**MATHEMATICS**

Program Purpose: Students who complete Mathematics courses will demonstrate critical thinking skills, analyze abstract concepts, and transition from the concrete to the abstract in mathematical thinking.

The Mathematics Associate in Science Degree program offers training in both pure and applied mathematics, leading to careers in research, education, business, industry, and government, including such professions as educators, statisticians, actuaries, and operations research analysts. Many areas, such as the physical and social sciences, engineering, economic, and business, are dependent upon the use of applied mathematics in developing solutions to practical problems. Students who complete Mathematics courses will demonstrate critical thinking skills, analyze abstract concepts, and transition from the concrete to the abstract in mathematical thinking.

**ASSOCIATE IN SCIENCE IN MATHEMATICS FOR TRANSFER DEGREE**

The Associate in Science Degree in Mathematics for Transfer (AS-T) is intended for students who plan to transfer and complete a Bachelor’s degree in Mathematics, or a similar major at a CSU campus. Students completing the AS-T degree in Mathematics are guaranteed admission to the CSU system, but not necessarily to a particular CSU campus or major of their choice. Students should consult with a counselor for more information on university admission and transfer requirements, as this AS-T in Mathematics may not be the best option for students intending to transfer to a particular CSU campus or to a college or university that is not part of the CSU system.

To earn an AS-T in Mathematics, students must complete the following:

- 60 semester or 90 quarter CSU transferable units.
- Minimum grade point average (GPA) of at least 2.0 in all CSU transferable coursework. While a minimum of 2.0 is required for admission, some majors may require a higher GPA.
- A minimum of 21-22 specified major units. All courses in the major must be completed with a grade of C or better (Title 5 §55063).
- Certified completion of the California State University General Education-Breadth pattern or the Intersegmental General Education Transfer Curriculum (IGETC for CSU) pattern.

In addition to General Education degree requirements, complete the following:

REQUIRED CORE: |
Units |

MATH M25A/M25AH Calculus with Analytic Geometry I/Honors | 5.0 |

MATH M25B Calculus with Analytic Geometry II | 5.0 |

MATH M25C Calculus with Analytic Geometry III | 5.0 |

MATH M31 Introduction to Linear Algebra | 5.0 |

Units from ELECTIVE COURSES | 3.0-4.0 |

TOTAL |
21.0-22.0 |

Select and complete one course from the following list: |
Units |

CS M10A Introduction to Computer Programming Using Structured C++ | 4.0 |

MATH M15/M15H Introductory Statistics/Honors | 4.0 |

MATH M21 Discrete Mathematics | 3.0 |

MATH M35 Applied Differential Equations | 3.0 |

PHYS M20A Mechanics - Solids/Fluids | 4.0 |

**PROGRAM STUDENT LEARNING OUTCOMES**

Students completing the Associate in Science in Mathematics for Transfer (AS-T) will be able to:

- Demonstrate critical thinking skills, analyze abstract concepts, and transition from the concrete to the abstract in mathematical thinking.
- Apply formal systems of reasoning in solving problems or analyzing arguments.
- Express results or conclusions using correct mathematical notation.

**MATHEMATICS COURSES**

**MATH M01 – ELEMENTARY ALGEBRA (5 UNITS)**

Prerequisites: None

Class Hours: 5 lecture

Reviews briefly arithmetic including integers, fractions, and decimals. Covers algebraic expressions, linear equations and inequalities, graphing lines, systems of linear equations, integer exponents, polynomials, factoring of polynomials, solving quadratic equations by the factoring method, and rational expressions. Applies to Associate Degree.

**MATH M03 – INTERMEDIATE ALGEBRA (5 UNITS)**

Prerequisites: MATH M01 or 1 year of high school beginning algebra with grade of C or better, or placement as measured by the college pre-assessment process.

Class Hours: 5 lecture

Reviews briefly linear equations and inequalities, graphing, factoring, and rational expressions. Covers systems of linear equations, rational functions, complex fractions, rational exponents and radicals, complex numbers, quadratic equations, graphs of parabolas, functions, composition and inverse functions, exponential and logarithmic functions. Applies to Associate Degree..

