Princeton is an excellent place to learn and do applied math – many of professors in many different departments, from engineering to biology to physics, are interested in this area. The strength of the math department and the breadth of possible applications is outstanding. Further, the department is very flexible with undergraduate requirements, so you can usually do anything that you want, as long as it has some mathematical component. The applied math program itself is small, but encourages its students to work with professors outside the core program. If you like math, but also care seriously about some other field, consider being a math major with an applied focus.

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#### Opportunities

**Employment possibilities**

Applied math is a very broad notion, and it can be tailored to fit many interests and possible career paths. After graduation you can work in finance, computer science, consulting, engineering, or a number of other quantitative fields – as long as you make sure to take the requisite courses. The combination of rigorous mathematical thinking with an awareness of real-world applications is valuable to potential employers.

If you like math, but also care about some other field, you will likely enjoy applied math. However, you will have the freedom to pursue your curiosity and explore a variety of applications that you may not be familiar with at this point. Have an open mind! Take courses in economics, physics, biology, computer science, neuroscience or any other discipline that you don’t know too much about. Maybe you’ll discover a new passion! In addition, you get to see what kind of math they are using, and focus on that in your math studies. As a personal example, this is how I realized just how important probability and statistics were across many applications, and motivated me to pursue them further.

**Work with excellent researchers, in a broad array of fields**

As a rule, Princeton faculty members are absolutely brilliant. It is an amazing opportunity to study with them. As a math major with an applied focus, you can do basically anything and everything with a quantitative component. This means that you have access to faculty not just from the math department, but also from many others.

#### Challenges

**Planning coursework**

It may not be entirely straightforward to plan your courses. This is in contrast to math, where it is quite clear what to do: take intro 200-level classes, then take the 300’s, and so on. For applied math, the courses are not organized in the same way and in the same place. Many crucial applied math courses are offered in other departments. For instance, optimization and statistics are in ORFE, algorithms is in Computer Science. Further, depending on what application you are interested in, additional advanced courses are required. While at this point you may not know what you are interested in, it is worthwhile to think ahead, and talk to upperclassmen, graduate students and faculty.

**Logistics of arranging work with faculty from other departments**

It is sometimes challenging to arrange independent work with faculty from other departments. Other departments assign independent work differently, and sometimes earlier than the math department. Therefore, the faculty members you are interested in working with may already have a large number of students. This has happened to me two times, where the faculty members had many other students but were nice enough to agree to also supervise me, though this is possibly a result of good fortune.

**Scattered groups sharing your interests**

You may find that, while the people and groups sharing your interests exist, they are scattered across several departments. This is important, because you may want to hang out with those people (undergrads and graduate students), attend their seminars, and see what they are they working on to get a better picture of the field. This scattered organization brings an extra level or organizational challenge.

#### Program in Applied and Computational Math (PACM) Certificate

Princeton offers the PACM certificate program for undergraduates interested in applied math. The certificate, in addition to looking good on a resume, comes with a series of seminars in which students can both present their independent work and hear about the projects undertaken by other certificate students. The certificate has three requirements: coursework, independent work, and certificate seminars. The required coursework is five classes from a wide range of pure and applied math topics, which is fairly flexible. The independent work component consists of a research project with a professor in addition or building off of other independent work requirements, i.e. junior paper and senior thesis. Finally, the certificate seminars are as described above: they entail giving a presentation on your independent work and listening to presentations of others.

For more detailed information on the certificate and on the PACM program, please see their website here.

#### Fields of Applied Math

Look for applied math courses in APC, CBE, COS, ECO, EEB, ELE, MAE, MAT, MOL, ORF, QCB, PHY etc. depending on your interests. Applied math is such a broad field. On the very applied side, data science and machine learning has become a huge field and comes with large potential to make tons of money. Quantitative biology is also a booming field. On the more theoretical side, there is legit proof based math in COS, ELE, and ORF in areas such as algorithms, information theory, probability, statistics, and optimization. Below is a selection of applied math courses but it is nowhere near complete.

#### Course list

APC 520/MAT 540 Mathematical Analysis of Massive Data

COS 226 Algorithms and Data Structures

COS 402 Artificial Intelligence

COS 423 Theory of Algorithms

ECO 312 Econometrics: A Mathematical Approach

EEB 414/MOL 414 Genetics of Human Populations

ELE 486 Transmission and Compression of Information

ELE 527 Random Graphs and Networks

ELE 528 Information Theory

ELE 530 Theory of Detection and Estimation

MAE 541 Applied Dynamical Systems

MAT 375 Graph Theory

MAT 377 Combinatorics

MAT 385 Probability Theory

MOL 342 Genetics

MOL 455 / COS 455 Introduction to Genomics and Computational Biology

ORF 309 Probability and Stochastic Processes

ORF 522 Linear Optimization

ORF 523 Conic and Convex Optimization

ORF 524 Statistical Theory and Methods

ORF 525 Generalized Regression Models

ORF 526 Probability Theory

ORF 527 Stochastic Calculus

ORF 565 Empirical Processes and Asymptotic Statistics

PHY 105 Advanced Physics (Mechanics)

PHY 106 Advanced Physics (Electromagnetism)

PHY 205 Classical Mechanics B (“Death Mech”)

PHY 207 Mechanics and Waves

PHY 408 Modern Classical Dynamics

#### Outlook and Advice

Applied math is really everywhere – consider, for instance, the problem of predicting new data points from past data. This is essentially a mathematical problem, yet it can be used in almost any field. I would encourage students in applied math to take courses in different departments and talk to a professors whose research sounds interesting. I would also add that they shouldn’t be afraid of not knowing enough math or, conversely, working on a project without “enough” math. What really matters is that you can pick up the necessary tools to understand and solve the problem you’re working on – from my perspective, applied math is all about taking problems from other disciplines and using mathematical techniques to solve them.

(Contributors to this page include Jim Tao ’14, Eugene Tang ’16 and Christopher Zhang ’17.)