# Mathematics Courses and Prerequisite Chart

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The course descriptions below are taken from the current course outlines of record.

## X SUPERVISED PROGRAMMED LEARNING - 1.5 to 5 UNITS

Self-paced learning in mathematics using programmed materials under instructor supervision. Credit may be earned in Mathematics 55, 55A, 55B, 65, 65A, 65B, 71, and 107, according to the level of achievement. 1.5-5 hours. (See course descriptions for transferability.)

## 1 CALCULUS I - 5 UNITS

An introduction to single-variable differential and integral calculus including: functions, limits and continuity; techniques and applications of differentiation and integration; differentiation and integration of trigonometric, exponential and logarithmic functions; the Fundamental Theorem of Calculus; areas and volumes of solids of revolution. Prerequisite: Mathematics 20 (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. 5 hours, 0-1 laboratory hour. Transfer: CSU, UC*; GE: LPC AA/AS, CSU Area B, IGETC Area 2

## 2 CALCULUS II - 5 UNITS

Continuation of single-variable differential and integral calculus. Topics covered include: inverse and hyperbolic functions; techniques of integration; parametric equations; polar coordinates; sequences, series, power series and Taylor series. Introduction to Cartesian coordinates in three dimensions and operations with vectors. Primarily for mathematics, physical science and engineering majors. Prerequisite: Mathematics 1 (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics placement process. 5 hours lecture, 0-1 laboratory hours. Transfer: CSU, UC*; GE: LPC AA/AS, IGETC Area 2

## 3 MULTIVARIABLE CALCULUS 5 - UNITS

Vector valued functions, functions of several variables, partial differentiation, multiple integration, change of variables theorem, scalar and vector fields, gradient, divergence, curl, line integral, surface integral, Green’s Stokes’ and divergence theorem, applications. Prerequisite: Mathematics 2 (completed with a grade of "C" or higher). 5 hours lecture. Transfer: CSU, UC; GE: IGETC Area 2

## 5 ORDINARY DIFFERENTIAL EQUATIONS - 3.5 UNITS

Introduction to differential equations including the conditions under which a unique solution exists, techniques for obtaining solutions, and applications. Techniques include generation of series solutions, use of Laplace Transforms, and the use of eigenvalues to solve linear systems. Generation of exact solutions, approximate solutions, and graphs of solutions using MATLAB. Prerequisite: Mathematics 3 (completed with a grade of C or higher). 3 hours lecture, 1.5 hours laboratory. Transfer: CSU, UC; GE: IGETC Area 2

## 7 ELEMENTARY LINEAR ALGEBRA - 3.5 UNITS

An introduction to linear algebra including: techniques and theory needed to solve and classify systems of linear equations using Gaussian elimination and matrix algebra; properties of vectors in n-dimensions; generalized vector spaces, inner product spaces, basis, norms, orthogonality; eigenvalues, eigenspaces; and linear transformations. Selected applications of linear algebra, including the use of MATLAB™ to solve problems involving advanced numerical computation. Prerequisite: Mathematics 2 (completed with a grade of “C” or higher). 3 hours lecture, 1.5 hours laboratory. Transfer: CSU, UC; GE: IGETC Area 2

## 10 DISCRETE MATHEMATICS - 4 UNITS

Designed for majors in mathematics and computer science, this course provides an introduction to discrete mathematical structures and their applications, including: propositional and predicate logic; rules of inference; quantifiers; elements of integer number theory; set theory; methods of proof; induction; combinatorics and discrete probability; functions and relations; recursive definitions and recurrence relations; elements of graph theory and trees. Applications include: analysis of algorithms, Boolean algebras and digital logic circuits. Prerequisite: Mathematics 1 (completed with a grade of “C” or higher). 4 hours lecture, 1 hour laboratory. Transfer: CSU, UC; GE: IGETC Area 2

## 20 PRE-CALCULUS MATHEMATICS - 5 UNITS

Rational and polynomial functions with emphasis on logical development and graphing. Solution of polynomial equations and inequalities, graphing conic sections, mathematical induction, binomial theorem; strengthening of skills in working with exponential, logarithmic, and trigonometric functions, equations, graphs, and applications. Prerequisite: Mathematics 36, 36Y or Mathematics 38 (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. 5 hours lecture, 1 hour laboratory. Transfer: CSU, UC*; GE: LPC AA/AS, CSU Area B, IGETC Area 2

## 33 FINITE MATHEMATICS - 4 UNITS

Straight lines, systems of linear equations, matrices, systems of linear inequalities, linear programming, mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to probability. Applications in business, economics and social sciences. Prerequisite: Mathematics 55 or 55B or 55Y (completed with a grade of "C" or higher) or an appropriate skill level as demonstrated through the mathematics assessment process. 4 hours lecture, 1 hour laboratory. Transfer: CSU, UC*; GE: LPC AA/AS, CSU Area B, IGETC Area 2

## 34 CALCULUS FOR BUSINESS AND SOCIAL SCIENCES - 5 UNITS

Functions and their graphs; limits of functions; differential and integral calculus of algebraic, exponential and logarithmic functions. Applications in business, economics, and social sciences and use of graphing calculators. Partial derivatives and the method of LaGrange multipliers. Prerequisite: Mathematics 55 or 55B or 55Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics Assessment process. 5 hours lecture, 1 hour laboratory. Transfer: CSU, UC*; GE: LPC AA/AS, CSU GE Area B; IGETC Area 2.

