# Mathematics

Department website: http://www.sbcc.edu/mathematics/

## Program Description

Each year, the list of careers demanding familiarity with basic mathematical skills grows. Animation, urban planning, geography, environmental science, architecture, business management, nursing, dentistry, forestry management, psychology and photography represent only a small sample from this list. Many careers require more sophisticated mathematical skills, such as physics, engineering, and computer science.

The Mathematics Department at Santa Barbara City College offers a broad curriculum to meet the needs of students with a wide variety of goals. The department offers the following sequences and courses to help our students achieve their career goals:

- A standard college-level sequence in single and multivariable calculus, analytic geometry, linear algebra and differential equations for freshman and sophomore students who plan to transfer to four-year colleges or universities in STEM fields.
- Transfer-level courses in statistics, mathematics for liberal arts majors, and college algebra.
- A two-course sequence in calculus for Business, Biological Sciences and Social Science majors, as well as courses in support of Career Technical Education programs.
- A complete precalculus program, including elementary algebra, intermediate algebra, college algebra and trigonometry to review old or gain new mathematical skills. A pre-algebra course provides an opportunity for students to refresh their arithmetic skills in order to fully participate in their educational endeavors.

In all of the department’s course offerings, there is a strong commitment to training the student in analytical and logical thinking skills as part of a problem-solving attitude which can be transferred outside the formal educational setting.

The Mathematics Department offers an AS-T Degree in Mathematics for Transfer. This degree provides the foundational knowledge in Mathematics to students who want to earn a Baccalaureate Degree in Mathematics. This degree is in compliance with the Student Transfer Achievement Reform Act {Senate Bill 1440, now codified in *California Education Code *Sections 66746-66749} and guarantees admission to a California State University (CSU) campus for any community college student who completes an “associate degree for transfer,” a newly established variation of the associate degrees traditionally offered at a California community college. Upon completion of the transfer associate degree, the student is eligible for transfer with junior standing into the California State University (CSU) system. Students will be given priority consideration when applying to a particular program that is similar to the student’s community college area of emphasis. For more information on transfer degrees, visit www.sb1440.org.

## Planning a Program of Study

The required first-year Calculus, and indeed all of our math courses, are offered each semester (except possibly in summer). The Physics courses are offered sequentially, beginning each spring with PHYS 121 Mechanics Of Solids And Fluids. Care should be taken, however, that one semester of calculus is completed before attempting the Physics sequence. It is recommended that students take courses in order. A programming language course should be taken as soon as possible because of its usefulness as a computational tool.

The mathematics major at Santa Barbara City College meets the accepted normal curriculum. However, transfer students are advised to review, in depth, the current catalogs of institutions to which they plan to transfer for additional course requirement information.

Because mathematics is such a precisely structured discipline, students who have not acquired adequate skills and understanding at one course level will find it most difficult to succeed in the next higher course. For this reason, an important part of the Mathematics Program at Santa Barbara City College is appropriate placement of students into classes to increase their chances of success in mastering course content.

Placement into a math class can occur one of three ways:

- If students are beginning their college career and have not taken college level math classes at another accredited college or university, then they need to visit the assessment center. For assessment information and hours, call the Assessment Center at (805) 730-4149 or sbcc.edu/assessmentcenter.
- If students are transferring from another college or if have already taken college-level math classes, then they need to submit evidence of previous math courses to the Transcript Evaluation Office. For course evaluation information, go to sbcc.edu/teo.
- If students are continuing at SBCC, they should follow the appropriate sequence posted in the Schedule of Classes. There are several branches of the sequence, and
**each student should consult with a math instructor or counselor**to make sure he/she has chosen the correct path for his/her educational goals.

Students are urged to take placement examinations and enroll in math classes as soon as possible, preferably taking math their first semester. It is not wise to postpone taking required math courses. Doing so might significantly delay transfer.

## Preparation for Transfer

Course requirements for transfer vary depending upon the college or university a student wishes to attend. Therefore, it is **most important for a student to consult with his/her counselor and departmental adviser before planning an academic program for transfer**. Information sheets for majors, outlining transfer requirements, are available in the Counseling Center and the Transfer Center.

## Mathematics (MATH)

MATH 001 Basic Mathematics (3 Units)

Hours: 54 (54 lecture)

Basic math course, including place value, reading and writing numbers; arithmetic operations on whole numbers; fraction concepts and operations on fractions; decimal concepts and operations on decimals; ratio and proportion; percentage; systems of measurement; numerical geometry; graph reading; operations on signed numbers. Application of arithmetic to everyday life is emphasized throughout the course.

