Mathematical Foundations for Finance, FIN 500J

Phil Dybvig
314-398-3186 (cell)

Washington University Olin School

Focus: Mathematical tools needed for subsequent courses and practice

Mathematics is the language of modern financial economics, and finance makes extensive use of mathematical tools commonly used in Economics and Engineering. This course is intended to provide students with an introduction (or review) of these tools.

This course is for first-year MSF students in the Corporate Finance track, and there is no formal prerequisite beyond being in this track. As in most quantitative courses, students with the strongest math backgrounds will breeze through most easily. Mastering the material in this course will make subsequent courses and career easier.

Please do not get behind in this course! The lectures will make use of tools developed in previous lectures and will make links to earlier topics. This is good reinforcement for students who are keeping up, but it can be a problem for a student who gets behind. If you are starting to get behind, please seek help before it becomes a big problem. You can obtain help from me, the TAs, or your friends.

Feedback Some of these materials are new this year, so I am especially grateful for any feedback. A good job of pointing out any problems with the course so I can make it better will increase your grade at the margin.

Organization of the course The course will be in a traditional lecture format, with problem sets and a final exam.

Course Requirements Grades will be based 70% on the final exam and 30% on the problem sets. Class participation may change a grade near a cutoff, as may useful feedback on the course materials. Understandably, job search or other obligations may occasionally conflict with class. It is your responsibility to find out from your classmates what you miss when you are absent.

Problem Sets The problem sets are available on my web page or through Blackboard (which also points at the web page). Problem sets have several parts. The normal parts without any special label are required for all students. The "extra for experts" parts go beyond the regular course material for students who find the class easy. The "challengers" are very tough questions intended to be hard for even the very best students.

Rules for Problem Sets Students are permitted to get help from anyone for the normal and extra-for-experts parts of the homework, but students are required to do their own write-ups. The challenger questions are strictly individual efforts. All homeworks and related programs should be handed in through Blackboard by the date listed on the course materials page.

Final Exam The final exam will be held Thursday, October 20, 2:30-4:00 PM, location TBA. This will be a closed-book exam, and no portable electronic devices such as calculators and cell phones, or written or printed information you bring with you can be used in the exam. (Unfortunately, many portable electronic devices can store information and can be used for communications, so allowing students to use them makes cheating too easy.) Usually, my exams are straightforward and if you have done the homeworks yourself, go to the lectures, and study the slides, you should do well. If you miss the exam for whatever reason or you need to take the exam at another time, let me know in advance and I will substitute an oral exam. This avoids even the appearance that someone may have access to exam questions or answers in advance. This is also ``incentive compatible'' because most students do not like oral exams and will avoid missing the exam without a good reason.

Course materials Course materials include slides and problem sets that are available on the web. Instead of a text, there are links to web sites that have useful supplemental materials and some optional books are on reserve. There is no separate packet.

Transparencies The lectures will be based on transparency slides that are available on the Web. You will probably want to print a paper copy of the slides before each class for cross-reference during class, for study, and for taking notes on. The slides are available from Blackboard or my teaching page on the WEB: or (Actually the Blackboard page is a link to my web page.) Many of the slides were created by Yajun Wang (a brilliant finance PhD student who finished recently and is now teaching at the University of Maryland), and they do an excellent job of teaching the material in a straigthforward way. I have also created a number of slides myself, and in places I have revised her slides to suit our class. I also invite you to visit my home page and research page:

Textbooks I am not assigning any textbooks this year, and I will rely more on web-based materials. In case you like learning from books, I am placing several books on reserve that can give you an alternative lens on the materials. If you are going to buy one book, it should be Mathematics for Economists, 1994, by Carl Simon and Lawrence Blume. The other two books I am putting on reserve are Probability and Statistics, 2002, by DeGroot and Schervish, and Numerical Methods for Engineers, by Steven Chapra and Raymond Canale. This last book is for people who want to go beyond the class and learn about numerical methods for some things we do analytically in the class.

Topics We cover many topics that are essential for working with sophisticated financial models. Here is an approximate outline:

You may notice that some of these topics sound like courses in themselves, for example, it is common to spend a half-semester in a linear algebra course on eigenvalues and eigenvectors, or to have a full semester course on probability theory. Obviously, we can only touch on a few things, and we will focus on what will be most useful in subsequent courses.

Readings The lectures and slides are self-contained, so it is not necessary to do any additional readings. If you want to do some readings to get another perspective, here are recommendations about how to time them with the lectures. In most cases, there is a lot information in the text that we don't need in the course, and there is some information in the course not covered in the book. SB, CC, and DS are the three optional textbooks given above: Simon and Blume, Chapra and Canale, and DeGroot and Schervish. OTG-ML is Matlab's Optimization Toolbox User's Guide. D is Paul Dawkins' online class notes on differential equations:

Here is a set of reading suggestions with approximate schedule:

main topicdate(s)readings
probability and statistics, part 1Sept 6 and 8DS ch 3, 4, and 5
calculus review
probability and statidstics, part 2
Sept 13 and 15SB ch 2, 3, 4, 5, A2, A4
DS ch 3, 5.6, and 5.7
vectors and matrices
eigenvalues and eigenvectors
Sept 20 and 22SB ch. 7, 8, and 9
SB ch. 23
multivariate calculus
Sept 27 and 29SB ch. 14, 16.1, and 16.2
SB ch. 17, 18, and 19
ordinary differential equationsOct 4 and 6D pp. 20-33, 102-121, 137-155, and 340-344
X-treme reviewOct 11 and 13N/A

Additional resources on the web (coming soon)

Teaching Assistance We will be assisted by Chen "Tracy" Li and Matt Templemire. They are both third-semester MSF students. Their and my contact information:

Chen "Tracy" Li314-757-3607
Matt Templemire573-291-3067
Phil Dybvig314-398-3196

About you In addition to enrolling through the proper authorities, please send me an e-mail with the following information:

If you enroll and later choose to drop the class, please let me know about that, too, with feedback about why the course didn't work for you.

About me Many years ago, I was a tenured full professor at Yale, and I came to Wash U in 1988 in the hope of building a top finance group, which we have done. More information on me is in the chatty blurb at or in my vitae at

Integrity Students are expected to conform to the Olin School's Code of Conduct and Code of Professional Conduct. If I learn about a violation, I will report it (with some sadness and a strong sense of duty).

Summary I invite you to join me in exploring some mathematical tools that are useful for finance.