# Mathematics courses

### MATH 10: Support Course for MATH 100: Quantitative Literacy (3 units)

This co-requisite course contains topics which directly support the content in MATH 100: Quantitative Literacy (3 units). It contains support for mathematical skills and knowledge used in MATH 100: Quantitative Literacy (3 units), supplemental instruction on MATH 100: Quantitative Literacy (3 units) content, and study skill development. (Coreq: MATH 100: Quantitative Literacy (3 units))

**Units:** 1 — 1

### MATH 15: Support Course for MATH 115: Finite Mathematics (3 units)

This co-requisite course contains topics which directly support the content in MATH 115: Finite Mathematics (3 units). It contains support for mathematical skills and knowledge used in MATH 115: Finite Mathematics (3 units), supplemental instruction on MATH 115: Finite Mathematics (3 units) content, and study skill development. (Coreq: MATH 115: Finite Mathematics (3 units))

**Units:** 1 — 1

### MATH 30: Support Course for MATH 130: Precalculus (5 units)

This co-requisite course contains topics which directly support the content in MATH 130: Precalculus (5 units). It contains support for mathematical skills and knowledge used in MATH 130: Precalculus (5 units), supplemental instruction on MATH 130: Precalculus (5 units) content, and study skill development. (Coreq: MATH 130: Precalculus (5 units))

**Units:** 1 — 1

### MATH 90: Pre-College Mathematics

An individually paced review of pre-college mathematics concepts and skills. The course consists of a set of modules in Elementary Algebra and Intermediate Algebra designed to prepare students for college-level mathematics. (Not open to Early Start Students)

**Units:** 1 — 2

### MATH 98: Mathematics Review I

An individually paced review of pre-college mathematics concepts and skills. Designed to prepare students for college-level mathematics. Focuses on basic concepts and skills and effective communication of quantitative information and concepts. Not for baccalaureate credit; however, the course grade (A-F) will show on student transcripts.

**Units:** 4 — 4

### MATH 99: Mathematics Review II

A continuation of Math 98 for those students who have not yet satisfied the ELM requirement. Not for baccalaureate credit; however, the course grade (A-F) will show on student transcripts.

**Units:** 4 — 4

### MATH 99: Mathematics Review II

A continuation of Math 98 for those students who have not yet satisfied the ELM requirement. Not for baccalaureate credit; however, the course grade (A-F) will show on student transcripts.

**Units:** 6 — 6

### MATH 100: Quantitative Literacy

The course uses quantitative methods to model and solve real world problems. It covers basic number theory, linear, quadratic, exponential and logarithmic functions; systems of equations and inequalities; probability theory; frequency distributions, measures of central tendency and dispersion, bivariate data, and correlation. The course uses technology as a tool to acquire, visualize, and analyze data.

**Units:** 3 — 3

### MATH 109: Trigonometry

Trigonometric and inverse trigonometric functions; trigonometric identities and equations; applications involving right triangles illustrating the law of sines and cosines.

**Units:** 3 — 3

### MATH 115: Finite Mathematics

Mathematical modeling and data analysis applicable to the social sciences and business such as the following: linear functions, systems of linear equations, matrices, linear programming including the simplex method and the mathematics of finance.

**Units:** 3 — 3

### MATH 116: Finite Mathematics II

Mathematical modeling and data analysis applicable to the social sciences and business selected from the following: logic, set theory, combinatorics, probability, probability distributions, statistics, Markov chains, graph theory, and game theory. (Prereq: MATH 115: Finite Mathematics (3 units))

**Units:** 4 — 4

### MATH 130: Precalculus

Functions and graphs, including polynomial, rational, exponential, logarithmic, and trigonometric functions. Applications, data analysis, mathematical modeling, and analytic trigonometry.

**Units:** 5 — 5

### MATH 150: Calculus I

Includes limits, continuity, derivatives including trigonometric functions, chain rule, curve sketching, extremum problems, implicit differentiation, related rates, Mean Value Theorem, logarithmic and trigonometric functions, introduction to integration, fundamental theorem of calculus, substitution, and applications. (Prereq: MATH 130: Precalculus (5 units))

**Units:** 4 — 4

### MATH 151: Calculus II

Includes the calculus of exponential and logarithmic functions, trigonometric and inverse trigonometric functions, techniques of integration, separable differential equations, Taylor polynomials, L'Hôpital's rule, improper integrals, series, and introduction to partial derivatives. (Prereq: MATH 150: Calculus I (4 units))

**Units:** 4 — 4

### MATH 170: Discrete Mathematics

Includes sets and sequences, elementary logic, relations, induction, counting principles, discrete probability, Boolean algebra, logic networks, matrices, graph theory, and trees. Applies these topics to real life and branches of science, particularly computer science. (Prereq: MATH 130: Precalculus (5 units))

**Units:** 4 — 4

### MATH 197: Independent Study

Student and faculty member select topic of study and number of credits.