## 38 TRIGONOMETRY WITH GEOMETRY - 5 UNITS

Plane trigonometry with topics from plane geometry. Geometry includes properties of polygons, parallel and perpendicular lines, congruence and similarity, area, volumes and surface area. Trigonometry includes definitions of the trigonometric functions, graphs of the trigonometric functions, trigonometric equations and inverse trigonometric functions, identities, polar coordinates and complex numbers. Applications involving right triangles, law of sines and law of cosines. Prerequisite: Mathematics 55 or 55B or 55Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. May not receive credit if Mathematics 36 or 36Y have been completed. 5 lecture hours, 1 laboratory hour. Transfer: CSU; GE: LPC AA/AS.

## 42 INTRODUCTION TO PROBABILITY AND STATISTICS - 3 UNITS

Descriptive statistics, including measures of central tendency and dispersion; elements of probability; tests of statistical hypotheses; correlation and regression; applications in various fields. Introduction to the use of a computer software package to complete both descriptive and inferential statistics problems. Prerequisite: Mathematics 55 or 55B or 55Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. 3 hours lecture, 1 hour laboratory. Transfer: CSU, UC*; GE: LPC AA/AS, CSU Area B, IGETC Area 2

## 44 STATISTICS AND PROBABILITY - 5 UNITS

Descriptive Statistics, measures of central tendency, dispersion and position; elements of probability; confidence intervals; hypothesis tests; two-population comparisons; correlation and regression; goodness of fit, analysis of variance, non-parametric tests; and application in various fields. Introduction to the use of a computer software package to complete both descriptive and inferential statistics problems. Prerequisite: Mathematics 55, 55B or 55Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. 5 hours lecture, 1 hour laboratory. Transfer: CSU, UC*; GE: LPC AA/AS, CSU Area B, IGTEC Area 2

## 45 COLLEGE ALGEBRA - 3 UNITS

Polynomial, rational, exponential, and logarithmic functions; theory of equations; matrices; translation of functions; sequences, series and the binomial theorem. Prerequisite: Math 55 or Math 55B or 55Y (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the Mathematics placement process. 3 hours, 1 laboratory hours. Transfer: CSU, UC*; GE: LPC AA/AS, CSU Area B

## 55 INTERMEDIATE ALGEBRA - 5 UNITS

Intermediate algebra concepts, including: An introduction to functions; linear and absolute value functions; absolute value equations and inequalities; compound linear inequalities; systems of linear equations in three variables and matrix solutions; rational expressions, functions and equations; radical expressions, functions and equations; rational exponents; complex numbers; quadratic functions and equations; inverse of a function; exponential and logarithmic functions; properties of logarithms; exponential and logarithmic equations; conic sections; and systems of non-linear equations and inequalities. Multiple representations, applications and modeling with functions are emphasized throughout. Prerequisite: Math 65 or 65B or 65Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. May not receive credit if Mathematics 55B or 55Y have been completed. 5 lecture hours, 1 laboratory hour. GE: LPC AA/AS

## 55A INTERMEDIATE ALGEBRA A - 2.5 UNITS

Concepts covered in the first half of Mathematics 55 Intermediate Algebra, including: An introduction to functions; linear and absolute value functions; absolute value equations and inequalities; compound linear inequalities; rational expressions, functions and equations; radical expressions, functions and equations; rational exponents; and complex numbers. Multiple representations, applications and modeling with functions are emphasized throughout. Prerequisite: Math 65 or 65B or 65Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. May not receive credit if Mathematics 55 or 55X have been completed. 2.5 lecture hours, 0 – 1 laboratory hour.

