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MATH 14 Support Topics for Business MATHEMATICS (MATH) 2 Units (May be taken for Pass/No Pass only) MATH TRAN Transfer Course Lecture: 36 12 Units Corequisite: MATH 140

MATH 5 Support Topics for Elementary Support will focus on essential algebra skills needed for success in 2 Units Business Calculus. For students concurrently enrolled in Math 140. (May be taken for Pass/No Pass only) Algebra support topics include analyzing linear, , rational, Lecture: 36 radical, exponential, and logarithmic functions, solving various Corequisite: MATH 51 including polynomial, rational, radical, exponential, and logarithmic equations, solving various inequalities including polynomial, rational, and Support will focus on essential , algebraic, and geometric absolute value inequalities, graphing techniques and curve sketching, skills needed for success in Elementary Algebra. Course is for students summation notation and Riemann sums, limits, differentiation rules and concurrently enrolled in Math 51. Support topics include order of the chain rule, integration techniques, functions of several variables, operations, rules of exponents, , linear, quadratic, rational, and double integration, and applications. radical equations, systems of equations, basic graphing techniques, factoring, polynomial, rational, and radical expressions, and applications. MATH 15 Support Topics for 2 Units MATH 7 Support Topics for Intermediate Algebra (May be taken for Pass/No Pass only) 2 Units Lecture: 36 (May be taken for Pass/No Pass only) Corequisite: MATH 150 Lecture: 36 Corequisite: MATH 71 Support will focus on essential geometry and algebra skills needed for success in Trigonometry. Course is for students concurrently Support will focus on essential algebra skills needed for success in enrolled in Math 150. Support topics include angle, triangle and Intermediate Algebra. Course is for students concurrently enrolled in parallelogram relationships, arc length and area of and sectors, Math 71. Support topics include real and their properties, linear transformations, simplifying algebraic expressions, solving algebraic expressions, and rational exponents, linear, quadratic, algebraic equations, functions, graphs, unit conversions, and algebraic rational, radical, exponential, and logarithmic equations, systems of proofs. linear and nonlinear equations, absolute value equations and inequalities, graphing techniques, writing equations of lines, functions and relations, MATH 16 Support Topics for Precalculus complex fractions, polynomial, rational, radical, and logarithmic 2 Units expressions, and applications. (May be taken for Pass/No Pass only) Lecture: 36 MATH 11 Support Topics for Corequisite: MATH 160 2 Units (May be taken for Pass/No Pass only) Support will focus on essential trigonometry and algebra skills needed for Lecture: 36 success in Precalculus Mathematics. Course is for students concurrently Corequisite: MATH 110 enrolled in Math 160. Support topics include set notation, complex rational expressions and radical expressions, lines, piecewise-defined Support will focus on essential skills required for success in Elementary functions, circles, modeling with functions, factoring, asymptotes, Statistics. For students concurrently enrolled in Elementary Statistics solving inequalities, simplifying exponential expressions, evaluating (Math 110). Review and support topics include the use of calculators trigonometric and inverse trigonometric functions, solving exponential, and technology to enhance understanding. Topics include inequality logarithmic, and trigonometric equations, vectors, and systems of relationships between numbers, graphing and interpreting linear equations. functions, applications with probabilities including notation, simulations, rounding, and significant digits. Applications with estimation, hypothesis MATH 18A Support Topics for Calculus I testing using appropriate calculations, and conclusions. 2 Units (Not Degree Applicable) (May be taken for Pass/No Pass only) MATH 13 Support Topics for College Algebra Lecture: 36 2 Units Corequisite: MATH 180 (May be taken for Pass/No Pass only) Lecture: 36 Formerly MATH 18 Corequisite: MATH 130 Support will focus on essential precalculus skills needed for success in Calculus. Course is for students concurrently enrolled in Calculus and Support will focus on essential algebra skills needed for success in (Math 180). Precalculus review topics include basic College Algebra. Course is for students concurrently enrolled in Math functions and transformations, equations of lines, difference quotients, 130. Support topics include algebraic expressions, integer and rational asymptotes, absolute value inequalities, zeros of polynomial functions, exponents, linear and nonlinear equations and inequalities, factoring function composition, applications of geometry and Pythagorean , systems of equations and inequalities, graphing techniques theorem, areas under curves using geometric formulas, sequences and and curve sketching, equations of lines, functions and relations, complex series. fractions, polynomial, rational, radical, exponential, and logarithmic expressions and equations, expanding binomials, and applications. 2 Mathematics (MATH)