MATH 004 Pre-Algebra (3 Units)

Prerequisites: MATH 1 or qualifying score on SBCC placement exam.

Skills Advisories: Proficiency in MATH 1 or MATH 41.

Hours: 54 (54 lecture)

Introduction to algebra. Topics include signed numbers, exponents, roots, evaluation of algebraic expressions, simplification of algebraic expressions, ratio and proportion, percents, measurement, geometry, coordinate plane, translation from English to algebra and solution of linear equations.

MATH 041 Fundamentals in Mathematics and Pre-Algebra (5 Units)

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 90 (90 lecture)

Foundational course, including language development, place value; definitions, concepts and operations on whole numbers, fractions, decimals, ratios, proportions, percentage and signed numbers; U.S. and metric measurement systems; introduction to algebra, rules of exponents, roots, evaluation and simplification of algebraic expressions; solving linear equations, basic polynomial factoring, and introduction to graphing. Application/word problems throughout the course.

MATH 041W Workshop for Fundamentals in Mathematics and Pre-Algebra (1 Unit)

Corequisites: MATH 41. Concurrent enrollment in Math 41.

Hours: 54 (54 lab)

Concurrent Open-entry/open-exit supplementary problem-solving course designed for students currently enrolled in Math 41. Co-requisites: Concurrent enrollment in Math 41.

MATH 074 Pre-algebra Refresher (1 Unit)

Hours: 18 (18 lecture)

Pre-algebra refresher for students who desire higher placement; students who've completed Math 004 but need review; or those who have attempted Math 95 and need pre-algebra review. Successful completion of this course may serve as a petition to challenge Math 4. Course does not replace a failing grade in Math 4.

MATH 077 Support for Intermediate Algebra (2 Units)

Prerequisites: MATH 95 or MATH 97 or placement by SBCC assessment through multiple measures.

Corequisites: MATH 107.

Hours: 36 (36 lecture)

Concurrent A review of core prerequisite skills, competencies, and concepts for intermediate algebra. Intended for students who are concurrently enrolled in Math 107 Intermediate Algebra at Santa Barbara City College. Review topics include skills developed in pre-algebra and elementary algebra, the vocabulary of algebra, translation from English to algebra, evaluation of literal expressions, solving and graphing linear equations and inequalities, systems of equations, factoring, algebraic operations on polynomials and rationals, and solving quadratics.

MATH 080 Elementary Algebra Refresher (1 Unit)

Hours: 18 (18 lecture)

For students who assessed into Math 95 and wish to improve their assessment level or who unsuccessfully attempted Math 107 and need review of elementary algebra. Successful completion may serve as a petition to challenge Math 95 through a comprehensive exam.

MATH 087 Intermediate Algebra Refresher (1 Unit)

Hours: 18 (18 lecture)

Intermediate algebra refresher for students who desire higher placement; students who have completed Math 107 but need review; or those who have attempted Math 120 and need review. Successful completion of this course may serve as a petition to challenge Math 107. Course does not replace a failing grade in Math 107.

MATH 093 Nursing and Allied Health Math (1 Unit)

Prerequisites: Math 4 or better or qualifying score on SBCC placement exam.

Hours: 18 (18 lecture)

Prerequisites: Math 4 or better or qualifying score on SBCC placement exam. For Nursing and Allied Health professionals, focuses on math skills necessary in an Allied Health occupational area. Basic math skills and algebra, metric system conversions, conversion the metric, apothecary and household units of measure, computational methods used in the preparation of medications.

MATH 095 Elementary Algebra (5 Units)

Prerequisites: MATH 4 or MATH 41 or placement by SBCC assessment using multiple measures.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 90 (90 lecture)

Beginning algebra, similar to a standard first-year high school algebra course. Includes a review of signed numbers and their properties, equations and inequalities in one variable, graphing linear equations, systems in two variables, integer exponents, rational and polynomial expressions, quadratic equations, the quadratic formula and graphing parabolas.

MATH 095N Study Skills In Math (1 Unit)

Corequisites: MATH 95.

Skills Advisories: Eligibility for ENG 98 and 103 and proficiency in MATH 4.

Hours: 18 (18 lecture)

Topics designed to increase student success in mathematics. Must be enrolled in Math 95 (100).

MATH 107 Intermediate Algebra (4 Units)

Prerequisites: MATH 95 or Math 77 or placement by SBCC assessment through multiple measures.

Skills Advisories: Eligibility for ENG 98 and 103.

