# Mathematics

Mathematics is the abstract deductive study of structure and pattern that serves as the foundation of science and technology. Transfer courses in mathematics emphasize the development of mathematical and quantitative reasoning skills beyond the level of intermediate algebra. Courses satisfy general education requirements for the Associate Degree for Transfer in Mathematics, and lower division transfer.

### Faculty

Name | Office Room Number | Phone | |
---|---|---|---|

Anderson, Brian | MA 119 | 626-852-8058 | banderson@citruscollege.edu |

Cole, Morgan | CI 113 | 626-000-4138 | mcole@citruscollege.edu |

Dominguez, Victoria | MA 212 | 626-857-4004 | vdominguez@citruscollege.edu |

Everest, Robert | MA 214 | 626-852-8054 | reverest@citruscollege.edu |

Gong, Catherine | MA 118 | 626-914-8758 | cgong@citruscollege.edu |

Gonzalez, Rudy | CI 112 | 626-914-8753 | rgonzalez@citruscollege.edu |

Gutierrez, Jesus | CI 108 | 626-857-4027 | jgutierrez@citruscollege.edu |

Lee, Sophia | CI 115 | 626-857-4172 | sophialee@citruscollege.edu |

Medrano, Esmeralda | MA 218 | 626-857-4085 | emedrano@citruscollege.edu |

Nguyen, Tracy | CI 103 | 626-000-4068 | tnguyen@citruscollege.edu |

Nguyenhuu, Rick | CI 111 | 626-914-8790 | rnguyenhuu@citruscollege.edu |

Odrich, Steve | MA 128 | 626-914-8796 | sodrich@citruscollege.edu |

Paek, Heddy | MA 117 | 626-914-8757 | hpaek@citruscollege.edu |

Scott, Chris | MA 215 | 626-914-8751 | cscott@citruscollege.edu |

Swan, Alfie | CI 114 | 626-914-8781 | aswan@citruscollege.edu |

Swatzel, James | MA 120 | 626-857-4108 | jswatzel@citruscollege.edu |

Tippins, Ralph | MA 213 | 626-914-8772 | rtippins@citruscollege.edu |

Trad, Mohamad | MA 115 | 626-852-8030 | mtrad@citruscollege.edu |

White, Sheila | MA 114 | 626-914-8784 | swhite@citruscollege.edu |

Zhuang, Ying | MA 122 | 626-914-8764 | yzhuang@citruscollege.edu |

### Contact Information

- Division
- Mathematics and Business
- Dean
- Michael Wangler
- Administrative Secretary
- Cynthia Audelo
- Division Office
- CI 208
- Division Phone Number
- 626-914-8792
- Discipline Website
- http://www.citruscollege.edu/academics/programs/math

This discipline prepares students to do the following:

- Use proper vocabulary and notation when describing mathematical concepts; be able to read books and documents and extract quantitative information.
- Develop level-appropriate computational skills: numeric calculation, evaluation of expressions, analysis of data and application of concepts.
- Develop an understanding of, and curiosity toward the physical world.
- Develop the analytic skills to devise questions and propose quantitative solutions.
- Demonstrate computational skills and an understanding of mathematical reasoning that will increase self-esteem and set them on a path of lifelong learning.
- Be adept at using instructional software found by navigating the Web and the Windows environment.
- Perform mathematics functions at a level appropriate to the course. This “level” may range from arithmetic through differential equations and may include statistics, teacher prep and other topics.

**MATH 025Arithmetic and PreAlgebra5 Units90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): Placement is based on multiple assessment measures.*

*Strongly recommended: ENGL 099 if required by English placement exam or if required by English level.*

Topics include the four basic operations of arithmetic on whole numbers, integers, fractions, decimals, ratios, proportions and percents, an introduction to fundamental algebraic concepts, solving equations and solving applied problems. NOTE: THE UNITS EARNED FOR THIS COURSE MAY NOT BE APPLIED TOWARD THE 60 UNITS FOR GRADUATION.

