Mathematics
Mathematics
Program Purpose: Students who complete Mathematics courses will demonstrate critical thinking skills, analyze abstract concepts, and transition from the concrete to the abstract in mathematical thinking.
The Mathematics program offers training in both pure and applied mathematics, leading to careers in research, education, business, industry, and government, including such professions as educators, statisticians, actuaries, and operations research analysts. Many areas, such as the physical and social sciences, engineering, economic, and business, are dependent upon the use of applied mathematics in developing solutions to practical problems.
Students who complete Mathematics courses will demonstrate critical thinking skills, analyze abstract concepts, and transition from the concrete to the abstract in mathematical thinking.
NOTE: Some courses may have credit limitations. Refer to the Credit Limitations and UC Credit Limitations areas, and the UC Transfer Course Agreement page for details.
Reviews briefly arithmetic including integers, fractions, and decimals. Covers algebraic expressions, linear equations and inequalities, graphing lines, systems of linear equations, integer exponents, polynomials, factoring of polynomials, solving quadratic equations by the factoring method, and rational expressions. OTHER: MATH M01 is equivalent to MATH M01A and MATH M01B. Unit credit may be received for either MATH M01 or (MATH M01A and MATH M01B, or MATH M04A), but not both.
Reviews briefly linear equations and inequalities, graphing, factoring, and rational expressions. Covers systems of linear equations, rational functions, complex fractions, rational exponents and radicals, complex numbers, quadratic equations, graphs of parabolas, functions, composition and inverse functions, exponential and logarithmic functions.
Covers quadratic equations, linear and non-linear inequalities, absolute value equations and inequalities, complex numbers, functions, polynomial functions, rational functions, exponential functions, logarithmic functions, and systems of equations. Includes the theory of polynomial equations and analytic geometry, conic sections, sequences and series.
Studies the trigonometric functions, their inverses and their graphs. Covers identities and proofs related to trigonometric expressions and solving trigonometric equations, right triangles, and general triangles using the law of cosines and the law of sines. Provides an introduction to polar coordinates, vectors, and vector operations.
Integrates college algebra and trigonometry. Includes basic algebraic concepts, equations and inequalities of the first and second degree, systems of equations and inequalities, functions and graphs, linear and quadratic functions, polynomial functions of higher degree, rational functions, exponential and logarithmic functions, trigonometric functions, analytical trigonometry, and polar coordinates.
Prepares students for transfer-level statistics by covering core concepts from elementary algebra, intermediate algebra, and descriptive statistics. Provides algebraic and statistical problem solving techniques. Uses technology to analyze data sets.
Prepares students for algebra. Emphasizes basic arithmetic operations on whole numbers, signed numbers, fractions, and decimals. Provides drills to reinforce operations. Focuses on problem solving and practical application such as percent, proportion, and measurement. Includes an introduction to basic algebra. Completing MATH M09 is the same as completing MATH M09A, M09B, and M09C. Taking MATH M09 and MATH M09A, M09B, M09C receives a maximum credit of 3 units.
Focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real numbers systems and subsystems. Emphasizes the comprehension and analysis of mathematical concepts and applications of logical reasoning.
Covers theory of functions including operations on functions, graphs, domain and range, and evaluation. Includes types of functions such as linear, quadratic, polynomial, rational, exponential and logarithmic functions. Analyzes graphs including curve sketching, intercepts, transformations, vertices and asymptotes. Covers linear and non-linear inequalities, solving exponential and logarithmic equations and complex numbers. Course is intended primarily as a prerequisite for students taking Business Calculus, and for students requiring college algebra content for non-STEM majors.
Introduces liberal arts students to mathematical ideas necessary for their careers and daily lives. Includes topics in logic, quantitative information in the real world, managing finances, statistical reasoning, and mathematics in politics. Enhances mathematical ideas with topics in fields such as the arts, quantitative reasoning, and more.
Explores the nature of statistical methods, including description of sample data, probability, theoretical frequency distributions, sampling, estimation, testing hypotheses and special topics. Provides problem-solving techniques.
Explores the nature of statistical methods, including description of sample data, probability, theoretical frequency distributions, sampling, estimation, testing hypotheses and special topics. Provides problem solving techniques. Uses technology to analyze large data sets. Honors work challenges students to be more analytical and creative through expanded assignments and enrichment opportunities.
Covers limits, continuity, and differentiation. Applies differential calculus to problems in business, economics, social and biological sciences. Introduces anti-differentiation and its applications in business and economics.
Includes integration, elementary and separable differential equations, functions of several variables, partial derivatives, relative maxima and minima, Lagrange multipliers, method of least squares, double integrals, infinite series, Taylor approximation, and Newton’s method. Applies calculus to problems in business, economics, and social and biological sciences.
Covers ratios, fractions, decimals and percents. Includes unit conversions, metric and household abbreviations, use of formulas, proportion and unit simplification. Coaches how to perform mental estimations and mental calculations.
Covers elements of discrete mathematics which have application to computer science. Includes the following topics: logic, sets, functions, relations, proof techniques, mathematical induction, recurrence relations, graphs, trees, discrete probability, Boolean algebra and a brief introduction to programming.