**MATH M05 – COLLEGE ALGEBRA FOR STEM STUDIES (4 UNITS)**

Prerequisites: MATH M03 or High School Algebra II

Class Hours: 4 lecture

Covers quadratic equations, linear and non-linear inequalities, absolute value equations and inequalities, complex numbers, functions, polynomial functions, rational functions, exponential functions, logarithmic functions, and systems of equations. Includes the theory of polynomial equations and analytic geometry. Completing MATH M05 and MATH M06 is equivalent to completing MATH M07. Applies to Associate Degree. Transfer credit: CSU; UC (Students completing MATH M05, MATH M06, and MATH M07 receive maximum credit of 6 units for MC and CSU. MATH M05 and MATH M07 combined: maximum credit, one course for UC).

**MATH M06 – TRIGONOMETRY (3 UNITS)**

Prerequisites: MATH M03 or High School Algebra II

Class Hours: 3 lecture

Covers functions, trigonometric functions, solutions of triangles, radian measure, analytic trigonometry, trigonometric identities and equations, composite angle identities, inverse trigonometric functions, complex numbers, and polar coordinates. Completing MATH M05 and MATH M06 is same as completing MATH M07. Applies to Associate Degree. Transfer credit: CSU (Students completing MATH M05, MATH M06, and MATH M07 receive maximum credit of 6 units for MC and CSU).

**MATH M07 – PRECALCULUS AND TRIGONOMETRY (6 UNITS)**

Prerequisites: MATH M03 or High School Algebra II

Class Hours: 6 lecture

Integrates college algebra and trigonometry. Includes basic algebraic concepts, equations and inequalities of the first and second degree, systems of equations and inequalities, functions and graphs, linear and quadratic functions, polynomial functions of higher degree, rational functions, exponential and logarithmic functions, trigonometric functions, analytical trigonometry, and polar coordinates. Recommended for students planning to enter the MATH M25A/B/C sequence. Completing MATH M07 is equivalent to completing both MATH M05 and MATH M06. Applies to Associate Degree. Transfer credit: CSU; UC (Students taking MATH M05, MATH M06, MATH M07 receive maximum credit of 6 units for MC and CSU; MATH M07 and MATH M05 combined is maximum credit, one course for UC).

**MATH M08 – PATHWAY TO STATISTICS (6 UNITS)**

Prerequisites: 1 year of high school pre-algebra or placement as measured by the college assessment process

Class Hours: 6 lecture

Prepares students for transfer-level statistics by covering core concepts from elementary algebra, intermediate algebra, and descriptive statistics. Provides algebraic and statistical problem solving techniques. Uses technology to analyze data sets. This course is not intended for students who plan to take courses in science, computer science, engineering, math, as well as business and other non-STEM majors. Does NOT meet the Math competency for the associate degree. Applies to Associate Degree.

**MATH M10 – MATHEMATICS FOR ELEMENTARY TEACHERS (3 UNITS)**

Prerequisites: MATH M03

Class Hours: 3 lecture

Focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real number systems and subsystems. Emphasizes the comprehension and analysis of mathematical concepts and applications of logical reasoning. Designed for students intending to teach in K-8. Not recommended for majors in physical sciences nor mathematics. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M11 – COLLEGE ALGEBRA FOR THE LIBERAL ARTS (3 UNITS) (Starting Fall 2020)**

Prerequisites: MATH M03

Class Hours: 3 lecture

Covers theory of functions including operations on functions, graphs, domain and range, and evaluation. Includes types of functions such as linear, quadratic, polynomial, rational, exponential, and logarithmic functions. Analyzes graphs including curve sketching, intercepts, transformations, vertices and asymptotes. Covers linear and non-linear inequalities, solving exponential and logarithmic equations and complex numbers.

**MATH M12 – MATH REASONING FOR THE LIBERAL ARTS (3 UNITS) (Starting Fall 2020)**

Prerequisites: MATH M03

Class Hours: 3 lecture

Introduces liberal arts students to mathematical ideas necessary for their careers and daily lives. Includes topics in logic, quantitative information in the real world, managing finances, statistical reasoning, probability, modeling linear and exponential functions, and mathematics in music, art, and politics.