**Units:** 1 — 6

### MATH 250: Multivariate Calculus

Vectors in three dimensions, solid analytic geometry, partial differentiation, multiple integration, differentiation under the integral sign, vector field theory. (Prereq: MATH 151: Calculus II (4 units))

**Units:** 4 — 4

### MATH 260: Linear Algebra

Introduces matrices and systems of linear equations and covers topics such as determinants, vectors in two and three dimensions, vector spaces, linear transformations, and eigenvector eigenvalue decompositions. Emphasizes applications to real-world issues. Students use computing technology for the course. (Prereq: MATH 130: Precalculus (5 units))

**Units:** 4 — 4

### MATH 265: Differential Equations and Linear Algebra

First order ordinary differential equations including direction fields, separation of variables, first order linear equations, growth and decay, nonlinear models. Linear algebra including systems of linear equations, matrix inverses, determinants, vector spaces and subspaces, basis and dimension. (Prereq: MATH 151: Calculus II (4 units))

**Units:** 4 — 4

### MATH 270: Mathematics for Computing

This course covers basic linear algebra, continuous and discrete probability, and a continuation of elementary discrete mathematics from MATH 170: Discrete Mathematics (4 units). It emphasizes mathematical theory as well as applicable methods. Topics include systems of linear equations, matrices, determinants, vector spaces, conditional probability, distributions and densities, expected value, functions of random variables, automata, and algorithmic complexity. (Prereq: MATH 150: Calculus I (4 units) and MATH 170: Discrete Mathematics (4 units))

**Units:** 4 — 4

### MATH 300: Major Proseminar

The capstone process begins in MATH 300: Major Proseminar (4 units). Students develop library research, scholarly reading, writing, and collaboration skills needed to develop, implement, and complete their capstone projects. Moreover, students investigate different philosophical viewpoints and notions of truth relating to mathematics and explore the utility of mathematics. Students also develop a learning plan that integrates their major concentration, capstone interests, and personal and professional goals. [Prereq: (GE Area A1 and A2 and A3) and MATH 322: Foundations of Modern Math (4 units) and (Junior or Senior Standing)]

**Units:** 4 — 4

### MATH 304: Modern Algebra

Develops understanding of the power of mathematical abstraction and symbolism through the study of advanced algebraic structures. Studies matrices, groups, integral domains, rings, and fields and discusses their relationship to the pre-college algebra curriculum. Emphasizes problem solving and requires students to use a variety of algebraic representations and techniques to model and analyze problem situations and solutions. (Prereq: MATH 308: Elementary Math - Adv Viewpt A (3 units))

**Units:** 4 — 4

### MATH 305: Modern Geometry

Introduces Euclidean and non-Euclidean geometries as vehicles for studying axiomatic systems, for representing real world phenomena, and for visualizing mathematical ideas. Emphasizes aesthetic and practical applications of geometry and methods of proof. Students are required to do formal constructions and proofs using compass, straightedge, and computer software. (Prereq: MATH 308: Elementary Math - Adv Viewpt A (3 units))

**Units:** 4 — 4

### MATH 306: Logic and Foundations

A careful analysis of methods of proof, axiomatic systems, consistency, the elaboration of mathematical structures from a minimal set of axioms and basic principals of symbolic logic. Students gain an understanding of the nature and purpose of axiomatic systems, and the ability to prove fundamental theorems utilizing various mathematical systems. (Prereq: MATH 308: Elementary Math - Adv Viewpt A (3 units))

**Units:** 4 — 4

### MATH 308: Elementary Math - Adv Viewpt A

The first of a two-course sequence intended for future elementary teachers. Students develop an in-depth understanding of key concepts in K-8 mathematics and of students' learning of K-8 mathematics concepts. (Prereq: MATH 100: Quantitative Literacy (3 units))

**Units:** 3 — 3

### MATH 309: Elementary Math - Adv Viewpt B

Second in a sequence of courses intended for future elementary and middle school teachers. Students in this course will develop an in-depth understanding of additional key concepts in K-8 mathematics and further develop their understanding of children's learning processes in mathematics in general. (Prereq: MATH 308: Elementary Math - Adv Viewpt A (3 units))

**Units:** 3 — 3

### MATH 320: Applied Probability and Statistics

Provide foundation for applied probability and statistics methods including basic probability theory, sampling and experimental design, descriptive statistics, estimation of parameters, hypothesis testing, regression analysis, correlation, and an introduction to non-parametric statistics and statistical computing. (Prereq: Math 150)

