cover all (or even most) of the mathematics used in the core classes.RequirementsThe main evaluation will be a three hour, closed book, closed notes examination tentativelyscheduled for Thursday, September 17 from 8:30 to 11:30. (This time becomes official if there are nocomplaints today.) Your grade will be the maximum of your grade on the final examination, and aweighted average of your final exam grade (75%), and your performance on quizzes. You must passthe final examination in order to enroll in Economics 200A. Officially this course is part of the FallQuarter, so you have the unusual ability to enroll in the class after it you completed it.Problems are a necessary part of learning the material. I will make available relevant problemsfrom a basic calculus book by Apostal, Chiang’s book on mathematics for economists, and anvector calculus book by Marsden, Tromba, and Weinstein. These problems mostly cover elementarymaterial. You may want to concentrate on these problems if you are having difficulty with the coursematerial. Relevant problems are also available in the texts. There will be a list of problems postedon the web page. I will suggest problems from texts in most class periods. You should attempt todo them throughout the course.1Texts and Course Material(SB) C. Simon and L. Blume, Mathematics for Economists(N) W. Novshek, Mathematics for Economists(D) A. Dixit, Optimization in Economic Theory, 2nd edition(MA) K. G. Binmore, Mathematical Analysis(C) K. G. Binmore, Calculus(CH) A. Chiang, Fundamental Methods of Mathematical Economics(SB) should be available in the University Books tore. I have copies of all books (and others). Inaddition to these books, my web page contains course notes prepared by Joel Watson and me. Theseare a work in progress. I will make an effort to update and augment these notes throughout theclass.There are many books that cover the basic material of this course. Feel free to use another bookas a primary reference. (If you are not sure whether another book is adequate, then check with me.)If you are searching for a text, here are my views. (SB) is officially the text for the course. Ithas the following strengths: it contains many economic examples; it covers the topics that I intendto cover; it covers other material that you should know; it has many problems and solutions. Onthe other hand, it is poorly organized and its level of treatment is uneven. My lectures will be quitedifferent from the text material. (N) is concise, covers most of the topics, and has many problemsand solutions. Its coverage of one-variable calculus is brief and its approach to optimization ismechanical. (D) is a nice introduction to optimization from the perspective of economics. (MA)is a concise introduction to “advanced” one-variable calculus. It presents definitions and theoremswith care and provides an introduction to proofs. It is slightly more advanced than the course willbe. It may be a good place to look if the material in the first week seems to easy. (C) is morebasic than (MA). It has reasonable coverage of most of the topics of multi-variable calculus. (CH)is a standard reference for courses in mathematics for economists, but I find it too mechanical. Itmay be a good place to look if the lectures seem difficult. Dixit contains material relevant to theoptimization topics.PaternalismOver the years I have convinced myself that I know many wise things that will help you adjustto the class and, more generally, the graduate program. I found myself spending more and moretime saying these things on the first day of class. Now I think that it is not worth spending muchclass time on this advice, but I compiled a list of recommendations:1. You cannot learn mathematics by reading a book. It is better to work problems. It is betterstill to pose problems yourself and try to solve them.2. Performance in Econ 205 is related to how much math you already know. It is a good predictorof success in first-year courses. It is a bad predictor of the quality of your dissertation.3. The hardest part of graduate school is starting your research project. (In particular, it is notEcon 205.)4. No one on the faculty wants you to fail.5. . . . but be nice to Mary Jane.6. You do not need to know everything already.27. Work – and play – with classmates. You’ll learn more from them than your professors. Someof them will be friends and colleagues for life.8. Figure out what is important to you.9. Good research projects are not scarce, but they are hard to find.Topical Outline and ReferencesThe table on the next page lists the topics that I hope to cover. (I rarely reach differentialequations and integration.) It relates the topics to pages in five of the texts mentioned ab ove. Thenumber of pages devoted to each topic varies drastically from text to text. The quality and the levelof treatment vary as