Students majoring in mathematics must satisfy one of the following sets of requirements. Courses may be credited toward the major only if a grade of C or higher is earned.

I. Requirements for a Specialty in Pure and Applied Mathematics

Lower Division

Calculus: CAS MA 123 and 124, or 127, or 129, or equivalent; Multivariate Calculus: CAS MA 225 or 230; Elementary Differential Equations: CAS MA 226 or 231; Linear Algebra: CAS MA 242 or 442; CAS CS 111; and one other mathematics or computer science course selected in consultation with a mathematics faculty advisor.

Upper Division

At least one of the two following sequences:

• CAS MA 411, 412 Advanced Calculus and Complex Variables
• CAS MA 511, 512 Introduction to Analysis

At least one of the following sequences:

• CAS MA 531, 532 Computability and Logic and Foundations of Mathematics
• CAS MA 539, 555 Scientific Computation and Numerical Analysis I
• CAS MA 541, 542 Modern Algebra
• CAS MA 555, 556 Numerical Analysis
• CAS MA 561, 562 Methods of Applied Mathematics
• CAS MA 563, 564 Differential Geometry/Topology
• CAS MA 569, 570 Operations Research
• CAS MA 573, 574 Differential Equations/Applied Dynamics
• CAS MA 581, 582, 583 Probability and Statistics (any two)

Four additional CAS mathematics courses numbered 200 or above are required. Two of these four can be related courses. For specific information concerning related courses, contact the department.

II. Requirements for a Specialty in Statistics

Lower Division

Calculus: CAS MA 123 and 124, or 127, or 129, or equivalent; Multivariate Calculus: CAS MA 225 or 230; Linear Algebra: CAS MA 242 or 442; Introduction to Probability and Statistics: CAS MA 213, 214; Introduction to Computer Science: CAS CS 111.

Upper Division

• CAS MA 416 Analysis of Variance
• CAS MA 575 Linear Models

Two of the following three courses:

• CAS MA 581 Probability
• CAS MA 582 Mathematical Statistics
• CAS MA 583 Introduction to Stochastic Processes

Four additional CAS mathematics courses are required: two at the 200 level or above, and two chosen from among MA 500–599 and MA 684.

This degree program is for students who wish to combine the fields of mathematics and philosophy, usually with an emphasis on logic.

Prerequisites

CAS MA 123 and 124, or 127, or 129, or equivalent; MA 225 or 230; MA 293; and CAS PH 100 or 110.

Principal Courses

At least six courses in mathematics and six courses in philosophy at the 200 level or above, with a grade of C or higher.

Required Mathematics Courses

CAS MA 242 or 442; MA 531 (or PH 461 or PH 661) and MA 532 (or PH 462 or PH 662); MA 411–412 or 511–512; any one of the following: MA 294, 341, or any course numbered 400 or higher.

Required Philosophy Courses

CAS PH 468; three courses in philosophy above the 100 level; any two of the following: CAS PH 422, 443, 460, 474.

Students in this major should have advisors in both the Mathematics & Statistics Department and the Philosophy Department.

Principal Courses

Lower Division

CAS MA 123 and 124, or 127, or 129, or equivalent, 225 or 230, 242 or 442, 293, and 294. CAS CS 111 and 112 or equivalent, and CS 210.

Upper Division

CAS CS 330, 332, and 350; two additional computer science courses numbered above 400; one two-course sequence selected from: CAS MA 531–532, MA 541–542, MA 555–556, MA 569–570; two additional MA courses numbered 200 or above.

Students in this major should have advisors in both the Mathematics & Statistics Department and the Computer Science Department.

Prerequisites

CAS MA 123 and 124, or 127, or 129, or equivalent and CAS EC 101 or 111 and EC 102 or 112.

Principal Courses

A minimum of eight economics courses (distributed according to the description given in the Economics section of this site). A minimum of seven mathematics courses (in addition to Calculus I and II as above) distributed as follows: CAS CS 111 or 113, and CAS MA 225 or 230, MA 242 or 442, 569; plus three others with at least one being CAS MA 400 or above, selected from among CAS MA 213, 214, 226 or 231, 416, 511, 581, 582, CAS CS 112.

Finally, students must satisfy a statistics requirement, either by taking CAS MA 213, 214, or by taking courses with comparable statistics content offered in the Department of Economics.

Students in this major should have advisors in both the Mathematics & Statistics Department and the Economics Department.

This BA/MA program is identical to that of the BA/MA in economics described in the Economics section of this site, except that the candidate must satisfy all requirements for the joint major in economics and mathematics as well as the MA in economics. The departmental BA/MA statement and further information are available from the Graduate Studies Coordinator in the Department of Economics. For general information please see BA/MA Program.

This program combines a general bachelor’s degree mathematics program with the mathematics education courses required for high school teaching certification. Advisors in both the CAS Mathematics Department and the SED Mathematics Education Department must be consulted, as the scheduling of course programs requires careful planning.