**Units:** 4 — 4

### MATH 322: Foundations of Modern Math

Introduces elements of mathematical proof, focusing on the various forms and methods, including direct proof; indirect proof; existence and uniqueness proofs; mathematical induction; strong induction. Proof methods are applied to mathematical statements taken from number theory, geometry, and calculus. Develops the tools, terminology, and symbols of advanced mathematics including deductive logic, sets, functions, equivalence relations, number systems, and cardinality of sets. (Prereq: MATH 151: Calculus II (4 units) and MATH 170: Discrete Mathematics (4 units))

**Units:** 4 — 4

### MATH 325: Number Theory

Introduces the properties of integers. Topics include the division and Euclidean algorithms, mathematical induction, congruences, fundamental theorem of arithmetic, perfect numbers, number theoretic functions, and prime number theorem. (Prereq: MATH 322: Foundations of Modern Math (4 units))

**Units:** 4 — 4

### MATH 326: History of Mathematics

The history of mathematics from ancient to modern times. Students learn to solve problems using only the tools of the past. Mathematics is developed in the context of its impact on the development of science and the interaction of mathematics with other fields of human endeavor such as philosophy, arts, and social values. (Prereq: MATH 322: Foundations of Modern Math (4 units))

**Units:** 4 — 4

### MATH 329: College Geometry

The Hilbert postulates and axiomatic systems, isometries in the Euclidean Plane, non-Euclidean geometries, finite geometries, and the construction of geometries from fields. (Prereq: MATH 322: Foundations of Modern Math (4 units))

**Units:** 4 — 4

### MATH 330: Advanced Linear Algebra

Linear equations and matrices, vector spaces, dual spaces and inner product spaces, linear transformations, determinants, eigenvalues and eigenvectors, systems of linear differential equations, and applications. (Prereq: MATH 265: Differential Equations and Linear Algebra (4 units) and MATH 322: Foundations of Modern Math (4 units))

**Units:** 4 — 4

### MATH 340: Ordinary Differential Equations

Series solution of linear differential equations with variable coefficients, systems of differential equations, phase plane analysis, existence and uniqueness theorems, singular points, stability theory, transform analysis, and applications. (Prereq: MATH 265: Differential Equations and Linear Algebra (4 units))

**Units:** 4 — 4

### MATH 350: Complex Analysis

Complex numbers; analytic functions, Cauchy-Riemann equations; linear fractional transformations; construction and geometry of the elementary functions; Green's theorem, Cauchy's theorem; Jordan curve theorem, Cauchy's formula; Taylor's theorem, Laurent expansion; analytic continuation; isolated singularities, Liouville's theorem; Abel's convergence theorem and the Poisson integral formula.The fundamental theorem of algebra. (Prereq: MATH 250: Multivariate Calculus (4 units))

**Units:** 4 — 4

### MATH 361S: Mathematics Tutors

Service learning placements in middle or high schools help students deepen their understanding of mathematical principles, techniques, and methodologies for effective instruction. Students also study how issues of social justice and equity affect mathematical literacy and why it is important for everyone to be mathematically literate. [Prereq: (Junior or Senior Standing) and (MATH 130: Precalculus (5 units) and SL 200)]

**Units:** 5 — 5

### MATH 362LS: Math Service Learning Lab

Service learning component of Math 362S which may include aiding or tutoring in mathematics classes or facilitating mathematics activities in after-school programs. (Coreq: MATH 362S: Service Learning for Mathematics Consultants (5 units))

**Units:** 0 — 0

### MATH 362S: Service Learning for Mathematics Consultants

Service learning placements in local non-profit organizations, school districts and community organizations help students deepen their understanding of mathematical and statistical principles, techniques, and methodologies for effective consulting. Students will also study how the need for mathematical and statistical analysis can influence issues of social justice and equity within the local and global community. [Prereq: (Junior or Senior Standing) and GE Area D3 and (MATH 320: Applied Probability and Statistics (4 units) or STAT 100: Introduction to Statistics (3 units) or STAT 250: Applied Stat:Sci Tech (4 units))]

**Units:** 5 — 5

### MATH 370: Logic and Computation

An advanced study of logic and discrete structures that have application in computer science. Includes logic, propositional and predicate calculus, proof structures, algorithms, and complexity. Emphasizes applications to core areas of computer science, such as computer architecture, programming languages, the theory of computation, artificial intelligence, software engineering, and relational databases. (Prereq: MATH 151: Calculus II (4 units) or MATH 170: Discrete Mathematics (4 units))

**Units:** 4 — 4

### MATH 372: Mathematics of Music

Topics include tempering of scales, harmony and the overtone series, intervals, the chromatic scale and modular arithmetic, algebraic properties of diatonic harmony, Fourier series and timbre, polyrhythms and metric modulation and an exploration of connections with set theory. The course will incorporate listening to a wide variety music, including western classical, jazz and music from various parts of the world. (Prereq: MATH 151: Calculus II (4 units))

