The Mathematics Major 2013-14

Within the mathematics major, there are three concentrations leading to the B.A. degree: pure mathematics, mathematics education, and computational mathematics. These programs are designed to give students a strong background for graduate study, for teaching, or for work in industry or government. The mathematics program also provides an excellent liberal arts background from which to pursue a variety of career opportunities.

Study and Research Opportunities

  • B.A. with concentrations in Pure Mathematics, Mathematics Education, and Computational Mathematics
  • Undergraduate Minor

High School Preparation

High school students planning to major or minor in mathematics at UC Santa Cruz should complete the high school courses required for UC admission and obtain a strong background in mathematics, including courses in algebra, geometry, and trigonometry at a minimum.

Students must meet the prerequisite for each Math course they take at UCSC, including their first Math course (Precalculus or Calculus). A CSU/UC Mathematics Placement Exam is given at orientations and every quarter, just prior to the beginning of classes and priority enrollment. Students may take the exam a maximum of two times. (See the UC Santa Cruz Mathematics Placement Exam section for more information and a link to a practice exam.)

High school course credit cannot be used for placement; however, a score of 4 or 5 on the calculus Advanced Placement AB Exam allows students to enroll in second-quarter calculus; a score of 3 on the AP AB Exam allows students to enroll in first-quarter calculus. A score of 4 or 5 on the BC Exam gains students entry to third-quarter calculus. A score of 5, 6, or 7 on the IB HL Mathematics Exam allows students to enroll in second-quarter calculus. Scores must be verified by an academic adviser.

Transfer Preparation

Transfer students may find it helpful to complete IGETC general education requirements before transferring to UC Santa Cruz. Those planning to major in mathematics should optimally have courses in single variable differential and integral calculus. Courses in differentiation and integration of multivariable calculus are recommended only if they are equivalent to UC Santa Cruz courses. Students transferring from California community colleges may check the ASSIST.ORG articulation web site for equivalent courses, and all transfer students should read the information on the review process for transfer math courses:

It is also recommended that prior to transfer, students complete a course in linear algebra and one in ordinary differential equations. All transfer students should meet with the Mathematics Department adviser to establish a two-year plan.


  • Actuarial science
  • Avionics
  • Civil service
  • Computer programming
  • Computer hardware or software design
  • Cryptanalysis
  • Economic analysis
  • Financial operations analysis
  • Forensic mathematics
  • Information systems analysis
  • Insurance
  • Numerical analysis
  • Operations research
  • Psychometrics
  • Quality control analysis
  • Robotics
  • Statistics
  • Systems analysis
  • Teaching

These are only samples of the field’s many possibilities.

Introductory Requirements

Introductory requirements for all concentrations in the mathematics major are:

  • Mathematics 20A-B, Honors Calculus (two quarters) or Mathematics 19A-B, Calculus for Science, Engineering, and Mathematics (two quarters)
  • Mathematics 21, Linear Algebra 
  • Mathematics 23A-B, Multivariable Calculus (two quarters)
  • Mathematics 100, Introduction to Proof and Problem Solving

The mathematics education concentration has one additional introductory requirement, Applied Mathematics and Statistics 5, Statistics. For some non-mathematics majors, Mathematics 11A-B, Calculus with Applications (two quarters) can be substituted for Mathematics 19A-B, Calculus for Science, Engineering, and Mathematics (two quarters), but they are not recommended for students planning to major in computer engineering, computer science, electrical engineering, information systems management, or physics.

UC Santa Cruz Mathematics Placement Exam

Students whose areas of study require precalculus or calculus courses are strongly advised to take the placement exam and the required courses early in their academic careers. The placement exam is offered numerous times throughout the academic year. For test dates and information, see: The exam is offered at orientations for incoming students. A current photo ID is required for entry into the placement exam. The Mathematics placement exam (MPE) may be taken a maximum of two times and scores are valid for one year.

If your MPE score is You may enroll in this course
100 2, College Algebra for Calculus

3, Precalculus


11A, Calculus with Applications*

400 19A, Calculus for Science, Engineering, and Mathematics
500 20A, Honors Calculus

*Some majors in science and engineering require Math 19A-B. Students planning to concentrate in those majors who receive 300, an Applied Calculus ready score on the MPE, should take courses 3 and 19A-B rather that courses 11A-B. All students are advised to consult with the department sponsoring their major before deciding which mathematics pathway to take.

Academic Advising

Academic advising is available from Physical and Biological Sciences Undergraduate Affairs. Undergraduate Affairs publishes the web site which contains detailed information about the degree programs, sample schedules, transferring credit, placement exams, faculty research, and opportunities in the Physical and Biological Sciences majors.

More Information


Undergraduate Affairs
Physical and Biological Sciences Undergraduate Affairs
142 Jack Baskin Engineering Building
University of California, Santa Cruz
1156 High Street
Santa Cruz, California 95064
(831) 459-4143

See Also