Program Overview

Mathematics Option and Minor (Ma)

The mathematics option is designed to give students an understanding of the broad outlines of modern mathematics, to introduce current research and to prepare them for advanced work in pure mathematics or related fields. Math students go well beyond the basics to study the structures of algebra, analysis and geometry, as well as the rudiments of combinatorics and set theory. Students learn to write coherent and complete proofs of various assertions, to work out non-trivial examples and to use computational tools.

Aims and Scope

The schedule of courses in the undergraduate mathematics option is flexible. It enables students to adapt their programs to their needs and mathematical interests and gives them the opportunity to become familiar with creative mathematics early in their careers. Some students go to use their background in mathematics as an entry to other fields, such as physics, computer science, statistics, economics, business, finance, medicine and law.

Ma Option Requirements

• Ma 2.
• Ma 3 or Ma 140 a.
• Ph 2 bc or Ph 12 bc
• Ma 5 abc, Ma 10, Ma 108 abc, Ma 109 abc.
• Ma/CS 6 a or Ma 121 a.
• Ma/CS 6 c or Ma 116 a or Ma/CS 117 a.
• 45 additional units of Ma numbered 110 to 190 or ACM numbered 95 or above. Courses in other options with high mathematical content may be used to fulfill this requirement with the approval of the undergraduate option representative for mathematics. Of these 45 units, at most 18 can be from courses other than Caltech Ma courses.
• Math majors must take two quarters (18 units) of a single course, chosen from the Ma course listings with numbers between 110 and 190, inclusive. In years where one of these courses is given as a one-term course only, it cannot be used to satisfy this requirement. These two quarters may include courses taken to satisfy requirements 2, 5, 6 or 7.
• Requirements 1– 6 may not be taken pass/fail unless the course is only offered as pass/fail.
• Passing grades must be earned in a total of 486 units, including the courses listed above.

Ma Typical Course Schedule

| | Units per term
---|---|---
| | | |
Second Year
Ma 2, 3 | Sophomore Mathematics | 9 | 9 | -
Ph 2 bc or 12 bc | Sophomore Physics | - | 9 | 9
Ma 5 abc | Introduction to Abstract Algebra | 9 | 9 | 9
| HSS Electives | 9 | 9 | 9
| Electives 1 | 18 | 9 | 18
| Total |45 |45 |45
Third Year
Ma 10 | Oral Presentation | 3 | - | -
Ma 108 abc | Classical Analysis | 9 | 9 | 9
Ma/CS 6 ac | Introduction to Discrete Mathematics | 9 | - | 9
Ma 110-190/ACM 95+ | Advanced Mathematics | 9 | 9 | 9
| HSS Electives | 9 | 9 | 9
| Electives 1 | 9 | 18 | 9
| Total |48 |45 |45
Fourth Year
Ma 11 | Mathematical Writing | - | - | 3
Ma 109 abc | Introduction to Geometry and Topology | 9 | 9 | 9
Ma 110-190/ACM 95+ | Advanced Mathematics | 9 | 9 | -
| HSS Electives | 9 | 9 | 9
| Electives 1 | 18 | 18 | 18
| Total |45 |45 |39

Mathematics Minor (Ma)

The mathematics minor is intended to supplement one of Caltech’s undergraduate degrees. It is designed for students who wish to broaden their knowledge beyond their major to include mathematics. Students completing the mathematics minor requirements will have the phrase ”minor in mathematics” added to their transcripts.

Ma Option Minor Requirements

• Ma 2, or equivalent courses approved by the option representative.
• Ma 3 or Ma 140a, or equivalent courses approved by the option representative.
• Two three-terms Ma courses, chosen among Ma 5abc, Ma 108abc, Ma 109abc.
• 18 additional units of selected Ma courses, approved by their minor adviser or the option representative.
• Requirements may not be taken pass/fail unless completed during fall or winter of the first year or when the course is only offered as pass/fail.