**Units:** 4 — 4

### MATH 374: Mathematical Modeling

The construction of mathematical models to solve real world problems. Model types include continuous, discrete, deterministic and stochastic. The entire modeling process from construction of the model, fitting data to the model, analysis of the model including model selection, and verification of the model covered. Examples from a variety of disciplines including biology, physics, economics and finance. (Prereq: MATH 250: Multivariate Calculus (4 units) or MATH 265: Differential Equations and Linear Algebra (4 units))

**Units:** 4 — 4

### MATH 375: Numerical Analysis for Mathematics and Statistics

Methods of numerical approximation of the value of functions, polynomials, systems of equations and integrals using a programming language such as R, C++ or Mathematica. Topics may include accuracy of approximate calculations, root finding methods, interpolation, numerical differentiation and integration, numerical solutions to ordinary differential equations, regression, optimization and Monte Carlo methods. (Prereq: MATH 151: Calculus II (4 units) and CST 231: Problm-Solving/Programng (4 units))

**Units:** 4 — 4

### MATH 376: Partial Differential Equations

Derivation of partial differential equations; separation of variables; equilibrium solutions and Laplace's equation; Fourier series; method of characteristics for the one dimensional wave equation. Solutions of non-homogeneous equations. (Prereq: MATH 265: Differential Equations and Linear Algebra (4 units))

**Units:** 4 — 4

### MATH 385: Enumerative Combinatorics

An introduction to basic notions and techniques in Enumerative Combinatorics. Basic structures of enumeration including enumerative families like binomial coefficients, Catalan numbers, Fibonacci numbers, Eulerian numbers, Bell numbers, and Stirling numbers; compositions and partitions; recurrences; permutations and permutation statistics; generating functions; partially ordered sets; applications to Symmetric functions. (Prereq: MATH 170: Discrete Mathematics (4 units))

**Units:** 4 — 4

### MATH 386: Graph Theory and Its Applications

Introductory graph theory with applications. Graphs and digraphs. Eulerian and Hamiltonian graphs. The traveling salesman problem, connectivity, trees, planarity, colorings, scheduling, minimal cost networks and graph models. (Prereq: MATH 170: Discrete Mathematics (4 units) or MATH 151: Calculus II (4 units))

**Units:** 4 — 4

### MATH 395: Special Topics

Studies a particular topic in Mathematics. May be repeated for credit when topics vary.

**Units:** 1 — 6

### MATH 397: Independent Study

Student and faculty member select topic of study and number of credits.

**Units:** 1 — 6

### MATH 400: Capstone Seminar

Under the guidance of a faculty member, students complete a formal write up and present research in an area of their interest. (Prereq: MATH 300: Major Proseminar (4 units))

**Units:** 4 — 4

### MATH 410: Modern Algebra I

Detailed study of the theory of basic algebraic systems, groups, and rings. Topics include subgroups, permutation groups, homomorphisms, subrings, ideals, and quotient rings. (Prereq: MATH 265: Differential Equations and Linear Algebra (4 units) and MATH 322: Foundations of Modern Math (4 units))

**Units:** 4 — 4

### MATH 411: Modern Algebra II

A rigorous treatment of rings and fields. Examples from many branches of mathematics. Ideals and quotient rings, categorization of rings, Euclidean domains, polynomial rings and fields, unique factorization domains, extension fields, and Galois theory. (Prereq: MATH 410: Modern Algebra I (4 units))

**Units:** 4 — 4

### MATH 420: Mathematical Analysis I

A rigorous introduction to the n-dimensional real number system. Topics include construction of the real numbers, topology of real numbers, continuity, derivatives and integration in multiple dimensions, sequences and series, and sequences and series of functions. (Prereq: MATH 250: Multivariate Calculus (4 units) and MATH 322: Foundations of Modern Math (4 units))

**Units:** 4 — 4

### MATH 421: Mathematical Analysis II

A continuation of MATH 420: Mathematical Analysis I (4 units). Topics include implicit function theory, conformal mappings, Lagrange multipliers, special functions, transforms, uniform convergence of integrals, calculus of variations, Fourier series, and Lebesgue integration. (Prereq: MATH 420: Mathematical Analysis I (4 units))

**Units:** 4 — 4

### MATH 496: Capstone Directed Study

Under the guidance of a faculty member, students complete Capstone projects. Provides one-on-one guidance for students' research in mathematics, statistics, or mathematics education. To be taken concurrently with MATH 401. Course may be repeated up to three times.

**Units:** 2 — 2

### MATH 497: Independent Study

Student and faculty member select topic of study and number of credits.

**Units:** 1 — 6

### MATH 597: Independent Study

Student and faculty member select topic of study and number of credits.

**Units:** 1 — 6