**MATH M15 – INTRODUCTORY STATISTICS (4 UNITS)**

Prerequisites: MATH M03

Class Hours: 4 lecture

Explores the nature of statistical methods, including description of sample data, probability, theoretical frequency distributions, sampling, estimation, testing hypotheses and special topics. Provides problem solving techniques. Uses technology to analyze large data sets. Students cannot complete both MATH M15 and MATH M15H because credit will only be awarded to the first course completed. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M15H – HONORS: INTRODUCTORY STATISTICS (4 UNITS)**

Prerequisites: MATH M03

Class Hours: 4 lecture

Explores the nature of statistical methods, including description of sample data, probability, theoretical frequency distributions, sampling, estimation, testing hypotheses and special topics. Provides problem solving techniques. Honors work challenges students to be more analytical and creative through expanded assignments and enrichment opportunities. Students cannot complete both MATH M15 and MATH M15H because credit will only be awarded to the first course completed. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M16A – APPLIED CALCULUS I (3 UNITS)**

Prerequisites: MATH M05 or MATH M07

Class Hours: 3 lecture

Covers limits, continuity, and differentiation. Applies differential calculus to problems in business, economics, social and biological sciences. Introduces anti-differentiation and its applications in business and economics. Applies to Associate Degree. Transfer credit: CSU; UC (MATH M16A, MATH M25A and MATH M25AH combined: maximum one course for credit)

**MATH M16B – APPLIED CALCULUS II (3 UNITS)**

Prerequisites: MATH M16A or MATH M25A

Class Hours: 3 lecture

Includes integration, elementary and separable differential equations, functions of several variables, partial derivatives, relative maxima and minima, Lagrange multipliers, method of least squares, double integrals, infinite series, Taylor Approximation, and Newton’s method. Applies calculus to problems in business, economics, and social and biological sciences. Applies to Associate Degree. Transfer credit: CSU; UC (MATH M16A, MATH M25A and MATH M25AH combined: maximum one course for credit)

**MATH M21 – DISCRETE MATHEMATICS (3 UNITS)**

Prerequisites: MATH M25A

Recommended Prep: CS M10A

Class Hours: 3 lecture

Covers elements of discrete mathematics which have application to computer science. Includes the following topics: logic, sets, functions, relations, proof techniques, mathematical induction, recurrence relations, graphs, trees, discrete probability, Boolean algebra, and a brief introduction to programming. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M25A – CALCULUS WITH ANALYTIC GEOMETRY I (5 UNITS)**

Prerequisites: MATH M05 and MATH M06 or MATH M07

Class Hours: 5 lecture

Covers limits, continuity, differentiation and integration of algebraic functions. Also covers differentiation and integration of transcendental functions with applications Students cannot complete both MATH M25A and MATH M25AH courses because credit will only be awarded to the first course completed. Applies to Associate Degree. Transfer credit: CSU; UC (MATH M16A, MATH M25A and MATH M25AH combined: maximum one course for transfer credit)

**MATH M25AH – HONORS: CALCULUS WITH ANALYTIC GEOMETRY I (5 UNITS)**

Prerequisites: MATH M05 and MATH M06 or MATH M07

Class Hours: 5 lecture

Covers limits, continuity, differentiation and integration of algebraic functions, and differentiation and integration of transcendental functions with applications. Emphasizes mathematical rigor and in-depth analysis of real-world applications. Honors work challenges students to be more analytical and creative through expanded assignments and enrichment opportunities. Students cannot complete both MATH M25A and MATH M25AH courses because credit will only be awarded to the first course completed. Applies to Associate Degree. Transfer credit: CSU; UC (MATH M16A, MATH M25A and MATH M25AH combined: maximum one course for transfer credit)

**MATH M25B – CALCULUS WITH ANALYTIC GEOMETRY II (5 UNITS)**

Prerequisites: MATH M25A, MATH M25AH, or MATH M16B

Class Hours: 5 lecture

Reviews integration. Covers area, volume, arc length, sur face area, centers of mass, physics applications, techniques of integration, improper integrals, sequences, series, Taylor’s Theorem, parametric equations, polar coordinates, and conic sections with translations. Applies to Associate Degree. Transfer credit: CSU; UC (MATH M25B and MATH M16B combined: maximum credit, one course)

