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Courses and Curriculum

Courses in Applied Mathematics are designed for students with a wide range of goals and are not limited to the needs of students following an applied mathematics concentration. There are many opportunities for students to explore different subject areas and see which they find most interesting.

When choosing courses, consider what your goals are. Do you wish to pursue applied mathematics at a graduate level? Do you wish to gain a good basis in applied mathematics at an undergraduate level, but intend later to pursue some other related area? Are you simply taking courses for general understanding and knowledge?

Prospective Concentrators or Students interested in upper-level APMA

How do the new changes in APMA affect you?

Please see this document to understand how the new APMA concentration requirements and course prerequisites might affect you: https://docs.google.com/document/d/1VAHWcjN2bXyXCETviQSzpR-qaFKX4oDkr3eBde0oV8g

Prerequisites

Most of the upper-level APMA courses require multivariable calculus and linear algebra, and many require basic computer programming skills. Any students who are interested in upper-level APMA courses, including all prospective concentrators, should begin working on these prerequisite courses as soon as possible.

• Single-variable calculus sequence: MATH 90 and one of MATH 100, 190
• Multivariable calculus: one of APMA 260, MATH 180, 200, 350
• Linear algebra: one of APMA 260, MATH 520, 540
• Intro computing: one of APMA 160, 200, CSCI 111, 150, 170, 190

Multivariable calculus, linear algebra, and the APMA computing courses can be taken in any order after the single-variable calculus sequence is complete. 

• APMA 260 combines multivariable calculus and linear algebra into one semester. It is not an accelerated course, but selects the topics from those two areas that are most important for our APMA curriculum.
• APMA 200 (Introduction to Modeling) requires only the single-variable calculus sequence and can be a good introduction to Applied Math and to computing without a long list of prerequisites.

Foundational Courses

Once the prerequisite courses are satisfied, the most common entry points into our curriculum are

• APMA 355 (Applied Ordinary Differential Equations with Theory) requires multivariable calculus and linear algebra.
• APMA 1655 (Introduction to Probability and Statistics with Theory) requires multivariable calculus and linear algebra.
• APMA 1210 (Operations Research: Deterministic Models) requires multivariable calculus, linear algebra, and computing.

Each of these courses are intermediate level courses on foundational topics that are useful for our upper-level curriculum. APMA 1655 and 1210 are 1000-level courses largely for historical reasons, not because they are inherently more challenging.

• APMA 365 (Applied Partial Differential Equations I with Theory) follows naturally after APMA 355. The APMA 355/365 sequence is required for all APMA and joint-APMA concentrators.

Upper-level Courses

We have a variety of regularly-offered 1000-level courses and several special topics courses each semester:

• APMA 193*/194* (where * is any combination of numbers or letters) are our senior seminars. Senior seminars vary by instructor. They are not always restricted to seniors, but they are designed to integrate knowledge across multiple APMA courses, so they are most effective when taken after being exposed to a variety of our regular upper-level courses. Senior seminars satisfy the capstone requirements for the APMA (ScB), APMA-Bio, and APMA CS concentrations.
• APMA 1910, 1920 are not traditional math courses and cannot be used to satisfy 1000-level APMA elective credit or capstone credit for our concentrations. They can be used as STEM electives for the APMA concentration or for the one free elective in APMA-Bio.
• APMA 1970, 1971 are independent study courses, often used to get course credit for undergraduate research. APMA 1971 is the WRIT version. APMA 1970 can be taken multiple times to support research that lasts for more than one semester. When used for undergraduate research, these courses can satisfy the capstone requirements for the APMA (ScB), APMA-Bio, and APMA CS concentrations. They can also be used to document research for satisfying the honors requirements in our concentrations.
• APMA 350, 360, 650, 1650 are not intended for concentrators and cannot be used to satisfy concentration credit for any of the APMA concentrations.

APMA and joint-APMA concentrators should work with their concentration advisor to determine their individual pathway through the curriculum.

Foundational Courses not intended for further study in APMA

We offer versions of some of our most popular foundational courses that have fewer prerequisites and are intended for students in other fields who would like exposure to these topics, but who do not need them as preparation for advanced study.

• APMA 350 (Applied Ordinary Differential Equations) requires only the single variable calculus sequence and some past exposure to linear algebra. (Linear algebra is a suggested, but not enforced, prerequisite or corequisite.) It covers roughly the same topics as APMA 355, but has less emphasis on mathematical theory.
• APMA 360 (Applied Partial Differential Equations I) requires APMA 350 and multivariable calculus. It covers roughly the same topics as APMA 365, but has less emphasis on mathematical theory.
• APMA 650 (Introduction to Probability and Statistics) has no prerequisites. It covers the same topics as APMA 1650 and 1655, but with much less emphasis on mathematical theory and no calculus.
• APMA 1650 (Introduction to Probability and Statistics with Calculus) requires only the single variable calculus sequence. It covers the same topics as APMA 650 and 1655, but with less emphasis on mathematical theory than APMA 1655 and exposure to the use of calculus in this field, unlike APMA 650. APMA 1650 is a 1000-level course for historical reasons, not because it is inherently more challenging than APMA 650.

Students who take one or more of these courses and later decide that they would like to pursue more advanced coursework in APMA or concentrate in one of the APMA concentrations need to do the following steps:

• Complete the multivariable calculus and linear algebra prerequisites for our upper-level courses.
• Either (1) take the “with theory” version of the relevant course or (2) complete the bridgework program for that course. For instance, if a student took APMA 650 and later wanted to take a course that required APMA 1655, the student could either take APMA 1655 or complete the APMA 1655 bridgework program. Since APMA 650 and 1655 share a lot of content, many students may prefer to take the bridgework program and not repeat that content.
• We have bridgework programs for APMA 355, 365, 1655. Before participating in a bridgework program, a student must successfully complete multivariable calculus, linear algebra, and a non-theory version of the relevant course. Bridgework is completed over the summer or winter break and culminates with an in-person exam at the beginning of the semester. The exams cannot be rescheduled and can only be taken once each semester. Admission into the bridgework program and passing the exam can be used to satisfy APMA course prerequisites and APMA or joint-APMA concentration requirements that need the “with theory” version of a course. 

Do not plan on using the bridgework program to avoid taking a “with theory” course. The bridgework exams will be challenging and we will be inflexible with scheduling. The bridgework is only meant for students who have an unexpected change of focus. If you think you might want to take upper-level APMA or to concentrate in APMA, please take our “with theory” courses.