**MATH 029Pre-Algebra4 Units72 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 020 or placement is based on multiple assessment measures.*

This course is designed to prepare a student for Elementary Algebra. Topics include a review of arithmetic, a study of signed numbers, an introduction to fundamental algebraic concepts, solving equations, and solving applied problems. NOTE: THE UNITS EARNED FOR THIS COURSE MAY NOT BE APPLIED TOWARD THE 60 UNITS FOR GRADUATION.

**MATH 030Elementary Algebra5 Units90 lecture hoursEquivalent to: MATH 129, MATH 130**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 025 or MATH 029 or placement is based on multiple assessment measures.*

*Strongly recommended: ENGL 099 if required by English placement exam or if required by English level.*

Fundamental operations with polynomials and rational expressions, products and factoring, linear and quadratic equations in one variable, inequalities, exponents, radicals, graphing linear equations, systems of equations, applications and introduction to functions.

**MATH 031Plane Geometry4 Units72 lecture hoursEquivalent to: MATH 131**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 030 or MATH 032 or placement is based on multiple assessment measures.*

A first course in geometry. Elementary logic, properties of geometric figures, parallel and perpendicular lines, ratio and proportion, congruence, area, and volume.

**MATH 032Beginning and Intermediate Algebra I5 Units90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 029 or placement is based on multiple assessment measures.*

*Strongly recommended: ENGL 099 if required by English placement exam or if required by English level.*

Properties of real numbers and expressions; linear equations and inequalities in one and two variables; systems; proportion and variation; exponents; polynomials; factoring; graphs; applications. NOTE: The precollegiate algebra sequence is MATH 029, 030, 150 OR MATH 029, 032, 142. CREDIT MAY NOT BE EARNED FOR BOTH MATH 032 AND MATH 030.

**MATH 140Pre-Statistics5 Units (AA/AS)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 025 or MATH 029.*

This course surveys a variety of mathematical topics needed to prepare students for college-level statistics. Pre-Statistics is designed for students in majors such as those in liberal arts, humanities, and social sciences. It should not be taken by students majoring in science, technology, engineering, math, business, nursing, or any other major requiring a specific math course other than statistics. Topics include: performing operations on and evaluation of algebraic expressions, designing observational studies and experiments, graphical and tabular display of data, summarizing data, computing probabilities, describing associations of two variables graphically, graphing equations of lines and linear models, solving linear equations and inequalities, and finding linear models.

**MATH 142Beginning and Intermediate Algebra II5 Units (AA/AS; Citrus GE)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 032.*

Rational, radical, quadratic, exponential and logarithmic expressions, functions, and equations; complex numbers; inverse functions; conic sections. NOTE: The precollegiate algebra sequence is MATH 029, 030, 150 OR MATH 029, 032, 142. THIS COURSE MAY NOT BE TAKEN CONCURRENTLY WITH EITHER MATH 148, 149 OR MATH 150. STUDENTS MAY NOT EARN MORE THAN A TOTAL OF FIVE UNITS IN ANY COMBINATION OF MATH 142, 148, 149, AND MATH 150.

**MATH 144Technical Mathematics5 Units (AA/AS; Citrus GE)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 030 or MATH 032 or placement is based on multiple assessment measures.*

Reviews and extends concepts from elementary algebra and geometry, and introduces new content from trigonometry, statistics, and other mathematical topics that can be applied to problems that arise in a career and technical setting. Simplifying algebraic expressions, functions, basic graphing, systems of linear equations, linear and quadratic equations, triangles, circles, quadrilaterals, polygons, prisms, spheres, cylinders, statistical graphs, measures of central tendency, measures of variation, normal distribution, right-angle trigonometry, radian measure, Law of Sines, Law of Cosines, sine and cosine graphs, binary and hexadecimal numbers, measurement, metric system, signed numbers and powers of ten. Emphasis is on technical applications and problem-solving skills including the appropriate use of technology.

