Recommended for students whose majors do not include a specific mathematics requirement. Objectives are to show some of the essence and quality of mathematics, and to enhance precision in the evaluation and expression of ideas, thereby developing a student's quantitative reasoning skills. Designed to give students an understanding of some of the vocabulary, methods, and reasoning of mathematics with a focus on ideas.

Prepares students for courses requiring fundamental algebra skills. Topics include: review of basic algebra; scientific notation, rounding, and percents; factoring; exponents; linear equations and inequalities with applications; quadratic equations with applications; graphing with applications; absolute value equations and inequalities; systems of linear equations and inequalities; and an introduction to exponential and logarithmic expressions.

Prepares students for Pre-calculus and other higher math courses requiring intermediate algebra. Topics include: linear equations and inequalities, absolute value equations and inequalities, systems of linear equations, quadratic equations, polynomial expressions and equations, rational expressions and equations, roots and radicals, and exponential & logarithmic properties and equations.

Prepares students for MATH 107A and MATH 107B. Students will explore mathematical patterns and relations, formulate conjectures, and prove their conjectures. Topics from number theory, probability and statistics, and geometry.

Prerequisite: Score of 46 or higher on ALEKS PPL exam or MATH 10

Mathematics for business world, including functions, math of finance, linear programming and rates of change. Applications to economics and business will be emphasized throughout.

Prerequisite: Score of 51 or higher on ALEKS PPL exam or MATH 10

Limits, differentiation with applications, integration and applications in the Social Sciences and Life Sciences.

Prerequisite: Score of 61 or higher on ALEKS PPL exam or MATH 12

Continuation of MATH 26A, integration and applications to the Social Sciences and Life Sciences. Multi-variate analysis including partial differentiation and maximization subject to constraints; elementary differential equations; sequences and series. Calculus of the trigonometric functions as time allows.

Note: Not open to students already having credit for MATH 31 or equivalent.

Prerequisite: MATH 26A or appropriate high school based AP credit.

Designed to prepare students for calculus. Topics: trigonometry, points and lines in the Cartesian plane; lines and planes in space; transformation of coordinates; the conics; graphs of algebraic relations; the elementary transcendental functions.

Prerequisite: Score of 61 or higher on ALEKS PPL exam or MATH 12

Functions and their graphs; limits; the derivative and some of its applications; trigonometric and hyperbolic functions and their inverses; the integral; the fundamental theorem; some applications of the integral.

Prerequisite: Score of 76 or higher on ALEKS PPL exam or MATH 29 or MATH 29B

MATH 30 continuation. Methods of integration; improper integrals; analytic geometry; infinite sequences and series.

Prerequisite: MATH 30 or appropriate high school based AP credit.

Continuation of Calculus II. Algebra and calculus of vectors; functions of several variables; partial differentiation; multiple integration; vector analysis.

Prerequisite: MATH 31.

Careful development of matrices, systems of equations, determinants, vector spaces, linear transformations, orthogonality, real and complex eigenvalues; R3 viewed as a vector space with generalization to Rn.

Prerequisite: MATH 30 or appropriate high school based AP credit.

First order differential equations, second order differential equations with constant coefficients. Laplace transforms, small systems of linear differential equations, numerical methods, introduction to second order differential equations with variable coefficients.

Prerequisite: MATH 31.

Supplemental instruction for Math 10 focused on developing study skills and effective learning strategies.

Corequisite: Math 10

Computational strategies in mathematical problem solving; implementation of mathematical algorithms; programming concepts including variables, control flow, data structures, and functions; data visualization, typesetting, and report generation.

Prerequisite: MATH 30 or appropriate high school based AP credit

Individual projects or directed reading. Permits a student to pursue study and research in an area not otherwise available through the regular curriculum.

Note: Open only to students who appear competent to carry on individual work; admission requires the approval of the faculty member under whom individual work is to be conducted, and approval of the advisor and the Department Chair.

Linear algebra and its elementary applications. Topics: Matrix algebra; simultaneous linear equations; linear dependence and vector spaces; rank and inverses; determinants; numerical solution of simultaneous linear equations; linear transformations; eigenvalues and eigenvectors; unitary and similarity transformations; quadratic forms.