Required CAS Courses

• CAS MA 123 Calculus I
• CAS MA 124 Calculus II
• CAS MA 213 Basic Statistics and Probability
• CAS MA 225 Multivariate Calculus
• CAS MA 226 Differential Equations
• CAS MA 242 Linear Algebra
• CAS MA 293 Discrete Mathematics
• CAS MA 341 Introduction to Number Theory
• CAS MA 505 History of Mathematics
• CAS MA 528 Introduction to Modern Geometry or
  SED ME 559 Mathematics for Teachers: Geometry
• CAS MA 541 Modern Algebra I

One additional course must be chosen from the following list: CAS CS 111, PY 211, or any CAS mathematics course numbered 200 or above.

Note:The following substitutions are permitted: MA 123–124 may be replaced by either MA 127 or MA 129, and MA 225, 226, and 242 may be replaced by MA 230, 231, and 442, respectively.

Required SED Courses

• SED CT 575 General Methods of Instruction, 5–12
• SED ED 100 Introduction to Education (normally taken in the first year; can be taken in the second year)
• SED ED 410/412 Social Context of Education/Civic Context of Education (taken in the junior year)
• SED ME 508 Student-Teaching Practicum (second semester of the senior year; on-site practice in teaching).
• SED ME 547 Methods of Teaching Mathematics: High School
• SED ME 563 Problem-Solving Lab

Note: The following 2-credit courses are also required: SED DS 502 (Adolescent Psychology) and SED SE 251 (Special Education).

Students entering the BA/MA program in mathematics will elect one of two options: mathematics or statistics. Both options emphasize breadth of coverage of basic topics of current general importance, as opposed to narrow specialization. The objective of the program in statistics is to train general practitioners capable of making immediate contributions in industry, the medical sciences, government, or private educational and research institutions. Potential applicants must first complete at least one upper-level course (400 level or higher statistics course for the statistics option, and 500 level or higher mathematics course for the mathematics option). As part of the application, one of the letters of recommendation should be provided by the instructor of such a course. Students in the BA/MA program must elect and complete the BA major in mathematics (1701). In addition, students must complete the master’s degree requirements, which consist of a coherent program of eight graduate-level (500 or above) mathematics courses and comprehensive exams. No overlap is permitted between mathematics courses taken to satisfy the BA requirements and those taken to satisfy the MA requirements. The total number of courses taken for both degrees, including distribution courses and electives, can be reduced to as few as 36, provided that all requirements are met.

For further specific information concerning the BA/MA program in mathematics, please consult an advisor in the department. For general information please see BA/MA Program.

The BA/MA in mathematics and cognitive & neural systems is an interdepartmental program in the College of Arts & Sciences and the Graduate School of Arts & Sciences. The program allows undergraduate majors in mathematics to begin working toward an MA in cognitive and neural systems while still completing Mathematics Department BA requirements.

Admission to the BA/MA Program in Mathematics and Cognitive & Neural Systems

College of Arts & Sciences students currently in or entering the junior year are eligible to apply for admission. Students admitted to the BA/MA program will typically have completed at least one CNS course and will be making satisfactory progress toward a BA in mathematics.

The application should include a letter from the student’s Department of Mathematics advisor. Application forms for admission to the BA/MA program may be obtained from the Graduate School of Arts & Sciences Office, College of Arts & Sciences, Room 112.

Requirements

Students are required to complete all requirements for the BA in Mathematics as specified on this site, plus all requirements for the MA in cognitive and neural systems, as specified in the Graduate School of Arts & Sciences Bulletin. In particular, 32 courses (128 credits) are required for the BA and eight courses (32 credits) are required for the MA degree for a total of 40 courses. For general information please refer to BA/MA Program, and contact Professor Barbara Shinn-Cunningham in the Department of Cognitive & Neural Systems for details.

Students must earn a minimum grade of C in courses taken toward a minor. All student minors develop their programs in consultation with an advisor.

Mathematics

The prerequisite for the minor is CAS MA 123 and 124, or 127 or 129 or equivalent. The principal courses required are CAS MA 225 or 230, 226 or 231, 242 or 442, and at least two CAS MA courses numbered 400 or above. In addition, it is strongly recommended that students take CAS CS 111 Introduction to Computer Science.

Mathematical Statistics

The prerequisite for the minor is CAS MA 123 and 124, or 127 or 129 or equivalent. Principal courses required are CAS MA 213, 214, 225 or 230, and two chosen from 581, 582, and 583. In addition, it is strongly recommended that students take CAS CS 111 Introduction to Computer Science.

Statistical Methods

Principal courses required are CAS MA 115 or 213, 116 or 214, 416, 684; one course at the CAS MA 400–600 or CS 400–600 level, and one additional MA or CS course. The two latter courses are to be selected with the written approval of a statistics advisor.