Since this handbook is offered by the UC San Diego Department of Mathematics, it discusses undergraduate majors in this department. Other University of California campuses have their own mathematics departments.
When you decide on a major, you are committing yourself to taking at least 12 upper division courses (in addition to several lower division preparatory courses) in a subject. For all but one of this Department’s eight majors, almost all of those are specific courses with just a few options (electives) for the student to decide on.
The official source of the curriculum for each Department of Mathematics undergraduate major is the UC San Diego General Catalog. The same portion of the Catalog has ample information about department policies pertaining to undergraduate education. Every student should be aware of these policies.
Here are more detailed descriptions of each major (along with the applicable degree and campus major code) than what the General Catalog provides:
(1) “Major in Mathematics” (commonly known as pure mathematics), B.S., MA29
B.A. effective 1967 Fall Quarter. B.S. effective 2010 Fall Quarter.
This major provides a foundation in analysis and algebra. It is good partial preparation for people planning to attend graduate school in mathematics including those who want to become researchers in mathematics or teach the subject at the post-secondary level. Although the major is adaptable in that most of its upper division mathematics coursework is chosen by the student, taking random electives according to what will enable you to graduate soonest will leave you with an academic record in your major that shows a lack of emphasis and might even be taken to mean that you lack self-discipline. Instead, it is recommended that your upper division electives be focused on one or two areas of mathematics. If you intend to go to graduate school, your chosen electives and grades earned should convince graduate admissions committees that you can handle challenging sequences of courses. With instructor approval, you can even take graduate level mathematics courses, and you can have these applied toward the requirements of your major with an approved petition (submitted to the Department).
(2) “Major in Applied Mathematics”, B.S., MA27
B.A. effective 2001 Fall Quarter. B.S. effective 2010 Fall Quarter.
Course requirements for this major include upper division linear algebra, real analysis, and statistics. Students have the option to take additional courses in probability, numerical analysis, and other areas of mathematics. Up to 12 units of upper division courses may be taken from outside the department in a mathematical area if approved by petition. If the curriculum is planned well, this major could be preparation for graduate school in mathematics and teaching at the post-secondary level.
(3) “Major in Mathematics—Scientific Computation”, B.S., MA34
B.S. effective 2003 Winter Quarter.
This major prepares students to use scientific computation to solve complicated numerical problems. Requirements include upper division linear algebra, statistics, numerical analysis, optimization, and scientific computing. Up to 12 units of upper division courses may be taken from outside the department in a scientific computation area in the sciences or engineering if approved by petition.
(4) “Major in Probability and Statistics”, B.S., MA35
B.S. effective 2007 Winter Quarter.
Course requirements include real analysis, numerical methods, probability, statistics, and computational statistics. Up to 8 units of upper division courses may be taken from outside the department in an applied mathematical area if approved by petition. (By optionally taking additional rigorous courses in real analysis, this major can be good preparation for those students who want to study probability and statistics in graduate school.)
(5) “Major in Mathematics—Applied Science”, B.S., MA31
B.A. effective 1997 Fall Quarter. B.S. effective 2012 Winter Quarter.
Faculty advisor: David Meyer
Half of this major’s upper division coursework includes linear algebra, real analysis, and other mathematics courses chosen by the student, and half is selected by the student for approval from one or two other departments (such as physics, chemistry, economics, cognitive science, computer science, or any in engineering). This makes the major act as a joint major in mathematics and applied science. The curriculum allows the flexibility of completing a cohesive program designed around a student’s academic interests.
(6) “Major in Mathematics—Computer Science”, B.S., MA30
B.A. effective 1998 Fall Quarter. B.S. effective 2010 Fall Quarter.
This major gives mathematically minded students a specialization in theoretical computer science. It is not equivalent to an undergraduate degree in computer science nor is it meant to substitute for such. However, since computing applications often require a strong foundation in mathematics, this major could help to prepare someone to work in such a setting. (An internship could provide additional valuable training.) Course requirements include abstract algebra, statistics or probability, combinatorics, numerical analysis, and at least three of each of lower division and upper division courses in computer science. Up to 16 additional units of upper division coursework from approved course lists in mathematics and/or computer science are required.
(7) “Joint Major in Mathematics and Economics”, B.S., MA33
B.A. effective 1998 Winter Quarter. B.S. effective 2010 Fall Quarter.
This major prepares mathematically focused students for graduate studies in economics. (A major of identical name and curriculum is offered by the UC San Diego Economics Department.) At least seven upper division courses from each department (mathematics and economics) must be taken. They include advanced courses in linear algebra, real analysis, econometrics, and microeconomics.
(8) “Major in Mathematics—Secondary Education”, B.A., MA32
B.A. effective 1997 Fall Quarter.
Faculty advisor: Guershon Harel
This major is partial preparation for teaching mathematics at the secondary school level. (To learn about various paths for earning a California teaching credential and teaching in California high schools, contact the California Commission on Teacher Credentialing, or the UC San Diego Department of Education Studies.) Students take introductory courses in number theory, history of mathematics, mathematical computing, statistics/probability, geometry, abstract algebra, and real analysis. Although a student in this major COULD attempt to embark on a career path outside of lower level academia, that might be difficult to successfully accomplish given the name of the major and associated perceptions.