Lawyers, programmers, reporters, teachers, managers-indeed, members of almost every profession-require the quantitative and analytical skills developed by students who major in mathematics. More and more, employers are looking for applicants who are good thinkers. General problem-solving skills, the ability to synthesize information and reason logically, rather than narrow technical expertise, are seen as an advantage for employment. A mathematics major is not merely vocational training but, rather, an opportunity to equip oneself with skills, knowledge, flexibility, and ability to learn-all necessary in a changing world. In addition to fields that use mathematics directly, such as operations research, teaching, software engineering, statistical consulting, and actuarial work, a degree in mathematics provides good background for entry to jobs in business or admission to medical or dental school, M.B.A. programs, law school, engineering school, and public health programs..

Major Requirements

The following courses are required (12 units):

MA 231, 232, 310, 311, 335, 451, 461
three courses from MA 207, 240, 317, 421, 422, 452, 454, 455,
458, 462, PH 121, PH 122, at least two of which are in MA
one course in computer science numbered CS 170 or above
MA 499

A student may be exempt from CS 170, MA 207, MA 231, and MA 232 by placement, AP credit, or IB credit.

Mathematics majors intending to seek employment immediately upon graduation in fields other than actuarial science are encouraged to take MA 207, 240, 317, and CS 250. Those intending an actuarial career are encouraged to take MA 317, 421, and 422; it is also recommended that they take some relevant courses in other disciplines, particularly AC 221, AC 222, EC 201, EC 202, BA 201, BA 372, CS 250, and CS 290.

Students planning on graduate study in pure mathematics are encouraged to take MA 317, 452, 455, 458, and 462. Those planning graduate work in applied mathematics are encouraged to take MA 317, 454, and CS 250.

An interdisciplinary major in mathematics and computer science is available for students who wish to combine these two areas. Please see the Interdisciplinary Major Requirements section of this catalog for requirements for this major.

Courses required for a mathematics major may be used to meet minor requirements in computer science and physics.
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Minor Requirements

The following courses are required (5 units):

MA 231
MA 232
MA 310
two elective units in MA at the 240 level or above, excluding MA 298, 398, and 498

Courses in Mathematics

MA 115 Fundamentals of Algebra (1)

A college algebra course including operations of rational expressions, solving equations and inequalities, graphs, and functions. Satisfactory completion of this course, or exemption by placement examination or ACT or SAT scores, is required prior to registration for any other mathematics course. Not open to students who have passed any mathematics course above MA 115. Fall, Spring.

 

MA 122 History and Applications of Trigonometry (1)

A course in the basic concepts of trigonometry, focusing on their historical and contemporary use in solving problems. Designed for non mathematics/science majors, this course is not open to students who have passed MA 231 or equivalent. Prerequisite: MA 115 or placement. Fall.

 

MA 124 Precalculus Mathematics (1)

A preparation for students who plan to study calculus. This course focuses on modeling real world phenomena using polynomial, rational, exponential, logarithmic, and trigonometric functions. An understanding of these functions is developed graphically, numerically, analytically, and verbally. Not open to students who have passed MA 231 or equivalent. Prerequisite: Placement. Fall, Spring.

 

MA 125 Survey of Mathematics (1)

A survey course designed for non mathematics/science majors. This course includes topics drawn from a wide variety of areas within mathematics at the discretion of the instructor. Not open to students who have passed MA 231 or equivalent. Prerequisite: MA 115 or placement. Fall, Spring.

 

MA 207 General Statistics (1)

Statistical techniques with an emphasis on statistical inference; hypothesis testing, parameter estimation, analysis of variance, regression, correlation. Emphasis is placed on business problems. Prerequisite: MA 115 or equivalent, or consent. Fall, Spring.

 

MA 228 Survey of Calculus (1)

An introduction to elementary calculus with emphasis on the differentiation and integration of polynomial, rational, and exponential and logarithmic functions. Partial derivatives with applications to business, economics, and the social sciences. Intended for the non-mathematics/science major. Students may not receive credit for both MA 231 and MA 228. Prerequisite: MA 115 or placement.

 

MA 231 Calculus I (1)

A course in calculus emphasizing graphical, numerical, analytical, and descriptive points of view. Topics include functions, derivatives, definite integrals, and the Fundamental Theorem of Calculus. Three one-hour class sessions and one 80-minute laboratory period per week. Prerequisite: MA 124 or placement. Fall, Spring.

 

MA 232 Calculus II (1)

A course in calculus emphasizing graphical, numerical, analytical, and descriptive points of view. Topics include definite integrals, approximation techniques, indefinite integrals, elementary differential equations, modeling, Taylor polynomials, and infinite series. Three one-hour class sessions and one 80-minute laboratory period per week. Prerequisite: MA 231 or placement. Fall, Spring.

