Undergraduate Major in
Applied + Computational Mathematics

Undergraduate Option Rep

Prof. Peter Schroeder

Undergraduate Option Manager

Carmen Nemer-Sirois

Applied and Computational Mathematics Option
The undergraduate option in applied and computational mathematics within the Computing & Mathematical Sciences department seeks to address the interests of those students who want to combine their basic studies in mathematics with considerable involvement in applications. This program is designed to give students a thorough training in fundamental computational and applied mathematics and to develop their research ability in a specific application field. The fields of application include a wide range of areas such as fluid mechanics, materials science, and mathematical biology, engineering applications, image processing, and mathematical finance. The training essential for future careers in applied mathematics in academia, national laboratories, or in industry is provided, especially when combined with graduate work, by successful completion of the requirements for an undergraduate degree in applied and computational mathematics. Complete programs will be worked out with faculty advisers.

Option Requirements

  1. Mathematical Fundamentals: Ma 2; Ma 3; Ma 6 ab or Ma 121 ab; Ma 6c or CS 21; Ma 108 ab. Taking the analytical tracks of Ma 1 bc is strongly encouraged.
  2. Programming Fundamentals: CS 1 or CS 1X; and basic numerical algorithms: ACM 11.
  3. Communication Fundamentals: SEC 10; one of SEC 11-13.
  4. Core Classes:
    • Introductory Methods: ACM 95ab.
    • Linear Algebra: ACM 104 or ACM 107.
    • Probability: ACM 116 or CMS 117.
    • Mathematical Methods: ACM 101 ab.
    • Numerical Analysis: ACM 106 ab.
  5. ACM Electives: In addition to all of the above requirements, three 100+ ACM courses approved by the advisor; up to 9 units of ACM 80 abc or ACM 81 abc can be counted towards this requirement with advisor approval.
  6. Sequence: In addition to all of the above requirements, one 27-unit 100+ sequence in science engineering, or social sciences approved by the option representative.
  7. Scientific Fundamentals: In addition to all of the above requirements, 18 units selected from Bi 8, Bi 9, Ch 21abc, Ch 25, Ch 41 abc, ME 11 abc, ME 12 abc, Ph 2 abc, or Ph 12 abc.
  8. Passing grades must be obtained in a total of 486 units, including the courses listed above. Courses satisfying option requirements must be taken for grades (except when courses are only available P/F) and passed with a grade of C‐ or higher.

Double Majoring

Students interested in simultaneously pursuing a degree in a second option must fulfill all the requirements of the ACM option. Classes cannot be counted towards both options unless specifically required by both. To enroll in the program, the student should meet and discuss his/her plans with the option representative. In general, approval is contingent on good academic performance by the student and demonstrated ability for handling the heavier course load.


Because of large enrollments, students won't usually be able to have an advisor from the CMS faculty during their freshman year. Students seeking an ACM advisor should contact the undergraduate option secretary at academicscms.caltech.edu.

Study Abroad Requirements

Students interested in studying abroad must fulfill the 'Core Classes' requirement via enrollment in courses at Caltech, i.e., these courses cannot be substituted by courses taken abroad. Substitutions of equivalent courses are allowed for other requirements at the approval of the Option Administrator.


There are many opportunities for undergraduate research in the applied and computational mathematics field. Students may work with faculty in the Computing + Mathematical Sciences Department and in other departments and JPL. There are a wide variety of research opportunities in computing across campus, ranging from applied physics research to numerical relativity.

Campus-wide, there is a SURF (Summer Undergraduate Research Fellowships) program you may want to apply for. Please visit the SURF website for more information. The application deadline is typically in February. Students should begin talking with professors at least two months before the deadline.

Typical Course Schedule

Units Per Term
Second Year 1st 2nd 3rd
Ma 2 Differential Equations 9 - -
Ma 3 Introduction to Probability and Statistics - 9 -
Ma 6 ab alt.
Ma 121 ab +
Ma 6 c alt.
CS 21 (0/9/18)
Introduction to Discrete Mathematics 9 9 9
Science Requirement See requirements listed above 9 9 -
ACM 11 Introduction to Matlab and Mathematics - - 6
CS 1 Introduction to Computer Programming 9 - -
HSS Electives 9 9 9
Electives (see option requirements 5, 6 above) - 9 18
45 45 42
Third Year 1st 2nd 3rd
Ma 108 ab Classical Analysis 9 9 -
ACM 95 ab Introduction to Methods of Applied Math - 12 12
ACM/IDS 104 (or 107) Appl. Linear Algebra 9 - -
ACM/EE/IDS 116 (or 107) Introduction To Probability Models 9 - -
HSS electives 9 9 9
Electives (see option requirements 5, 6 above) - 3 -
SEC 10 Technical Seminar Presentation - 3 -
One of SEC 11-13 Written Tech. Comm. in Engineering and Applied Science - - 3
45 45 36
Fourth Year 1st 2nd 3rd
ACM/IDS 101 ab Methods of Applied Mathematics 12 12 -
ACM/EE 106 ab Intro. Methods of Computational Mathematics 12 12 -
HSS Elective 9 9 9
Electives 9 9 27
42 42 36