Course MAT200 in Fall 2011

Linear Algebra and Multivariable Calculus for Economists

Last offered in Spring 2012.  Replaced by MAT175, beginning Fall 2012.

This course covers selected topics from Linear Algebra and Vector Calculus to provide a minimal mathematical foundation for more advanced quantitative work in the Economics department. Although economic examples will be used freely, this is a math course, not an economics course. Examples from other disciplines may also be discussed. The first half of the course is a quick overview of basic linear algebra topics, all of which are covered with more depth in 202. The second half of the course develops techniques for optimization of functions of several variables, many of which are also taught in 201. For the most part we will look at functions of 2 or 3 variables, but the techniques readily extend to higher dimensions, and students should have an open mind, ready to work with more than three variables on occasion. Emphasis on concrete calculations and intuitive reasoning rather than formal proofs.


Vectors and matrices, systems of linear equations, determinants and matrix inversion, Gaussian elimination, Euclidean space, functions of several variables including quadratic forms, partial derivatives and chain rules, linear approximation and differentials, the implicit function theorem, first- and second-order tests for multivariable optimization and constrained optimization.


Students sometimes have the mistaken idea that they can "kill two birds with one stone" by taking 200 instead of 201/202. This is not the case. The material covered in 200 is substantially less than the material covered in 201/202.

Students may get Princeton credit for only two of the three courses 200, 201 and 202. Thus, if you need 201/202, you cannot take 200 as a "warm-up". On the other hand, it does happen that students take 200 and realize that they want or need to know more about multivariable analysis. They can follow up with 201 or 202, but not both. It is not rare that students attempt the mathematically more ambitious sequence and continue with 200 after finding 201 or 202 too challenging.

Who Takes This Course

The typical student plans to major in math-track economics or is interested in the finance certificate. Intended for students who want to use mathematics and mathematical thinking as a tool for later studies in economics.

Students who took AB calculus only should take 104 instead.


  • Students who plan to take 300 level courses in the math department should take 201/202 instead to acquire the necessary mathematical maturity.
  • Students who plan to pursue graduate studies in economics are advised to take 201/202 instead.
  • Students with strong mathematical interest and aptitude (as evidenced by a BC calculus score of 5 and a math SAT score of 750 or more) should consider 203 or 215 instead.
Placement and Prerequisites:

A solid knowledge of single-variable calculus and precalculus is needed as evidenced by 104 or its equivalent (e.g. 4 or better on the BC calculus exam).

If your background is weak or rusty consider 104 to get an excellent review of the knowledge assumed in this course.

General information about placement and contact information for the placement officer can be found on the math placement page.

Sample Material

 Working problems from these sample exams can give you a good idea of the expectations and content in this course as you think about which course is right for you. Just reading the questions or the solutions can be very misleading however. Try the problems yourself!

Note: Rumor has it that there are some typos in these solutions. Oh, well. In any case, the questions are the more important information here.

  1. How hard should I expect to work?
    • This course requires a steady time commitment. We expect that the weekly problem sets will take at least 3 hours to complete. To do well on exams, you need to work a lot of extra problems from old exams. So all in all we expect this course to take a minimum of 10 hours/week outside of class, on average.
  2. If I think 200 is too hard, what should I do?
    • Try an old final exam in 104. If you can do most of the problems with confidence, you should stay in 200. Otherwise, you may want to switch to 104 to get a thorough review of all the math assumed in 200.
  3. If I think 200 is too easy, what should I do?
    • Have you had a quiz yet? You may be in for a surprise. Homework will generally be easier than exams in this course. The general math FAQ page has a whole section on how Princeton's calculus courses work which may give you a more realistic view of the situation.
    • If you are also taking other very demanding and time-consuming courses, you might consider just enjoying the fact that MAT200 is too easy, for as long as that feeling lasts. The topics in the second half of the course are generally considered more difficult than the topics in the first half.
    • Consider taking 201 or 202 instead.
  4. If I want to switch courses, what should I do?
    • Talk with your 200 teacher. You may also want to talk with the teacher in charge of the other course. If you are going to switch, do it soon!
  5. I can't fit this course into my schedule. Can I take this course for Princeton credit at another university?
  6. I have more questions that are not answered here. What should I do?
    • First, check the general math FAQ page for more information. (There is a whole section there on how Princeton's calculus courses work.) If you still have questions, representatives from the math department will be available at freshman registration.