MATH 18B Support Topics for Calculus II MATH 61 Plane Geometry 2 Units (Not Degree Applicable) 3 Units (Degree Applicable) (May be taken for Pass/No Pass only) Lecture: 54 Lecture: 36 Prerequisite: MATH 51 or MATH 51B or appropriate placement Corequisite: MATH 181 Points, lines, polygons and circles; their relationships to each other on Support will focus on essential precalculus and calculus skills needed plane surfaces; congruence, similarity and area. Introduction to inductive, for success in Calculus and Analytical Geometry II. This course is for deductive and indirect reasoning. The formal proof is introduced and students concurrently enrolled in Calculus and Analytical Geometry II practiced throughout the course. Stress is placed on accuracy of (MATH 181). Support topics include trigonometric functions, partial statement as a background for analytical and scientific reasoning. fractions, polynomial graphs, derivatives, antiderivatives, integration, MATH 70S Integrated Intermediate Algebra application of integrals, parametric equations and polar coordinates, 5 Units (Degree Applicable) sequences, seriesm, and power series. Lecture: 90 MATH 50 Pre-Algebra Prerequisite: MATH 50 or appropriate placement. 3 Units (Not Degree Applicable) Lecture: 54 Math 70S and 110S form a two-semester sequence that leads students Prerequisite: LERN 49 or appropriate placement. through college level statistics. Simplification, solving of equations, graphing, and applications are covered. Each is applied to the following Fundamental principles of mathematics designed to ease the transition mathematical functions: polynomial, rational, radical, exponential from arithmetic to algebra. Concepts, computational skills, thinking skills and logarithmic. Rates and proportions, linear systems of equations, and problem-solving skills are balanced to build proficiency in elementary inequalities, sequence, series, design of experiments, one- and two- topics from algebra and mastery in arithmetic. descriptive statistics are also covered. MATH 51 Elementary Algebra MATH 71 Intermediate Algebra 4 Units (Not Degree Applicable) 5 Units (Degree Applicable) Lecture: 72 Lecture: 90 Prerequisite: MATH 50 or appropriate placement Prerequisite: MATH 51 or MATH 51B or appropriate placement.

Basic algebra, equivalent to first year high school algebra. Includes: Extends concepts from elementary algebra to prepare students for operations with signed numbers and algebraic expressions; linear, college-level mathematics courses. Polynomial, rational, radical, quadratic, rational, and radical equations; linear inequalities of one and exponential and logarithmic expressions are simplified, equations solved two variables; slope, graphing, and equations of lines; introduction to and functions graphed and studied; linear and nonlinear systems of functions; systems of linear equations; exponent rules; polynomial equations and inequalities; conic sections; sequence, series and the operations; scientific notation; factoring; rational expressions; variation; radicals; fractional exponents; formulas; applications. MATH 71A Intermediate Algebra - First Half MATH 51A Elementary Algebra - First Half 3 Units (Not Degree Applicable) 3 Units (Not Degree Applicable) Lecture: 54 Lecture: 54 Prerequisite: MATH 51 or MATH 51B or appropriate placement. Prerequisite: MATH 50 or appropriate placement Algebra of functions, polynomials, and rational expressions; functions Contains the first half of elementary algebra. Operations with signed and their graphs; systems of equations with two or three variables; numbers and algebraic expressions, linear equations and inequalities, absolute value and compound inequalities. Covers approximately half of exponent rules, polynomial operations, scientific notation, factoring, the MATH 71 topics. A student must complete both MATH 71A and 71B solving quadratic equations by factoring, rational expressions and to have taken the equivalent of MATH 71, Intermediate Algebra. equations, formulas, variation, and applications. MATH 71B Intermediate Algebra - Second Half MATH 51B Elementary Algebra - Second Half 3 Units (Degree Applicable) 3 Units (Not Degree Applicable) Lecture: 54 Lecture: 54 Prerequisite: MATH 71A Prerequisite: MATH 51A Quadratic equations and graphs; exponents, radicals and ; Contains the second half of elementary algebra. Includes: Cartesian conic sections. Covers remaining MATH 71 topics. A student must , slope, graphing, and equations of lines, solving complete both MATH 71A AND 71B to have taken the equivalent of systems of linear equations, algebraic operations with radicals, solving MATH 71, Intermediate Algebra. equations with radicals, solving second degree equations using methods of and the . Students must complete both MATH 51A and MATH 51B to have taken the equivalent of Elementary Algebra (MATH 51). Mathematics (MATH) 3