Hours: 72 (72 lecture)

Second course in algebra, including algebraic manipulation of polynomials, rational expressions, exponents, radicals, linear equations, ratio and proportion, inequalities, word problems, quadratic equations, systems of linear and quadratic equations. An introduction to functions and nonlinear equations. Exponential and logarithmic functions and their applications.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

MATH 107N Study Skills in Intermediate Algebra (1 Unit)

Corequisites: MATH 107.

Skills Advisories: Eligibility for ENG 98 and 103.

Hours: 18 (18 lecture)

Proficiency in MATH 95. Topics to increase student success in Intermediate Algebra.

MATH 108 Mathematical Concepts for Elementary School Teachers-Number Systems (4 Units)

Prerequisites: MATH 107 or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 72 (72 lecture)

Recommended for prospective and in-service elementary school teachers. Mathematical investigations and problem solving involving sets, number sense, integers, and rational and real numbers. (C-ID MATH 120)

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, CSU Transferable, UC Transferable

C-ID: Math 120.

MATH 114 Mathematics for Liberal Arts Majors (4 Units)

Prerequisites: MATH 107 or MATH 097 or qualifying score on SBCC exam.

Skills Advisories: ENG 98 and 103.

Hours: 72 (72 lecture)

Intended to broaden students' understanding of methods, history and applications of mathematics. Logic, mathematical proofs, numeration systems, modular arithmetic, coordinate geometry and graphing, elementary probability and statistics, linear programming and financial math.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

MATH 117 Elementary Statistics (4 Units)

Prerequisites: MATH 107 or MATH 097 or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 110 or ENG 110H.

Hours: 72 (72 lecture)

General education mathematics course. Introduction to design of experiments, descriptive statistics and sampling distributions. Central Limit Theorem, statistical inference, confidence interval estimation, tests of hypotheses, correlation and linear regression, categorical variables, Chi-square, one-way ANOV, and multiple comparisons procedure.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 117, 117H and PSY 150 combined: maximum credit one course.

C-ID: MATH 110.

MATH 117H Elementary Statistics, Honors (4 Units)

Prerequisites: MATH 107 or MATH 111 or better or qualifying score on SBCC placement exam.

Limitations on Enrollment: Acceptance into the Honors Program.

Skills Advisories: Eligibility for ENG 110 or ENG 110H.

Hours: 72 (72 lecture)

General education mathematics course. Introduction to design of experiments, descriptive statistics and sampling distributions, Central Limit Theorem, statistical inference, confidence interval estimation and tests of hypotheses, correlation and linear regression, categorical variables and Chi-square distribution. One-way ANOVA, multiple comparisons procedure.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 117, 117H and PSY 150 combined: maximum credit one course.

C-ID: MATH 110

MATH 120 College Algebra (4 Units)

Prerequisites: MATH 107 or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 72 (72 lecture)

Study of functions and their graphs, including polynomial, rational, exponential and logarithmic functions. Systems of equations and conics.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 120, 137 and 138 combined: maximum credit, 5 semester/7.5 quarter units.

MATH 130 Calculus for Biological Sciences, Social Sciences and Business I (5 Units)

Prerequisites: MATH 111 or 120 or better or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 90 (90 lecture)

Calculus of one variable, limits, continuity, differentiation, Riemann approximations, definite and indefinite integrals; introduction to integration techniques, exponential and logarithmic functions, curve-sketching, maxima/minima problems, related rates and applications.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 130 and MATH 150 combined: maximum credit, one course.

C-ID: MATH 140.

MATH 131 Calculus For Biological Sciences, Social Sciences And Business II (3 Units)

Prerequisites: MATH 130.

Skills Advisories: Eligibility for ENG 98 and ENG 103 and MATH 130.

Hours: 54 (54 lecture)

Techniques of integration for single and multivariable calculus, functions of several variables, partial differentiation, maxima/minima problems, differential equations, and probability. Optional topics: infinite series, Taylor's Theorem and the calculus of trigonometric functions.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 131 and 160 combined: maximum credit, one course.

MATH 137 Precalculus I - College Algebra And Functions (5 Units)

Prerequisites: Math 107 or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 90 (90 lecture)

Short review of intermediate algebra topics; extensive treatment of functions and graphing techniques including translations, symmetries, reflections and graphs of inverse functions. Identities and conditional equations; analysis and applications of polynomial, rational, exponential and logarithmic functions are covered. Other topics include solving linear and nonlinear systems, using matrix algebra, and roots of higher-degree polynomials. Brief introduction to logic and the structure of proofs.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 120, 137 and 138 combined: maximum credit, 5 semester/7.5 quarter units.