Covers limits, continuity, differentiation and integration of algebraic functions. Teaches differentiation and integration of transcendental functions with applications.
Covers limits, continuity, differentiation and integration of algebraic functions, and differentiation and integration of transcendental functions with applications. Honors work challenges students to be more analytical and creative through expanded assignments and enrichment opportunities.
Reviews integration. Covers area, volume, arc length, surface area, centers of mass, physics applications, techniques of integration, improper integrals, sequences, series, Taylor’s Theorem, parametric equations, polar coordinates, and conic sections with translations.
Reviews integration. Covers area, volume, arc length, surface area, centers of mass, physics applications, techniques of integration, improper integrals, sequences, series, Taylor’s Theorem, parametric equations, polar coordinates, and conic sections with translations. Honors work challenges students to be more analytical and creative through expanded assignments and enrichment opportunities.
Covers vectors in plane and in three-dimensional space, dot and cross products, spherical and cylindrical coordinates, vector-values functions, functions of several variables, partial derivatives, gradients, and Lagrange multipliers. Presents multiple integrals and their applications, vector calculus with line and surface integrals, Green’s, Stokes', and Divergence Theorems and applications.
Develops the techniques and theory needed to solve and classify systems of linear equations. Covers solution techniques including row operations, Gaussian elimination, and matrix algebra. Investigates the properties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Presents vector space and matrix theory including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Involves selected applications of linear algebra.
Covers ordinary differential equations, equations with constant coefficients, variation of parameters, Laplace transforms, systems of linear equations, first order differential equations, series solutions, and existence and uniqueness of solutions. Emphasizes applications to physics and engineering, and provides an introduction to numerical solutions.
Introduces statistical learning for data science. Emphasizes the following types of statistical models: Regression (Multiple Linear and Polynomial Regressions), Classification (Naive Bayes, Discriminant Analysis, Logistic Regression), Supervised Machine Learning (K-Nearest Neighbor, Tree models and their extensions), and Unsupervised Machine Learning (Principal Component Analysis, K-Means clustering). Covers applications of statistical programming for data science and the ethical use of data.
Introduces machine learning algorithms with linear algebra for data science. Emphasizes the mathematical foundations of ensemble methods, discriminant analysis, deep learning, and neural networks as well as the ethical use of data. Covers applications of algebraic programming for data science.
Allows independent study for students who wish to extend their knowledge of a particular area of mathematics through research and study. Utilizes an approved independent project. Includes one-on-one work with instructor. Interested students should contact a Mathematics instructor for assistance in developing a contract for learning about a specific topic.
Reviews the prerequisite materials necessary to be successful in MATH M25A. Includes rationalizing denominators, factoring, logarithms, piecewise functions, and trigonometric functions.
Reviews the prerequisite materials necessary to be successful in MATH M25B. Includes differentiation of algebraic and transcendental functions, integration, u-substitution, and the chain rule for differentiation.
NONCREDIT COURSES
Prepares student for the prerequisite materials necessary to be successful in Math M01. Includes fractions, decimals, exponents, and solving linear equations. Offered Pass/No Pass only (no letter grade possible).
Prepares student for the prerequisite materials necessary to be successful in MATH M03. Includes linear equations, quadratic equations, factoring polynomials, quadratic, rational, exponential and logarithmic functions, and graphing. Offered Pass/No Pass only (no letter grade possible).
Reviews the prerequisite material necessary to be successful in either MATH M05, MATH M07 or MATH M11. Includes factoring expressions; equations of lines; rational, radical and quadratic expressions and equations; and logarithms.
Provides review for topics necessary for success in College Algebra, including linear equations and inequalities, graphing, factoring, and rational expressions. Covers systems of linear equations, rational functions, rational exponents and radicals, complex numbers, quadratic equations, graphs of parabolas, functions, composition and inverse functions, exponential and logarithmic functions.
Reviews topics necessary for success in College Algebra for Liberal Arts, including linear equations and inequalities, graphing, factoring, and rational expressions. Covers systems of linear equations, rational functions, rational exponents and radicals, complex numbers, quadratic equations, graphs of parabolas, functions, composition and inverse functions, exponential and logarithmic functions.
Reviews prerequisite material for successful completion of MATH M15. Reviews numbers and the number line, operations on numbers, sets and set notations, and equations and inequalities. Provides practice on graphing points and lines in two dimensions, reading tables and graphs, and approximating areas.
Reviews the prerequisite material necessary to be successful in MATH M15. Covers numbers and the number line, operations on numbers, sets and set notations, equations and inequalities. Includes graphing points and lines in two dimensions, reading tables and graphs, and approximating areas.
Dean
Matt Calfin, Phone (805) 378-1448
Faculty
Phil Abramoff, Kevin Balas, Renee Butler, Chris Copeland, Laurel Drane, Marcos Enriquez, Claudia Gutierrez, Vahe Khachadoorian, Michael Nava, Diana Nguyen, Tom Ogimachi, Curtis Paul, Rena Petrello, Brendan Purdy, Cynthia Reed, Daniel Rubinstein, Tammy Terzian, Katrina Topolinski
Counselors
Daniel Aguilar, Samantha Zaldivar