The requirements for the undergraduate certificate in applied and computational mathematics are the following:

- A total of five courses normally 300 level or higher (pass/D/fail not accepted), at least two of which are not from your home department and you are not using to satisfy the requirements of your major concentration.
- Independent work consisting of a paper/course project/computational laboratory, possibly in the context of a course offered by PACM faculty or an independent project you did with a professor during the academic year or in the summer. The independent work cannot be used to qualify for anything else; for instance, you
**cannot**use a junior paper or senior thesis for the independent work, without modification. You**can**take some other work (such as your senior thesis) and extend it, but only the extension will count towards the certificate. - Participation in the not-for-credit PACM certificate seminar, providing a forum for presentation and discussion of independent work among all certificate students and introducing them to other areas of applied mathematics.

### Coursework Requirement:

The five required courses may vary widely from department to department in order to include a broad spectrum of science and engineering students throughout the University. These courses should fit readily within the degree requirements of the respective departments of the engineering school or the economics, mathematics, physics, chemistry, molecular biology, and ecology and evolutionary biology, or other relevant departments, but will require a particular emphasis in applied mathematics. The five required courses must be distributed between the following two areas, with *at least two from each area*:

- Mathematical foundations and techniques, including differential equations, real and complex analysis, discrete mathematics, probability, and statistics, typically offered by the Department of Mathematics.
- Mathematical applications, including signal processing, control theory, optimization, mathematical economics, typically offered by the economics, science, and engineering departments.

Specific choices must be approved by the PACM undergraduate representative, Prof. Paul Seymour.

### Independent Work Requirement:

For independent work, normally you should contact one of the PACM core or associated faculty, consult with them on the topic, and have them agree to be your adviser. Exceptionally, you may (with permission) choose an adviser who is not with PACM, but then you must choose a PACM core or associate faculty member to be a second reader. After you choose your adviser for the PACM Certificate program, you must meet with them on a regular basis . This will allow them to keep track of your progress and make sure that the paper has a sufficient amount of mathematics content to qualify for a certificate.

Normally, you and your advisor will decide on some appropriate topic for the independent work. Alternatively, the independent work can be initiated as part of a course. The course must allow for a research project that can subsequently be extended into an independent work paper, and cannot be taken in the spring of your final year. There are several appropriate courses, offered by PACM core or associated faculty, on a wide range of topics of current interest in applied mathematics.

### Certificate Seminar Requirement:

You must present your independent work in the certificate seminar, in your senior year. The seminar is held in the spring. Also, you must attend at least 75% of the certificate seminars, totaled over your junior and senior years.