Mathematics for EconomistsEconomics 205, Fall 2010General InformationInstructor: Joel SobelOffice: 311 EconomicsOffice Hours: After classPhone: (858) 534-4367Email: [email protected] (with link to handouts for course):http://www.econ.ucsd.edu/%7Ejsobel/205f10/205f10home.htmTeaching Assistant: Lawrence Schmidt ([email protected])OrganizationThe class meets from 8:30 to (approximately) 11:00 every weekday from Monday, August 23through Monday, September 13, with the following exception: There is no class on September 6. 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. It provides some of 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 may 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 16 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 suggest problems and there areadditional problems posted on the web page. It is important that you find exercises that are at yourlevel – challenging, but not impossible. If the suggested problems are too easy or too hard, let meknow and I’ll find something appropriate for you. Relevant problems are also available in the texts.There will be a list of problems posted on the web page. I will suggest problems from texts in mostclass periods. You should attempt to do 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 Bookstore. 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, filled with errors, inconsistent notation, and irrelevant material. I will makean effort to update and augment these notes throughout the class.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.)(SB) is officially the text for the course. It has the following strengths: it contains many economicexamples; it covers the topics that I intend to cover; it covers other material that you should know; ithas many problems and solutions. On the other hand, it is poorly organized and its level of treatmentis uneven. My lectures will be quite different from the text material. (N) is concise, covers mostof the topics, and has many problems and solutions. Its coverage of one-variable calculus is briefand its approach to optimization is mechanical. (D) is a nice introduction to optimization from theperspective of economics. (MA) is a concise introduction to “advanced” one-variable calculus. Itpresents definitions and theorems with care and provides an introduction to proofs. It is slightlymore advanced than the course will be. It may be a good place to look if the material in the firstweek seems to easy. (C) is more basic than (MA). It has reasonable coverage of most of the topicsof multi-variable calculus. (CH) is a standard reference for courses in mathematics for economists,but I find it too mechanical. It may be a good place to look if the lectures seem difficult. Dixitcontains material relevant to the optimization topics.PaternalismWhen I started teaching this course (before you were born), I just introduced myself, describedthe topics, and began teaching math. Gradually, I spent more and more time telling the class thingsthat I thought would help it adjust to the graduate program. Now I have learned that the first dayof class is not a good time to get advice and, besides, you’ll hear similar advice from others. Hereis a short list of recommendations. Consult the list when you are ready.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. Be nice to Rebecca, Rafael, Nieves, . . . .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 above. Thenumber of pages devoted to