5 UNITS, Lecture 5 hours

Prerequisite: Mathematics 112 with a satisfactory grade or equivalent.

This course covers operations on real numbers and algebraic expressions, solving linear equations and inequalities in one variable, graphing linear equations and inequalities in two variables, solving systems of linear equations in two variables, exponents, operations on polynomials, factoring polynomials, operations on rational expressions, solving rational equations, simplifying radical expressions, solving radical equations, solving quadratic equations, and graphing quadratic equations.

3 UNITS (A), Lecture 3 hours

Prerequisite: Mathematics 115 with a satisfactory grade or equivalent.

The student learns the definitions, axioms and theorems of geometry relating to angles, lines, circles and polygons. Basic constructions are introduced. The meaning and techniques of logical proofs are heavily emphasized.

5 UNITS Lecture 5 hours

Prerequisite: Mathematics 115 with a satisfactory grade or equivalent.

Note: A maximum of 8 UNITS may be earned by any combination of Mathematics 125, 240, and 245.

Students learn techniques for solving compound linear inequalities as well as absolute value equations and inequalities, solving systems of linear equations in two and three variables, simplifying non-linear expressions and solving non-linear equations such as polynomial, rational, radical, exponential, and logarithmic. Students learn techniques for rewriting the equation in the standard form for parabola and circle, and graph. Students learn how to compute terms and sums of arithmetic and geometric series. Students will apply the binomial theorem to expand the binomial with given power. Applications are included in a wide variety of word problems.

1 UNIT (CSU) Laboratory 3 hours

Co-requisite: One of the following Co-req: Math 215, 216, 230, 236, 240, 245, 260, 261, 262, 263, 270, or 275.

Students supplement and enhance their learning in mathematics by providing tutorial and self-help assistance, calculators, computers, programmed text, and other learning aids for baccalaureate level mathematics courses.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 125 with a satisfactory grade or equivalent.

This course is the first of two in a sequence designed for prospective elementary school teachers. The student will learn topics including sets and relations, numbering systems, and elementary number theory. The main emphasis, however, will be understanding the structure of systems of whole numbers, integers, and rational numbers.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 215 with a satisfactory grade or equivalent.

This course is the second of two in a sequence for prospective elementary school teachers. Topics include decimal and real numbers, rational numbers, abstract mathematical systems, geometry and the metric system.

4 UNITS (UC: CSU) Lecture 4 hours

Prerequisite: Mathematics 125 with a satisfactory grade or equivalent.

This course is an introduction to probability, descriptive and inferential statistics including measures of central tendency and dispersion, sampling, and estimation. Hypothesis testing, analysis of variance, test of independence, linear correlation and regression analysis also are covered.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 125 with a satisfactory grade or equivalent.

Students receive instruction in topics which include linear equations and functions, applications of linear functions, systems of linear equations, matrices, system of linear inequalities, linear programming using the graphical method, mathematics of finance, logic, set theory, probability, basic counting, and statistics.

5 UNITS (UC: CSU) Lecture 5 hours

Prerequisite: Mathematics 125 with a satisfactory grade or equivalent.

This course consists of elementary differential and integral calculus of algebraic, exponential and logarithmic functions, as well as derivatives and the method of Lagrange multipliers. Applications to business and the social sciences are emphasized.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 236 with a satisfactory grade or equivalent.

Students learn advanced calculus topics with emphasis on business and social science applications. Topics include definite integrals, probability, techniques of integration, improper integrals, numerical integration, elementary differential equations, functions of several variables, partial derivatives, chain rule, total differentials, optimization of functions of several variables without and with constraints, method of Lagrange multipliers, double integrals. NOTE: This course is not offered every semester. See Class Schedule.

3 UNITS (CSU) Lecture 3 hours

Prerequisite: Both Mathematics 125 and 121 with satisfactory grades or equivalent.

A maximum of 8 UNITS of credit may be earned by any combination of Mathematics 125, 240 and 245.

Students in Math 240 study the sine, cosine, and tangent functions, including a study of their graphs, inverses of the functions, solution of triangles, models for periodic phenomena, identities, conditional equations, and polar coordinates. Students also learn the basic properties of the cotangent, secant, and cosecant functions.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 125 with a satisfactory grade or equivalent.

