- Las Positas College
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- Mathematics Courses

Mathematics

# Mathematics Courses and Prerequisite Chart

### Click HERE to see The Mathematics Prerequisite Flow Chart as of Fall 2016.

## Please Note:

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

## MATH EMPORIUM SUPERVISED PROGRAMMED LEARNING - 1.5 to 5 UNITS

Self-accelerated learning in mathematics using programmed materials under instructor supervision. Credit may be earned in Mathematics 55, 55A, 55B, 65, 65A, 65B, 71, 71A, 71B, 107, 107A or 107B, 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, 38, or 39 (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 50 or 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 (offered for students pursuing the A.S. Engineering Technology Degree)

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.

## 39 TRIGONOMETRY - 4 UNITS

Plane 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. 4 lecture hours, 1 laboratory hour. Transfer: CSU; GE: LPC AA/AS.

## 40 STATISTICS AND PROBABILITY - 4 UNITS

Descriptive statistics, including 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; applications in various fields. Introduction to the use of a computer software package to complete both descriptive and inferential statistics problems. Prerequisite: Mathematics 50, 55, 55B or 55Y (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the Mathematics assessment process. 4 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

## 47 MATHEMATICS FOR LIBERAL ARTS - 3 UNITS

An introduction to a variety of mathematical concepts for students interested in liberal arts. Intended to cultivate an appreciation of the significance of mathematics in daily life and help develop students mathematical reasoning. Topics include personal finance, probability & statistics, logic, exponential growth, and graph theory. Prerequisite: Mathematics 50, 55, 55Y, 55B or equivalent (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 B4, IGETC Area 2A.

## 50 CORE INTERMEDIATE ALGEBRA - 4 UNITS (Starting Fall 2016)

Core concepts of intermediate algebra are explored within the context of the function. Function concepts covered include: distinction between functions and relations, domain and range, function notation, multiple representation of functions, behavior of functions, operations with functions (including composition), and one-to-one and invertible functions. Types of functions considered: linear, absolute value, polynomial, rational, radical, exponential and logarithmic functions. The course includes an introduction to probability, counting and quantitative data. Standards for mathematical practice, applications of functions, and modeling with functions are emphasized throughout. Prerequisite: Mathematics 65, 65B, or equivalent (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the mathematics assessment process. 4 hours lecture, 1 hour laboratory. GE: LPC AA/AS

## 51 ALGEBRA BRIDGE - 2 UNITS

This course is intended for students who completed Math 50 Core Intermediate Algebra and need the equivalent of Math 55 Intermediate Algebra. The course covers content included in Math 55 but not Math 50. Topics include: operations with rational expressions; rational equations; operations with radical expressions; complex numbers; quadratic inequalities and equations quadratic in form; systems of three linear equations; properties of logarithms and logarithmic equations; conicsections; and non-linear systems. Students may not receive credit for both Math 55 and the combination of Math 50 and Math 51. Prerequisite: Mathematics 50 (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the mathematics assessment process. 2 hours lecture, 0 hour laboratory.

## 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

(Enrollment in this course is based on instructor referral only. Students must first enroll in a Math 55 Emporium course. These courses have section numbers that begin with an X, such as X05. During the semester your instructor will work with you to determine your eligibility to transfer into Math 55A, plus its support course if needed. For more information about Emporium courses, go to http://www.laspositascollege.edu/MathEmporium. If you have any question, please contact the Math Emporium Coordinator Jennie Graham at jgraham@laspositascollege.edu, or your counselor.)

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

## 55E INTERMEDIATE ALGEBRA A COREQUISITE SUPPORT - 2.5 UNITS

This credit course is a co-requisite for Intermediate Algebra A, the first half of Intermediate Algebra. This course is only available through manual enrollment for students who are taking Intermediate Algebra in the Emporium mode and have completed at least the Intermediate Algebra A material. This course will support students in achieving Intermediate Algebra A learning goals by providing support around mastering the necessary arithmetic, algebraic and geometric concepts that are relevant to their Intermediate Algebra A course. This course will provide study strategies that promote understanding and improve performance, more in-depth investigation of core concepts that are difficult for students to master, and learning skills. Corequisite: Math 55A Prerequisite: Math 65 or Math 65B with a minimum grade of C.

## 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

(Enrollment in this course is based on instructor referral only. Students must first enroll in a Math 65 Emporium course. These courses have section numbers that begin with an X, such as X05. During the semester your instructor will work with you to determine your eligibility to transfer into Math 65A, plus its support course if needed. For more information about Emporium courses, go to http://www.laspositascollege.edu/MathEmporium. If you have any question, please contact the Math Emporium Coordinator Jennie Graham at jgraham@laspositascollege.edu, or your counselor.)