**MATH M25C – CALCULUS WITH ANALYTIC GEOMETRY III (5 UNITS)**

Prerequisites: MATH M25B

Class Hours: 5 lecture

Covers vectors in plane and in three dimensional space, dot and cross products, spherical and cylindrical coordinates, vector-values functions, functions of several variables, partial derivatives, gradients, Lagrange multipliers. Also covers multiple integrals and their applications, vector calculus with line and sur face integrals, Green’s, Stokes’, and Divergence Theorems and applications. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M31 – INTRODUCTION TO LINEAR ALGEBRA (3 UNITS)**

Prerequisites: MATH M25B

Class Hours: 3 lecture

Develops the techniques and theory needed to solve and classify systems of linear equations. Covers solution techniques including row operations, Gaussian elimination, and matrix algebra. Investigates the proper ties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Presents vector space and matrix theory including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M35 – APPLIED DIFFERENTIAL EQUATIONS (3 UNITS)**

Prerequisites: MATH M25B

Class Hours: 3 lecture

Covers ordinary differential equations, equations with constant coefficients, variation of parameters, Laplace transforms, systems of linear equations, first order differential equations, series solutions, and existence and uniqueness of solutions. Emphasizes applications to physics and engineering as well as an introduction to numerical solutions. Applies to Associate Degree. Transfer credit: CSU; UC

**MATH M122 - INDEPENDENT STUDY - MATHEMATICS (0.5 TO 3 UNITS)**

Prerequisites: Completion of one course in Mathematics and instructor approval

Class Hours: 1.5 to 9 lab hours as arranged

Allows independent study for students who wish to extend their knowledge of a particular area of Mathematics through research and study. Utilizes an approved independent project. Includes one-on-one work with instructor. Interested students should contact a Mathematics instructor for assistance in developing a contract for learning about a specific topic. (Formerly MATH M22A/B). Applies to Associate Degree. Transfer credit: CSU; UC (determined after admission)

**MATH M707 - BRIDGE TO COLLEGE ALGEBRA AND TRIGONOMETRY (MATH M07) (0.5 UNIT)**

Prerequisites: None

Class Hours: 0.5 lecture

Prepares student for the prerequisite materials necessary to be successful in Math M07. Includes factoring, equations of lines, rational, radical and quadratic equations, and logarithms. Applies to Associate Degree.

**MATH M725A - BRIDGE TO CALCULUS WITH ANALYTIC GEOMETRY I (MATH M25A) (0.5 UNIT)**

Prerequisites: None

Class Hours: 0.5 lecture

Prepares student for the prerequisite materials necessary to be successful in Math M25A. Includes rationalizing denominators, factoring, logarithms, piecewise functions, and trigonometric functions. Applies to Associate Degree.

**MATH M725B - BRIDGE TO CALCULUS WITH ANALYTIC GEOMETRY II (MATH M25B) (0.5 UNIT)**

Prerequisites: None

Class Hours: 0.5 lecture

Prepares student for the prerequisite materials necessary to be successful in Math M25B. Includes differentiation of algebraic and transcendental functions, integration, u-substitution, and the chain rule for differentiation. Applies to Assoiciate Degree.

**MATH M901 - BRIDGE TO ELEMENTARY ALGEBRA (MATH M01) (8.05 HOURS)**

Prerequisites: None

Class Hours: 0.46 lecture

Prepares student for the prerequisite materials necessary to be successful in Math M01. Includes fractions, decimals, exponents, and solving linear equations. Does NOT apply to Associate Degree.

**MATH M903 - BRIDGE TO INTERMEDIATE ALGEBRA (MATH M03) (8.75 HOURS)**

Prerequisites: None

Class Hours: 0.5 lab

Prepares student for the prerequisite materials necessary to be successful in Math M03. Includes linear equations, quadratic equations, factoring polynomials, quadratic, rational, exponential and logarithmic functions, and graphing. Does NOT apply to Associate Degree.

**MATH M905S - SUPPORT FOR COLLEGE ALGEBRA (35.0 HOURS)**

Prerequisites: None

Co-requisite: MATH M05

Class Hours: 2 lab

Provides review for topics necessary for success in College Algebra, including linear equations and inequalities, graphing, factoring, and rational expressions. Covers systems of linear equations, rational functions, rational exponents and radicals, complex numbers, quadratic equations, graphs of parabolas, functions, composition and inverse functions, exponential and logarithmic functions. Requires concurrent enrollment in MATH M05. Does NOT apply to Associate Degree