## 55B INTERMEDIATE ALGEBRA B - 2.5 UNITS

Concepts covered in the second half of Mathematics 55 Intermediate Algebra, including: systems of linear equations in three variables and matrix solutions; inverse of a function; exponential and logarithmic functions; properties of logarithms; exponential and logarithmic equations; conic sections; systems on non-linear equations and inequalities. Multiple representations, applications and modeling with functions are emphasized throughout. Prerequisite: Math 55A or 55X (completed with a grade of “C” or higher). May not receive credit if Mathematics 55 or 55Y have been completed. 2.5 lecture hours, 0 – 1 laboratory hour. GE: LPC AA/AS

## 65 ELEMENTARY ALGEBRA - 5 UNITS

Elementary algebra concepts, including: real numbers and their properties; algebraic expressions; integer exponents; operations with polynomial expressions; linear and quadratic equations; linear inequalities and set notation; graphs of linear equations and inequalities; slope; systems of linear equations and inequalities; and, an introduction to rational expressions and modeling with linear and quadratic equations. Prerequisite: Mathematics 106 or 107 or 107Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. May not receive credit if Mathematics 65B or 65Y have been completed. 5 lecture hours, 1 laboratory hour. GE: LPC AA/AS

## 65A ELEMENTARY ALGEBRA A - 2.5 UNITS

Concepts covered in the first half of Mathematics 65 Elementary Algebra, including: real numbers and their properties; algebraic expressions; linear equations; linear inequalities and set notation; graphs of linear equations and inequalities in two variables; slope; systems of linear equations and inequalities; and, an introduction to modeling with linear equations. This course is designed for those with no previous algebra background. Prerequisite: Mathematics 106 or 107 or 107Y (completed with a grade of “C” or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. May not receive credit if Mathematics 65 or 65X have been completed. 2.5 lecture hours, 0 – 1 laboratory hour.

## 65B ELEMENTARY ALGEBRA B - 2.5 UNITS

Concepts covered in the second half of Mathematics 65 Elementary Algebra, including: integer exponents; operations with polynomial expressions; factoring techniques; quadratic equations and modeling with quadratic equations; and an introduction to rational expressions. Prerequisite: Mathematics 65A or 65X (completed with a grade of “C” or higher). May not receive credit if Mathematics 65 or 65Y have been completed. 2.5 lecture hours, 0 – 1 laboratory hour. GE: LPC AA/AS

## 71 APPLIED MATHEMATICS FOR TECHNICIANS - 3 UNITS

This course provides a survey of mathematical techniques used in the technical trades including: Arithmetic, both by-hand and with calculator; ratios, rates and proportions; metric and U.S. systems of measurements; an introduction to linear equations; scientific notation; plane and solid geometry; and, triangle trigonometry. There is an emphasis on practical applications related to a variety of technical fields throughout. 3 hours lecture. GE: LPC AA/AS

## 71A APPLIED MATHEMATICS FOR TECHNICIANS A- 1.5 UNITS

This course provides a survey of mathematical techniques used in the technical trades including: Arithmetic, both by-hand and with calculator; ratios, rates and proportions; metric and U.S. systems of measurement. There is an emphasis on practical applications related to a variety of technical fields throughout. 1.5 hours lecture.

## 71B APPLIED MATHEMATICS FOR TECHNICIANS - 1.5 UNITS

This course provides a survey of mathematical techniques used in the technical trades including: an introduction to linear equations; scientific notation; plane and solid geometry; and, triangle trigonometry. There is an emphasis on practical applications related to a variety of technical fields throughout. Prerequisite: Mathematics 71A or 71X (completed with a grade of “C” or higher). May not receive credit if Mathematics 71 or 71Y or INDT 74 have been completed. 1.5 lecture hours.

## 107 PRE-ALGEBRA - 4 UNITS

This course is intended to serve as a bridge between arithmetic and Elementary Algebra. It includes a review of arithmetic, operations involving signed integers, fractions and decimals, variables and variable expressions, simple linear equations and their graphs, percent and proportion, introduction to statistics, geometry and measurement, and application problems. 3 hours lecture, 3 hours laboratory.

## 107A PRE-ALGEBRA A- 2 UNITS

This course is intended to serve as a bridge between arithmetic and Elementary Algebra. It includes a review of concepts covered in the first half of Mathematics 107 Pre-Algebra, including: review of arithmetic, operations involving signed integers, fractions, variables and variable expressions, and simple linear equations. 1.5 hours lecture, 1.5 hours laboratory.

## 107B PRE-ALGEBRA B- 2 UNITS

This course is intended to serve as a bridge between arithmetic and Elementary Algebra. It includes a review of concepts covered in the second half of Mathematics 107 Pre-Algebra, including: decimals, graphs of simple linear equations, percent and proportion, introduction to statistics, geometry and measurement, and application problems. Prerequisite: Mathematics 107A or 107X (completed with a grade of “C” or higher). May not receive credit if Mathematics 107 or 107Y has been completed. 1.5 hours lecture, 1.5 hours laboratory.

## 100 PRE-ALGEBRA AND ALGEBRA REVIEW

Review basic mathematics and algebra content prior to taking the assessment exam for placement into a mathematics course or as a refresher prior to taking a mathematics course after a significant amount of time has passed since taking the prerequisite course or assessment. The course will consist of small group lecture and/or independent study using a computer program to review and refine those concepts as needed by each student. 3 hours laboratory.