MATH 71X Practical Intermediate Algebra MATH 110H Elementary Statistics - Honors 5 Units (Degree Applicable) 3 Units (Degree Applicable, CSU, UC, C-ID #: MATH 110) Lecture: 90 UC Credit Limitation Prerequisite: MATH 51 or MATH 51B or appropriate placement Lecture: 54 Prerequisite: (MATH 71 or MATH 71X or MATH 71B or appropriate Intermediate Algebra for the non-calculus path. Polynomial, rational, placement) and acceptance into the Honors Program. radical, exponential, and logarithmic expressions are simplified, equations solved, and real-world phenomena are modeled using least-squares Descriptive and inferential statistics and probability with an emphasis methods, functions graphed and analyzed; linear and nonlinear systems on understanding statistical methods. Descriptive analysis of sample of equations and inequalities; sequences, series, and probabilities; data statistics, distribution of discrete and continuous random variables, gathering instruments are used to sample data for curve fitting. estimation theory, tests of hypotheses, regression, correlation, and MATH 96 Strategies for Math Success analysis of variance. An honors course designed to provide an enriched 1 Unit (Not Degree Applicable) experience. May not receive credit for MATH 110 and MATH 110H. (May be taken for Pass/No Pass only) MATH 110S Integrated Statistics Lecture: 18 5 Units (Degree Applicable, CSU, UC) UC Credit Limitation Perspectives, understandings, and strategies to utilize a learning system Lecture: 90 for acquiring, understanding, remembering, and producing mathematical Prerequisite: MATH 70S or appropriate placement. knowledge. Course is appropriate for all levels of mathematics students. MATH 99 Special Projects in Mathematics An elementary course in descriptive and inferential statistics designed 2 Units (Degree Applicable, CSU) to support students who need more time to learn in an active learning Lecture: 36 environment. Observational and experimental studies, design of Prerequisite: Instructor authorization experiments, descriptive statistics, probability, discrete and continuous probability distributions, estimates, and hypothesis tests. For categorical In order to offer selected students recognition for their academic data, inferences include one or two sample proportions, one- and two- interests and ability and the opportunity to explore their disciplines to way tables (chi-square goodness of fit). For quantitative data, inferences greater depth, the Math Department from time to time offers special for one or two sample means, one-way Analysis of Variance (ANOVA). projects courses. The content of each course and the methods of study Inferences in linear correlation and regression are included. vary from semester to semester and depend on the particular project MATH 120 Finite Mathematics under consideration. Instructor authorization needed prior to enrollment. 3 Units (Degree Applicable, CSU, UC) MATH 100 Survey of College Mathematics Lecture: 54 3 Units (Degree Applicable, CSU, UC) Prerequisite: MATH 71 or MATH 71X or MATH 71B or appropriate Lecture: 54 placement Prerequisite: MATH 71 or MATH 71X or MATH 71B or appropriate placement Linear programming, theory, probability, statistics, stochastic processes, Markov chains, and math of finance. Applications for Mathematical methods and reasoning. Topics include: , logic, business, economics, and social sciences. counting methods, probability and statistics, with additional topics MATH 130 College Algebra selected from numeration and mathematical systems, theory, 4 Units (Degree Applicable, CSU, UC) geometry, , and mathematical modeling. UC Credit Limitation MATH 110 Elementary Statistics Lecture: 72 3 Units (Degree Applicable, CSU, UC, C-ID #: MATH 110) Prerequisite: MATH 71 or MATH 71B or appropriate placement UC Credit Limitation Lecture: 54 College-level Algebra course. Study of real numbers and sets, algebraic Prerequisite: MATH 71 or MATH 71X or MATH 71B or appropriate functions and relations, radicals and exponents, linear and quadratic placement equalities and inequalities, exponential and logarithmic functions, systems of linear and quadratic equations, complex numbers, series, Descriptive and inferential statistics and probability with emphasis theory of equations, mathematical induction and binomial formula. on understanding statistical methods. Descriptive analysis of sample MATH 140 Calculus for Business statistics, distribution of discrete and continuous random variables, 4 Units (Degree Applicable, CSU, UC) estimation theory, tests of hypotheses, regression, correlation, and UC Credit Limitation analysis of variance. Lecture: 72 Prerequisite: MATH 130 or MATH 160 or appropriate placement

