Math and Finance

Courses

Introductory Courses

Finance courses at Princeton are largely concentrated in the Operations Research and Financial Engineering (ORFE for short and ORF for shorter). One of the most common places to start is ORF 309 (Probability and Stochastic Systems), as it is cross-listed between the MAT and ORF departments. It is also a prerequisite to the majority of ORF classes, although if you have substantial background in probability, you might choose to skip it. Some of the concepts from ORF 309 also appear in COS 340 (Reasoning about Computation), occasionally taken by students combining MAT and ORF (see below). Along with statistics, optimization is an important part of the ORF curriculum; the basic introductory courses are ORF 307 (Optimization) and ELE 382 (Distribution Algorithms and Optimization Methods), a good alternative, although it is no longer focused solely on application in finance.

Upper-Level Courses

When ORF 474 (Special Topics) has covered Stochastic Calculus, it has been a popular course to take amongst math majors, as it is more mathematically intensive than most ORF courses. To supplement the topics covered in the Stochastic Calculus version of ORF 474 (the special topic may change each semester), MAT 350 and MAE 501/502 cover the differential and partial differential equation background needed for more advanced ORF courses. (Slightly easier versions would be MAT 303 and MAE 305/306). For these parts of ORF, MAT 331 (Complex Analysis) also appears to be tangentially useful, as the methods derived in MAT 331 can be applied in the above courses.

If you want to gain more in-depth understanding of the workings of the markets themselves, courses in the economics (ECO) department might prove to be very useful. Here, ECO 362/363 are a common starting point, as both are required to obtain the Certificate in Finance (see below). After that, 400-level ECO courses branch out in diverse directions and cover various forms of financial instruments. You can choose which are of interest (and of use) to you personally and professionally. For students still seeking quantitative ECO courses, ECO 517 (Econometrics) may be worthwhile; half the course covers probability and statistics, and the other half covers the concepts of econometrics.

Computer Science and ORF

Finally, you may also be interested in taking a few COS classes on the side to develop an understanding of the software tools that could be useful in finance. The introductory sequence is discussed in the “Math and Computer Science” part of the guide. After going through it, you might want to take COS 323 (Computing for the Physical and Social Sciences) and COS 340 (Reasoning about Computation), which provide further foundation in programming and theory, respectively. More particular to ORF, you might take either or both of COS 402 (Artificial Intelligence) and COS 424 (Interacting with Data), both of which introduce useful concepts and algorithms with many important applications in finance.

Certificate in Finance

Anyone wishing to incorporate significant study of finance into their undergraduate curriculum can pursue a Certificate in Finance. The certificate has three major requirements: (1) a few prerequisites in math, microeconomics, and statistics that must be completed prior to the start of junior year; (2) two core courses (ECO 362 (Financial Investments) and ECO 363 (Corporate Finance) and and three electives to be taken in junior and senior years; and (3) independent work including a significant financial component, normally integrated with the senior thesis. Applications to the program must be submitted by May 31 of one’s sophomore year, and admissions decisions are made in late June. Note that the application requires a (tentative) plan to fulfill the certificate’s requirements, as well as a short essay explaining one’s interest in finance. More details can be found on the certificate program’s webpage [Link: http://www.princeton.edu/bcf/undergraduate/].

Opportunities

Jobs and internships in finance cast students in many different roles and deal with many different parts of the financial markets. The majority fall into three categories: banking, trading, and consulting. For math majors, trading, being the most quantitative, is the most commonly pursued. Internships and jobs in trading can then be divided into two categories: those that are for a trading firm (Jane Street, DRW, Five Rings, Two Sigma, SIG, etc.) and those that are for a division in a bank (Goldman Sachs, Morgan Stanley, Credit Suisse, Citi, etc.). The interview processes for the two are very different, as the former relies mostly on brain teasers and have a tendency to be extremely quantitative, and the latter has a more qualitative approach in defining your potential fit to a team.

In searching for an internship, you must take the initiative to ask upperclassmen who have been through the process for their experiences, and also your interviewers themselves in defining what the internship would be like and what they are looking for. Ultimately, internships serve not only to provide useful experience but also to help you better determine what you are looking for in a future job in finance, as you are not allowed to do a substantial amount of work as purely an intern. An internship at a large (“bulge bracket”) bank would allow access to a much broader range of job functions covering a broader range of assets in the financial markets, which may be helpful to those who are unsure of their interests.

Contacts

Susan Zhang ’12 (susanz@)