Economics 519: Mathematics for Economists

August 2006

Class meetings

401kk McClelland Hall
Monday-Saturday, 9:30-11:30am, and 5:00-6:00pm


David Reiley
Office hours: 2:00-2:30pm, or by appointment
401cc McClelland Hall

Teaching Assistant

Natalia Lazzati

Course home page

Course Description

This is an intensive course in the mathematics one should know when beginning a doctoral program in economics. The textbook by Simon & Blume is excellent. The course objective is simply that you achieve an understanding of the concepts we will cover in the textbook and the ability to apply them. As you can see from the tentative schedule below, it will be a very fast-moving, very intensive course - a sort of mathematical boot camp. You'll have little time for other things during these three weeks, but the course will prepare you for the doctoral program in economics.

Teaching Philosophy

As an economist, I believe in efficient allocation of resources. Because I try to practice what I preach, you may find that my teaching style differs from what you are used to, or from what you will see from other faculty in the economics department.

Here's the plan. I want to reserve our class time (a precious resource) for two-way communication: questions, discussions, and cooperative problem-solving. Most of the one-way communication in this course will happen through assigned readings rather than through lectures.

In order for the interactive class format to work, you should do two things: (1) Make sure to complete each day's assigned reading before coming to class, so that we can discuss it and you can ask questions about anything you didn't understand. When doing the readings, try a few problems out of the book to check your understanding. (2) Be ready to think and talk when you come to class. In order to make sure that everyone has the chance to participate in class, I will call on each student from time to time.

Whenever you don't understand something, either from the readings or from class, please ask a question. Often other students are having the same difficulty as you are and all can benefit from the exchange. I need your feedback so that I can make the course meet your needs. Furthermore, if you’re scared of the idea that I might cold-call you during class, a great defensive move is to come prepared to ask me something, so that I know you’re actively participating.

I believe that the deepest learning occurs when students teach themselves. Therefore, I expect you to do most of your learning through the readings and assignments, both on your own and in cooperation with your classmates. I do not intend to "cover" everything in class lectures. Rather, my job in this course is to guide the learning by choosing readings and exercises for you, and to coach you through this learning process in a way that maximizes understanding with as little frustration as possible.

For example, when you get stuck on a page of reading you don't understand; don't waste hours on it, but instead note that you want to ask me about it, and then move on. Similarly, when you get stuck on a math problem you can't solve, you should plan to struggle for about 15-30 minutes to make sure you understand the problem and where you're stuck, but don't ever spend more than 30 minutes stuck on a single problem in this class. Instead, find a classmate and see if you can work it out together. If that doesn't work after 15 minutes, email me for a hint, or ask me or the teaching assistant in class. The book can't interact with you, but we can, and that's what we're here for. But in order to take full advantage of this learning opportunity, you're going to have to put in your own effort, early and often.


Reading assignments will come mainly from the required text: Mathematics for Economists, by Carl P. Simon and Lawrence Blume (Norton 1994; ISBN 0-393-95733-0).

As noted above, please make sure to do each day's reading assignment before that morning's class. So, for example, by the time you arrive for the first day's class, you should have read Chapters 10, 11, and 27 from the textbook, and made notes about anything you didn't fully understand.

Something else I'd like everyone to learn is the value of consulting alternative references. When you don't understand something in your assigned text, it can be a really good idea to consult other sources about the same topic, to see if one of them makes more sense to you. You can find additional references in the library and on the World Wide Web. I'd like to recommend three examples in particular:


There will be a problem set due in class each morning of the course, including the first day of class. During the summer, I expect you to obtain a copy of the textbook and work all the problems in my assigned summer problem set on differentiation, integration, basic probability, and basic linear algebra. (These topics can be found in Chapters 1-9, and appendices A4 and A5 in the text.) Plan to turn in this problem set on the first day. I'm hoping these problems will all be review for you. I'm assigning them just to make sure that everyone remembers these basic concepts, because it may have been a few years since you last computed an integral, or you may have missed learning Gaussian elimination or determinants in a linear-algebra course. If you're rusty or missing one of these topics, I believe the book is excellent and will help you get up to speed.

If, during the summer, you run into difficulty with one of the problems, you are welcome to email me for help. Since I will be traveling a lot this summer, I may not always reply immediately, I promise to get back to you as soon as I can. Please put "Econ 519" in the subject line of your email, so that the message will come to my attention promptly.

If you are worried about the pace of this mathematical "boot camp" and want to work ahead even beyond the first assigned problem set, you are welcome to read ahead in the book and try the exercises. See the course schedule below.

Suggestions for Surviving the Course

Once the course starts, it will be extremely fast-paced. Therefore, here are some suggestions to help you make the most efficient use of your time.


Your grade in this course will be based on your graded problem sets (50%) and your final exam (50%). I will give an open-book exam, where you may use any books or notes you like. The point of the course is not to memorize formulas and theorems, but to make sure you know how to use the concepts to solve problems. Here is a page where you can find past exams for the course.


This schedule is subject to change. Any changes will be announced in advance.

Date Reading Topic Homework due
31 July Ch 10, Sec 11.1 Vectors, linear independence Summer problem set
1 Aug Ch 11, Ch 27 Vector spaces PS #1
2 Aug App A1, Ch 12 Proofs, set theory, limits PS #2
3 Aug Ch 13,
Sec 14.1-14.5
Functions, differentiation PS #3
4 Aug

Sec 14.6-14.9,
Sec 15.1-15.4

More differentiation, implicit functions

Note: Sections 14.7, 15.2, and 15.3 are relatively abstract and hard to read. Master the other sections first. In these more abstract sections, remember to focus on the examples.

Here is a guide to reading Section 15.4.

PS #4
5 Aug Ch 16-17 Quadratic forms,
unconstrained optimization
PS #5
7 Aug Ch 18, plus
Chiang/Wainwright 13.2 on constraint qualifications

Constrained optimization I

Note: Some of the theorems can be hard to follow, so make sure to focus on understanding the examples in the text.

In Section 18.7, make sure to study the first application and the "One More Worked Example," but please skip "The Averch-Johnson Effect" for now, as it's complicated and potentially confusing.

If you find some of the reading in Chapters 18-19 tough to follow, I recommend Chapters 5-6 of Madden as an optional, alternative treatment.

PS #6
8 Aug

Ch 19

Constrained optimization II PS #7
9 Aug NO MEETING International student orientation  
10 Aug NO MEETING International student orientation  
11 Aug Ch 20, Sec 21.1-21.3,
Chiang/Wainwright 12.4,13.4

Useful categories of functions: homogenous, homothetic, concave, quasiconcave

PS #8
12 Aug Ch 29 Cauchy sequences, compactness, connectedness, alternative norms PS #9
14 Aug Ch 30 Advanced calculus theorems,
Taylor approximations
PS #10
15 Aug Sec 23.1, 23.3, 23.7, 23.8

Eigenvalues and eigenvectors;

PS #11
16 Aug NO MEETING Graduate College orientation  
17 Aug NO MEETING Graduate Teaching orientation  
18 Aug   Final exam