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

## 65E ELEMENTARY ALGEBRA A COREQUISITE SUPPORT -2.5 UNITS

This credit course is a co-requisite for Elementary Algebra A, the first half of Elementary Algebra. This course is only available through manual enrollment for students who are taking Elementary Algebra in the Emporium mode and have completed at least the Elementary Algebra A material. This course will support students in achieving Elementary Algebra A learning goals by providing support around mastering the necessary arithmetic, algebraic and geometric concepts that are relevant to their Elementary Algebra A course. This course will provide study strategies that promote understanding and improve performance, more in-depth investigation of core concepts that are difficult for students to master, and learning skills. Corequisite: MATH 65A Prerequisite: MATH 107 or MATH 107B with a minimum grade of C.

## 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

(Enrollment in this course is based on instructor referral only. Students must first enroll in a Math 107 Emporium course. These courses have section numbers that begin with an X, such as X05. During the semester your instructor will work with you to determine your eligibility to transfer into Math 107A, plus its support course if needed. For more information about Emporium courses, go to http://www.laspositascollege.edu/MathEmporium. If you have any question, please contact the Math Emporium Coordinator Jennie Graham at jgraham@laspositascollege.edu, or your counselor.)

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.

## 107E PRE-ALGEBRA A COREQUISITE SUPPORT - 2 UNITS

This credit course is a co-requisite for Pre-Algebra A, the first half of Pre-Algebra. This course is only available through manual enrollment for students who are taking Pre-Algebra in the Emporium mode and have completed at least the Pre-Algebra A material. This course will support students in achieving Pre-Algebra A learning goals by providing support around mastering the necessary arithmetic, algebraic and geometric concepts that are relevant to their Pre-Algebra A course. This course will provide study strategies that promote understanding and improve performance, more in-depth investigation of core concepts that are difficult for students to master, and learning skills.Corequisite: MATH 107A

## 201 MATH JAM SUPERVISED ASSISTED LEARNING (PRE-ALGEBRA) - 0 UNITS

Math Jam: Pre-Algebra (Math 107) This level is for students who are eligible to take Math 107: Pre-Algebra this next semester. Students will be learning Pre-Algebra material with the goal of preparing them to be successful in their upcoming Pre-Algebra class or to retake the ACCUPLACER™ exam at the end of the week and test into Math 65: Elementary Algebra.

## 202 MATH JAM SUPERVISED ASSISTED LEARNING (ELEMENTARY ALGEBRA) - 0 UNITS

Math Jam: Elementary Algebra (Math 65) This level is for students who are eligible to take Math 65: Elementary Algebra this next semester. Students will be learning Elementary Algebra material with the goal of preparing them to be successful in their upcoming Math 65 class or to retake the ACCUPLACER™ exam at the end of the week and test into a transfer level math class.

## 203 MATH JAM SUPERVISED ASSISTED LEARNING (INTERMEDIATE ALGEBRA) - 0 UNITS

Math Jam: Intermediate Algebra (Math 55) This level is for students who are eligible to take Math 55: Intermediate Algebra this next semester. Students will be learning Intermediate Algebra material with the goal of preparing them to be successful in their upcoming Math 55 class or to retake the ACCUPLACER™ exam at the end of the week and test into a transfer level math class.

## 204 MATH JAM SUPERVISED ASSISTED LEARNING (STATISTICS & PROBABILITY) - 0 UNITS

Math Jam: Statistics and Probability (Math 40) and Mathematics for Liberal Arts (Math 47) This level is only for students who are eligible to take a transfer level math class, such as Math 40 and Math 47. Students will be learning key concepts that are included in Math 40 and Math 47 with the goal of preparing them to be successful in their upcoming Math 40 class or to refresh their skills in preparation for a research class at Las Positas College.

## 205 MATH JAM SUPERVISED ASSISTED LEARNING (TRIGONOMETRY/PRE-CALCULUS & BUSINESS CALCULUS) - 0 UNITS

Math Jam: Trigonometry/Pre-Calculus (Math 38/20) and Business Calculus (Math 34) This level is only for students who are eligible to take a transfer level math class, such as Math 38, 20 or 34. Students will be learning appropriate Algebra, Trigonometry and Pre-Calculus material with the goal of preparing them to be successful in their upcoming classes, such as Math 38, Math 20, Math 1 or Math 34. Students who are eligible for a transfer level math class and also interested in placing higher in the STEM sequence (such as Math 20 or Math 1) can take this level to prepare to retake the ACCUPLACER™ exam.