Mathematical Foundations for Finance, FIN 500J: Course Materials

Philip H. Dybvig
Washington University in Saint Louis


I have finished grading the exams. As you probably expect, there is a big variation in the class, with scores ranging from 32 to 100. I am having a PhD student do spot checks of my grading and tabulate the grades. In the meantime, here is the tentative grade distribution and a copy of the exam and the answer key.

...Exam size 41K
...Exam solutions size 46K

score rangenumber of exams
30-39 1
50-59 4
60-69 7
70-79 4
80-89 3
90-100 5

Welcome to Mathematical Foundations for Finance! This course is an introduction and review of some mathematical tools that will be essential for your later coursework and your career. Ideally, you want to learn these tools well enough to have them at your fingertips, so you do not have to spend time looking them up when you need them.

Practice Exam Here is a practice exam. It is too long to be a real exam because I wanted to cover a variety of types of problems you might see on the actual exam. In the actual exam, I will also include a few relevant relatively complex formulas (the Kuhn-Tucker conditions and the basic formulas for eigenvalues and eigenvectors), but mostly you are supposed to remember the formulas you need.

Practice exam
...Practice Exam

Practice Problems! Here are some problems and answers from another class previously offered by Yajun Wang. The link on this pages tells which problems test topics covered in our class (but the other questions and answers are there in case you are curious). For this class, ignore the suggestion to check the results using Matlab.

Probability and Statistics
...problems 1, 2, and 4

Linear Algebra
...problems 1, 2, 3, and 4

Multivariable calculus and optimization
...problems 1, 4, and 5
...answers 1
...answers 4 and 5

Optimization: Kuhn-Tucker conditions
...problems 1, parts 1-5


I recommend that you print a set of slides before class for taking notes. I have developed some of the slides (in pdf), and there are also many slides (in PowerPoint) developed by Yajun Wang, a brilliant PhD student who graduated this year and is now on the faculty at the University of Maryland.

Probability and Statistics, part 1 (2 lectures)
...pdf slides size 96K
...Problem set 1 size 21K, due Tue Sept 13
...Problem set 1: partial answers size 30K

Calculus Review and Probability and Statistics, part 2 (2 lectures)
...calculus review pdf slides size 56K
...probability and statistics, part 2 pdf slides size 42K
...Problem set 2 size 25K, due Tue Sept 20
...Problem set 2: partial answers size 33K

Vectors and Matrices (2 lectures)
...matrix algebra ppt slides size 1184K
...eigenvalues and eigenvectors pdf slides size 50K
...Problem set 3 size 23K, due Tue Sept 27
...Problem set 3: partial answers size 21K

Multivariable Calculus and Optimization (4 lectures)
...multivariate calculus ppt slides size 756K and pdf slides size 28K (download both)
...optimization ppt slides size 1024K
...Kuhn-Tucker notes pdf notes 29K
...Problem set 4 size 29K, due Tue Oct 11
...Problem set 4: partial answers size 6K

X-treme Review based on previous slides (2 lectures)