MATH 137W Workshop for Precalculus I (1 Unit)

Corequisites: MATH 137.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 54 (54 lab)

A supplementary problem-solving course designed for students currently enrolled in MATH 137.

MATH 138 Precalculus II - College Algebra And Trigonometry (4 Units)

Prerequisites: MATH 137 or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 98 or ENG 110H.

Hours: 72 (72 lecture)

Advanced algebra course emphasizing analysis, graphing and applications of trigonometric functions. Such functions are developed from circular functions. Trigonometric identities and conditional equations, applications to triangles, vectors, complex numbers, parametric equations and polar coordinates are covered. Additional topics include sequences, series and the Binomial Theorem.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 120, 137 and 138 combined: maximum credit, 5 semester/7.5 quarter units.

C-ID: MATH 120.

MATH 138W Workshop for Precalculus II (1 Unit)

Corequisites: MATH 138.

Hours: 54 (54 lab)

Sills Advisories: ENG 98 and 103. A supplementary problem-solving course designed for students currently enrolled in MATH 138.

MATH 150 Calculus with Analytic Geometry I (5 Units)

Prerequisites: MATH 138 or better or qualifying score on SBCC placement exam.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 90 (90 lecture)

Limits, derivatives and integrals of algebraic, trigonometric, exponential and logarithmic functions. Differentials and applications of the derivative. Introduction to differential equations.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 130 and 150 combined: maximum credit, one course.

C-ID: MATH 210.

MATH 150W Workshop for Calculus with Analytic Geometry I (1 Unit)

Corequisites: Math 150.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 54 (54 lab)

A supplementary problem-solving course designed for students currently enrolled in MATH 150.

MATH 160 Calculus With Analytic Geometry II (5 Units)

Prerequisites: MATH 150.

Skills Advisories: Eligibility for ENG 98 and ENG 103.

Hours: 90 (90 lecture)

Techniques of integration; applications of definite integrals; polar equations; sequences and infinite series; introduction to differential equations and to vectors.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

UC Transfer Limit: MATH 131 and 160 combined: maximum credit, one course.

C-ID: MATH 220.

MATH 160W Workshop for Calculus with Analytic Geometry II (1 Unit)

Corequisites: MATH 160.

Skills Advisories: Eligibility for ENG 110 or ENG 110H.

Hours: 54 (54 lab)

A supplementary problem-solving course designed for students currently enrolled in MATH 160.

MATH 180 Transition to Advanced Mathematics (3 Units)

Prerequisites: MATH 160.

Hours: 54 (54 lecture)

Designed to introduce students to the rigors of advanced mathematics courses, with an emphasis on reading and writing proofs. Topics include set theory and logic, relations, functions, induction, countable and uncountable sets, the Heine-Borel Theorem and the Bolzano-Weierstrass Theorem. Some elementary group theory and/or topology is covered.

Transfer Information: CSU Transferable

MATH 188 Trigonometry Refresher (1 Unit)

Hours: 18 (18 lecture)

This short course is intended for students who wish to review trigonometry topics before or while taking Calculus or higher courses. A computer program is used to refresh concepts identified as needed for each student, plus weekly contact with the instructor. This course is not intended to replace Math 138.

MATH 200 Multivariable Calculus (4 Units)

Prerequisites: MATH 160.

Hours: 72 (72 lecture)

Functions of several variables, multiple integrals and applications, partial differentiation and applications, calculus of vector functions, Green's Theorem, Stokes' Theorem, and Divergence Theorem.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

C-ID: MATH 230.

MATH 210 Linear Algebra (4 Units)

Prerequisites: Math 160.

Hours: 72 (72 lecture)

Finite dimensional vector spaces, linear independence, basis, systems of linear equations, linear transformations, matrices, LU factorization, change of basis, similarity of matrices, eigenvalues and eigenvectors, applications, quadratic forms, symmetric and orthogonal matrices, canonical forms, introduction to infinite dimensional vector spaces.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

C-ID: MATH 250.

MATH 220 Differential Equations (4 Units)

Prerequisites: Math 200 and Math 210.

Hours: 72 (72 lecture)

Theory and applications of ordinary and partial differential equations. Topics include constant coefficient equations, series techniques, introduction to Laplace Transforms, qualitative and quantitative solutions to linear and nonlinear systems of differential equations, and separable partial differential equations.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

Transfer Information: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC Transferable

C-ID: MATH 240.