**MATH 150Intermediate Algebra5 Units (AA/AS; Citrus GE)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 030 or placement is based on multiple assessment measures.*

Real number properties, first degree equations and inequalities, absolute value equations and inequalities, formulas, applications, exponents, polynomials, the binomial theorem, factoring, linear systems, functions, rational expressions, radicals, complex numbers, quadratic equations, conics, inverse functions, and exponential and logarithmic functions.

**MATH 151Plane Trigonometry4 Units (AA/AS; CSU; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 031 or high school Geometry; MATH 142 or MATH 150 or placement for algebraic readiness is based on multiple assessment measures.*

The study of trigonometric functions, their inverses and their graphs, identities and proofs related to trigonometic expressions, trigonometric equations, solving right triangles, solving triangles using the Law of Cosines and the Law of Sines, polar coordinates, and introduction to vectors.

**MATH 160Survey of Mathematics4 Units (AA/AS; CSU; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 142 or MATH 150 or placement is based on multiple assessment measures.*

A course in mathematical concepts for the liberal arts student. Topics include sets and logic, problem solving, numeration systems, consumer applications, geometry, probability, statistics, and computer applications.

**MATH 162Introductory Mathematical Analysis4 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 142 or MATH 150 or placement is based on multiple assessment measures.*

Concepts of function and limits: applied calculus emphasizing techniques of integration and differentiation with applications in social and life sciences, business administration, economics, and engineering technology.

**MATH 165Introductory Statistics4 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Standard Letter**

*Prerequisite(s): MATH 140 or MATH 142 or MATH 150 or placement is based on multiple assessment measures.*

Introductory course to statistics and probability, descriptive analysis, and presentation of data, hypothesis testing, statistical inference, normal curve, chi square, and applications in diverse disciplines.

**MATH 168Mathematics for Elementary Teachers l4 Units (AA/AS; CSU; UC; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Standard Letter**

*Prerequisite(s): MATH 142 or MATH 150 or placement is based on multiple assessment measures.*

Course is designed for prospective elementary teachers. The course covers sets, logic, number systems, number theory and algebra functions. Techniques in instructional delivery explored.

**MATH 170College Algebra4 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Standard Letter**

*Prerequisite(s): MATH 142 or MATH 150 or placement is based on multiple assessment measures.*

College level course in algebra for majors in the liberal arts. Polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; analytic geometry.

**MATH 175Pre-Calculus5 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)90 lecture hours**

**Grade Mode: Standard Letter**

*Prerequisite(s): MATH 151 or placement is based on multiple assessment measures.*

Preparation for calculus; polynomial, rational, exponential, logarithmic, and trigonometric functions; analytic geometry; systems of equations; sequences and series; mathematical induction.

**MATH 190Calculus with Analytic Geometry l4 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 175 or placement is based on multiple assessment measures.*

A first course in differential and integral calculus of a single variable: functions; limits and continuity; techniques and applications of differentiation and integration; Fundamental Theorem of Calculus. Primarily for science, technology, engineering & math majors.

**MATH 191Calculus with Analytic Geometry ll5 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 190.*

A second course in differential and integral calculus of a single variable: integration; techniques of integration; infinite sequences and series; polar and parametric equations; applications of integration. Primarily for science, technology, engineering & math majors.

**MATH 210Calculus with Analytic Geometry lll5 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 191.*

Vectors, calculus of functions of more than one variable, partial derivatives, multiple integration, vector calculus, Green's Theorem, Stokes' Theorem, and divergence theorem.

**MATH 211Differential Equations5 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)90 lecture hours**

**Grade Mode: Pass/No Pass, Standard Letter**

*Prerequisite(s): MATH 210.*

First and second order (linear and non-linear) differential equations, with emphasis on modeling applications. Numerical methods. Basic linear algebra. Systems of linear and non-linear differential equations and their applications. Application of linear algebra to systems. Power series methods.

**MATH 212Introduction to Linear Algebra4 Units (AA/AS; CSU; IGETC 2A; UC; CSUGE B4; Citrus GE)72 lecture hours**

**Grade Mode: Standard Letter**

*Prerequisite(s): MATH 191.*

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. The course 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. This introduction to linear algebra course complements coursework in calculus.