Note: May not be taken for credit toward a mathematics major.

Prerequisite: MATH 26B or MATH 31.

Theory of divisibility; some number theoretical functions; congruencies (linear and quadratic); some Diophantine equations. Simple continued fractions.

Prerequisite: MATH 31.

Survey of second order linear differential equations, power series and Fourier series solutions, solution of partial differential equations by separation of variables.

Prerequisite: MATH 32, MATH 45.

Partial differential equations continued, complex function theory and its applications.

Prerequisite: MATH 105A.

First half of a one-year course in the structure of the real number system and its sub-systems and in the basic properties and concepts of geometry. Topics will include: definitions and properties of set theory and their use in the development of the natural and whole number systems, definitions and properties of the arithmetic relations and operations for the natural numbers, whole numbers, integers.

Note: May not be taken for credit toward a mathematics major or minor.

Prerequisite: MATH 17 and either a score of 46 or higher on ALEKS PPL exam or MATH 10

Continuation of MATH 107A. Topics will include: rational numbers, real numbers, measurement, Euclidean Geometry.

Note: May not be taken for credit toward a mathematics major or minor.

Prerequisite: MATH 107A.

Logic of mathematical proof, set theory, relations, functions. Examples and applications from set cardinality, algebra, and analysis.

Prerequisite: MATH 31, MATH 35.

First half of a one-year introductory course in algebraic concepts. Topics include: groups, subgroups, properties of groups, permutation groups, factor groups, homomorphism theorems.

Prerequisite: MATH 108.

Continuation of MATH 110A.

Note: Topics include: rings and fields. Applications may be selected from lattice, machine, and coding theories.

Prerequisite: MATH 110A.

Abstract linear spaces and linear transformations; invariant subspaces; canonical forms.

Prerequisite: MATH 110A.

Study of the axioms and theorems of Euclidean geometry. A comparison of several geometry axiom systems and their theorems, including those of some non-Euclidean and finite geometries.

Prerequisite: MATH 31; MATH 32 or MATH 35.

First half of a one-year upper division course in functions of a real variable. The first semester will consist of a rigorous development of the theory of real-valued sequences and continuity and differentiation for functions of one real variable.

Prerequisite: MATH 32 and MATH 108.

Continuation of MATH 130A. This semester will be devoted to a rigorous development of the theory of Riemann integration, infinite series, and sequences and series of functions.

Prerequisite: MATH 130A.

Axiomatic study of set theory. Topics usually considered include: relations and functions; set theoretical equivalence; finite and infinite sets; cardinal arithmetic; ordinal numbers and transfinite induction; variants of the Axiom of Choice.

Prerequisite: MATH 108.

Theory of linear programming, duality, simplex method, integer programming, applications.

Prerequisite: MATH 31; MATH 35 or MATH 100.

Study of the development of mathematical ideas and techniques and their impact on the general course of the history of western civilization.

Prerequisite: MATH 31 and upper division status in mathematics.

Individual projects or directed reading. Open only to those students who appear competent to carry on individual work. Admission to this course requires the approval of the faculty member under whom the individual work is to be conducted, in addition to the approval of the advisor and the Department Chair.

General algebraic systems and concepts; groups.

Prerequisite: MATH 110B.

Metric topology; the theory of the derivative; measure theory.

Prerequisite: MATH 130B.

Complex numbers, complex functions, analytic functions, complex integration, harmonic functions.

Prerequisite: MATH 130B; MATH 105B or MATH 134 is recommended.

The course gives a basic introduction to Lie algebras and their connections to Lie groups. Emphasis will be on examples given by matrices. Beyond an introduction to Lie algebras and groups, possible specific topics are: the classification and construction of simple Lie algebras; ADE classification; universal enveloping algebras; semi-simple Lie algebras and their representation theory; Lie group representations; subgroups and subalgebras; one-parameter subgroups; and the exponential map.

Prerequisite: Math 110A and Math 130A, or consent of instructor.

Any properly qualified student who wishes to pursue a problem may do so if the proposed subject is acceptable to the supervising instructor and to the student's advisor.