Students receive instruction to solve linear, rational, polynomial, exponential, and logarithmic equations; graph linear, rational, polynomial, exponential, and logarithmic functions; solve linear and nonlinear systems of equations and inequalities; sequences and series.

5 UNITS (CSU) Lecture 5 hours

Prerequisite: Mathematics 125 with satisfactory grades or equivalent.

Students learn the definitions, axioms, and theorems of geometry relating to angles, lines, circles, and polygons. Practice in critical thinking and developing logical proofs are emphasized. This course also includes the study of the sine, cosine, and tangent functions, including a study of their graphs, inverses of the functions, basic properties of the cotangent, secant, and cosecant functions, measurement of angles in degrees and in radians, evaluating triangles, solving trigonometric equations, models for periodic phenomena, trigonometric identities, vectors, complex number, and polar coordinates.

5 UNITS (UC: CSU) Lecture 5 hours

Prerequisite: Mathematics 240 with a satisfactory grade or equivalent.

Students prepare for calculus, which covers the properties of polynomial, rational, algebraic, trigonometric, inverse trigonometric, exponential and logarithmic identities and equations, trigonometric form of complex numbers and DeMoivre’s Theorem, conic sections with translation and rotation of axes, nonlinear systems of equations and inequalities, vector algebra with dot and cross products, polar coordinates and graphs of polar functions, partial fractions and mathematical induction.

5 UNITS (UC: CSU) Lecture 5 hours

Prerequisite: Mathematics 260 with a satisfactory grade or equivalent.

This is the first of a three-course sequence in calculus. Topics include limits and continuity, rates of change, derivatives, applications of differentiation, integrals, the Fundamental Theorem of Calculus, and applications of integration.

5 UNITS (UC: CSU) Lecture 5 hours

Prerequisite: Mathematics 261 with a satisfactory grade or equivalent.

This is the second in a three-course sequence in calculus. Topics include differentiation and integration of logarithmic, exponential, circular and hyperbolic functions and their inverses, indeterminate forms, improper integrals, standard techniques of integration, applications of integration to problems from economics, biology and probability, parametric equations and polar coordinates, infinite sequences and series, and representation of functions as power series.

5 UNITS (UC: CSU) Lecture 5 hours

Prerequisite: Mathematics 262 with a satisfactory grade or equivalent.

Students solve problems from vectors calculus, parametric equations, surfaces, partial differentiation, gradient, maxima and minima for functions of several variables, multiple integrals, surface integrals, and line integrals. Students consider physical and mechanical applications of Green’s Theorem, Divergence Theorem, and Stokes’ Theorem.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 261 with a satisfactory grade or equivalent.

This course develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include 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. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included.

5 UNITS (UC: CSU) Lecture 5 hours

Prerequisite: Mathematics 262 with a satisfactory grade or equivalent.

Students study logic, algorithms, number systems, mathematical induction, sets, counting principles, probability, Boolean algebra, logic network, Pigeonhole principle, cardinality and computability, recurrence relations and recursion, graph theory, switching circuits, trees.

3 UNITS (UC: CSU) Lecture 3 hours

Prerequisite: Mathematics 262 with a satisfactory grade or equivalent.

Students learn to categorize different types of differential equations. Students learn to use techniques such as separation of variables, exact differentials, homogeneity, and change-of-variable (substitution) to solve first-order equations as well as first-order Initial Value Problems (IVPs). Students apply this knowledge to solve real-world problems such as population growth and mixture problems. Students learn to solve higher-order linear differential equations using constant coefficient technique, the method of undetermined coefficients and variation of parameters. Students apply this knowledge to physics applications such as simple harmonic motion. Students solve equations of higher-order with variable coefficients applying specific techniques based on the type of the given equations. Topics Include: Cauchy-Euler Equations, Power Series solutions, Bessel’s Equations, and Legendre’s Equation. Students learn the Laplace transform and its properties and apply this knowledge to solving various differential equations as well as IVPs. Students use techniques for solving Systems of Linear Differential Equations.