 

MA 240 Discrete Structures (1)

An introduction to concepts fundamental to the analysis of algorithms and their realizations. Topics include set theory, induction, recursion, graphs, networks, and Boolean algebra. Prerequisites: MA 231 and a computer science course numbered CS 170 or above, or consent of the instructor. Fall, Spring.

 

MA 298, 398, 498 Teaching Experience in Mathematics (½ or 1)

Prerequisite: Consent of the chair of the division.

 

MA 310 Calculus III (1)

A course in calculus emphasizing graphical, numerical, analytical, and descriptive points of view. Topics include parametric equations, polar coordinates, vectors, multivariable and vector valued functions, partial derivatives, multiple integrals, vector fields, and line integrals. Three one-hour class sessions and one 80-minute laboratory period per week. Prerequisite: MA 232 or placement. Fall, Spring.

 

MA 311 Differential Equations (1)

An introduction to the study of ordinary differential equations with emphasis on solution techniques and applications. Whenever possible, numerical, qualitative and analytical methods are discussed, and students are encouraged to make use of computers in solving some of the problems. Prerequisite: MA 310 or consent. Fall.

 

MA 317 Linear Algebra (1)

Systems of equations, matrices, determinants, eigenvalues, matrix factorizations, vector spaces, linear transformations, and applications. Prerequisite: MA 232 or consent. Spring.

 

MA 335 Foundations of Higher Mathematics (1)

An introduction to the logic and methods used in advanced mathematics, with emphasis on understanding and constructing proofs. Prerequisite: MA 232. Spring.

 

MA 393, 493 Independent Study (½ or 1)

Directed readings, inquiry, and/or research project in mathematics or statistics. Prerequisite: Consent.

 

MA 421 Introduction to Mathematical Statistics I (1)

Basic probability theory, probability distributions, mathematical expectation, special discrete probability distributions, special probability densities, and moment-generating functions. Prerequisite: MA 310. Fall 2001.

 

MA 422 Introduction to Mathematical Statistics II (1)

A continuation of MA 421 with emphasis on selected topics in statistics, including sampling distributions, point estimation, interval estimation, hypothesis testing, regression and correlation, analysis of variance, and nonparametric methods. Prerequisite: MA 421. Spring 2002.

 

MA 451 Abstract Algebra I (1)

Topics include binary operations, groups, subgroups, group homomorphisms, factor groups, and a brief introduction to rings and fields. Prerequisite: MA 335 or consent. Fall 2001.

 

MA 452 Abstract Algebra II (1)

A continuation of MA 451. Topics include rings, fields, integral domains, ideals, ring homomorphisms, field of quotients, and extension fields. Prerequisite: MA 451. Spring 2002.

 

MA 454 Numerical Analysis (1)

An introduction to numerical methods of solution and their analysis. Topics include computer arithmetic, propagation of error, systems of linear and non-linear equations, numerical integration, curve fitting, and differential equations. Prerequisites: MA 310 and a computer science course numbered CS 170 or above, or consent. Spring.

 

MA 455 Introduction to Topology (1)

An introduction to the topology of Euclidean space and of surfaces. Topics include continuity, compactness, cell complexes, and the classification of surfaces. Applications include fixed-point theorems, the Jordan curve theorem, and map colorings. Prerequisites: MA 310 and 335, or consent. Spring 2003.

 

MA 458 Introduction to Complex Analysis (1)

Complex numbers, analytic functions, Cauchy Riemann equations, curves and integrals, Cauchy's Theorem and applications, Taylor and Laurent series, analytic continuation, Residue Theorem, harmonic functions, and conformal mappings. Prerequisites: MA 310 and 335, or consent. Fall 2002.

 

MA 461 Real Analysis I (1)

A rigorous treatment of sequences, limits, continuity, differentiation, infinite series, sequences and series of functions, uniform convergence and its implications for function series. Prerequisites: MA 310 and 335, or consent. Fall 2002.

 

MA 462 Real Analysis II (1)

A continuation of MA 461. Topics include integrals, derivatives, and functions of several variables. Prerequisites: MA 317 and 461. Spring 2003.

 

MA 499 Senior Project in Mathematics (1)

Special topics in mathematics beyond the scope of the regularly offered courses, expanding on previous knowledge or introducing new material that requires significant mathematical maturity. Seniors may be required to do a research project and/or give an oral presentation in addition to completing all other assignments. Prerequisite: One 300-level mathematics course and consent. Interim.