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

Supplemental instruction for Math 24 focused on developing study skills and effective learning strategies.

Corequisite: MATH 24

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.

Introduction to the art of counting. The focus will be on actually listing the objects being counted in small cases and using the knowledge gained in working with small cases to build toward general principles. Sum and product principles, models of counting, permutations and combinations, equivalence relations and partitions, inclusion-exclusion principle, recurrence relations, and generating functions.

Prerequisite: MATH 31

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

Prerequisite: MATH 31.

Vector and scalar fields, integral theorems, orthogonal curvilinear coordinates, vector spaces and linear transformations, applications to physical fields and operators.

Prerequisite: MATH 32.

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.

Students will build on their understanding of material of Math 17, Math 107A/B by deepening their understanding of the concepts taught in these courses. This will be done by examining these concepts in relationship to theories of learning and development. Students will examine mathematical concepts related to K-8 with respect to the treatment of reasoning, communication, and the perspective of cognitive and social constructivism; and throughout the course will consider the question of "What is mathematics?" and "How is mathematics learned?"

Prerequisite: MATH 17, MATH 107A or MATH 107B, and CHDV 30 or CHDV 35.

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.

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.

Complex plane; analytic functions; integration and Cauchy's Theorem; sequences and series; residue calculus; applications to potential theory; Fourier and Laplace transforms.

Prerequisite: MATH 32.

Numerical solutions of algebraic and transcendental equations; interpolation, inverse interpolation, finite differences, cubic splines, and applications; numerical differentiation and integration; direct and iterative numerical solutions of linear systems; discrete and continuous least squares approximation.

Prerequisite: MATH 31

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.

Reviews the major themes presented in the upper division program in Mathematics, and relates the themes to junior high school and high school curriculum. Required for all subject matter students.

Note: Not accepted for credit for non-Teaching Credential students.

Prerequisite: Successful completion of at least five of the following: MATH 102, MATH 110A, MATH 110B, MATH 121, MATH 130A, MATH 130B or MATH 190; MATH 110A or MATH 130A may be taken concurrently.

Supports Sacramento State students who are working in tutorial and related roles in mathematics programs on campus. Focus on questioning as a fundamental strategy for teaching mathematics, on classroom observation, and on communication among mathematics instructors in support of effective teaching and learning.

Note: May be repeated up to two times for credit.

Prerequisite: Students must be working as tutors in a campus-based program.

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.

Fields; vector spaces; Galois theory.

Prerequisite: MATH 210A.

Continuation of MATH 230A, with topics selected from: Theory of the integral, including Riemann, Riemann Stieltjes, and Lebesque integrals.

Note: May be taken twice with approval of the graduate coordinator.

Prerequisite: MATH 230A.

This class will cover divisibility properties of the integers, primes and primality tests, modular arithmetic, Chinese Remainder Theorem, quadratic reciprocity and quadratic forms, arithmetic functions, the Mobius inversion formula, and Diophantine equations. Possible additional topics include elliptic curves, algebraic numbers, primes in arithmetic progressions, the geometry of numbers and encryption.

Prerequisite: Math 110A or equivalent.

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.

Directed reading programs for master's candidates preparing for written comprehensive examinations.

Prerequisite: Advanced to candidacy and permission of the graduate coordinator.