Calculus for business, social science, and non-science majors. Algebraic, logarithmic, and exponential functions; limits; differentiation with applications; various techniques of integration with applications; differential equations; and multivariable calculus. 4 Mathematics (MATH)

MATH 150 Trigonometry MATH 280 Calculus and Analytic Geometry 3 Units (Degree Applicable, CSU) 5 Units (Degree Applicable, CSU, UC, C-ID #: MATH 230) Lecture: 54 Lecture: 90 Prerequisite: MATH 71 or MATH 71B or appropriate placement on Prerequisite: MATH 181 assessment measures Multivariate and vector calculus, which includes vectors in two and three Trigonometric functions and inverse trigonometric functions and the space and surfaces in space. Analysis of vector-valued functions. Partial graphical representations of these functions; solutions to right and derivatives, differentials, the chain rule, directional derivatives, and the oblique triangles with laws of sines and cosines; vectors; solutions to gradient. Extrema of functions of several variables with applications. trigonometric equations; identities; polar coordinates; complex numbers; Multiple integrals in various coordinate systems with applications. Vector and DeMoivre's Theorem. fields, line integrals, and independence of path. Green's Theorem, surface MATH 160 Precalculus Mathematics integrals, flux, divergence, and curl. Stokes' Theorem and the Divergence 4 Units (Degree Applicable, CSU, UC) Theorem. UC Credit Limitation MATH 285 and Differential Equations Lecture: 72 5 Units (Degree Applicable, CSU, UC) Prerequisite: MATH 150 or appropriate placement Lecture: 90 Prerequisite: MATH 280 Prepares students for the calculus sequence. Real-valued functions, including algebraic, trigonometric, exponential, and logarithmic functions. First order ordinary differential equations, with applications and Also includes proofs, inequalities, introductory analytical geometry, numerical methods. Solutions to higher order differential equations series, sequences, and vectors. using undetermined coefficients, variation of parameters, and power MATH 180 Calculus and Analytic Geometry series, with applications. Solutions to linear and non-linear systems 4 Units (Degree Applicable, CSU, UC) of differential equations, including numerical solutions. Matrix UC Credit Limitation algebra, solutions of linear systems of equations, and determinants. Lecture: 72 Vector spaces, linear independence, basis and dimension, subspace Prerequisite: MATH 160 or appropriate placement and , including the Gram-Schmidt procedure. Linear transformations, kernel and range, eigenvalues, eigenvectors, Differential and integral calculus with applications. Functions, limits, the diagonalization and symmetric matrices. derivative, curve sketching, optimization, and rules for differentiation of MATH 290 Differential Equations algebraic, exponential, logarithmic, and trigonometric functions with their 4 Units (Degree Applicable, CSU, UC) inverses, with applications. Indefinite and definite integrals. Lecture: 72 MATH 181 Calculus and Analytic Geometry Prerequisite: MATH 280 4 Units (Degree Applicable, CSU, UC, C-ID #: MATH 220) Lecture: 72 First-order ordinary differential equations, including separable, linear, Prerequisite: MATH 180 homogeneous, Bernoulli, and exact, with applications and numerical methods. Solutions to higher-order differential equations using Differential and integral calculus with infinite series and applications. undetermined coefficients, variation of parameters, power series, and Includes applications of integration, techniques of integration, numerical Laplace transforms, with applications. Solutions to linear and non-linear integration, indeterminate forms and improper integrals, differential systems of differential equations, including numerical solutions. equations, and polar coordinates. MATH 245 A Transition to Advanced Mathematics 3 Units (Degree Applicable, CSU, UC) Lecture: 54 Prerequisite: MATH 181

A transition to the rigors of upper- mathematics courses. Basic set theory and logic, relations, functions, mathematical induction, the well-ordering principle, countable and uncountable sets, the Schroder- Bernstein Theorem, the axiom of choice, Zorn's Lemma, the Heine-Borel Theorem, the Bolzano-Weierstrass Theorem. Special emphasis on how to present and understand mathematical proofs. MATH 260 Linear Algebra 3 Units (Degree Applicable, CSU, UC) Lecture: 54 Prerequisite: MATH 181

Matrices, linear systems, determinants, vector and inner product spaces, linear transforms, eigenvalues, and eigenvectors.