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.

Prerequisite: MATH 9 or three years of high school mathematics which includes two years of algebra and one year of geometry; and completion of ELM requirement.

Prepares students, especially in bioscience, economics and social science, for courses requiring basic algebra and trigonometry. Topics: measurement and scientific notation; review of basic algebra; factoring; laws of exponents; linear and quadratic equations; Cartesian coordinates and graphing; the trigonometric functions and their basic identities; solutions of right triangles; the laws of sines, cosines and tangents; solutions of general triangles; logarithms.

Note: Applicable to workload credit for establishing full-time enrollment status, but not applicable to the baccalaureate degree.

Prerequisite: One year each of high school algebra and geometry; and a passing score on the Elementary Algebra Diagnostic Test.

Prepares students for Precalculus and other courses requiring algebra. 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 and logarithmic equations.

Note: Applicable to workload credit for establishing full-time enrollment status, but not applicable to the baccalaureate degree.

Prerequisite: A passing score on the Elementary Algebra Diagnostic Test.

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: MATH 9 or three years of high school mathematics which includes two years of algebra and one year of geometry; completion of ELM requirement and the Intermediate Algebra Diagnostic Test.

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: MATH 9 or three years of high school math that includes two years of algebra and one year of geometry; completion of ELM requirement and the Intermediate Algebra Diagnostic Test.

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

Prerequisite: MATH 11 or three years of high school mathematics which includes two years of algebra and one year of geometry; completion of ELM requirement and the Intermediate Algebra Diagnostic Test.

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: MATH 11 or three years of high school mathematics which includes two years of algebra and one year of geometry; completion of ELM requirement and Intermediate Algebra Diagnostic Test.

Second semester of a two semester course that is designed to prepare students for calculus. Topics: exponential and logarithmic functions, trigonometric functions, analytic geometry, and applications. Lecture two hours.

Prerequisite: MATH 29A.

Corequisite: MATH 29M.

Workshop designed to deepen the understanding of pre-calculus developed in MATH 29B.

Note: May be taken for workload credit toward establishing full-time enrollment status, but is not applicable to the baccalaureate degree. Laboratory: 3 hours.

Corequisite: MATH 29B.

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: MATH 29 or four years of high school mathematics which includes two years of algebra, one year of geometry, and one year of mathematical analysis; completion of ELM requirement and Pre-Calculus Diagnostic Test.

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

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

Workshop designed to deepen the understanding of calculus developed in MATH 31.

Note: May be taken for workload credit toward establishing full-time enrollment status, but is not applicable to the baccalaureate degree. Laboratory: 3 hours.

Corequisite: Enrollment in a designated section of MATH 31.

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.

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.

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 passing score on the Intermediate Algebra Diagnostic Test.

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/B, 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

Advanced study of logic with special application to mathematics.

Prerequisite: MATH 108.

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.

Point set topology, continuity, compactness, connectedness.

Prerequisite: MATH 130B.

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.

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.

A survey course for students in the Blended Program in Mathematics that relates broad areas of educational psychology and theories of learning to instruction in the secondary mathematics classroom. The focus is on practical applications of theories through the design of lesson and unit plans. Students will design learning activities for diverse classes of learners, including English Language Learners, and build and refine assessment plans that include formative assessments. Lecture two hours.

Prerequisite: Admission to the Mathematics Blended Program.

The first of a two-part sequence supporting student teachers in the Mathematics Blended Program. Focus is on strategies for secondary mathematics instruction, the process of reflection on teaching, communication among mathematics teachers in support of effective teaching and learning, strategies for engagement, questioning, creating a safe classroom environment, classroom management, assessment, and familiarity with school and community resources. Emphasis on issues related to English Language Learners, special needs students, and intervention strategies. Seminar two hours.

Corequisite: Enrollment in EDTE 470A.

The second of a two-part sequence supporting student teachers in the Mathematics Blended Program. Focus is on strategies for secondary mathematics instruction, the process of reflection on teaching, communication among mathematics teachers in support of effective teaching and learning, strategies for engagement, questioning, creating a safe classroom environment, classroom management, assessment, and familiarity with school and community resources. Emphasis on issues related to English Language Learners, special needs students, and intervention strategies. Seminar two hours.

Corequisite: Enrollment in EDTE 470B.

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

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