# Mathematics

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

Each year, the list of careers requiring greater familiarity with mathematical and quantitative reasoning skills grows. Animation, data science, urban planning, geography, environmental science, architecture, business management, nursing, dentistry, forestry management, psychology and photography represent only a small sample. Advancing careers in Science, Technology, Engineering and Math (STEM) means students will be seeking degrees in mathematically sophisticated fields, such as physics, engineering and computer science, more than ever before. In addition to supporting improved career opportunities, the study of mathematics improves one’s problem-solving and critical thinking abilities, supports methods of logical reasoning and thinking analytically, develops flexibility of thought and creativity, and builds perseverance.

**Overview**

The Mathematics Department at Santa Barbara City College maintains a broad curriculum of courses scheduled in a variety of modalities to meet the needs of our diverse population of students. We offer the following pathways to help every student achieve their academic and career goals while supporting their interests and opening up opportunities to improve their lives:

**Statistics and Liberal Arts Mathematics (SLAM)**: Options provided through the math department for transfer-level quantitative reasoning courses include elementary statistics, mathematics for liberal arts majors, data science, college algebra and trigonometry.

**Calculus for the Biological Sciences and Business:** Our two-course sequence in applied calculus is open access and tailored to students in business and biology degree programs.

**Science, Technology, Engineering, Mathematics (STEM):** Our STEM mathematics pathway consists of a conventional college-level sequence in single and multivariable calculus, linear algebra, and differential equations, to serve students who plan to transfer to a four-year college or university in a STEM field.

Additionally, we offer:

**Precalculus for STEM Majors: **Available for dual enrollment students, Middle College students, or new to college future STEM majors that did not complete precalculus in high school, our one semester precalculus course is designed to equip students for advancing through the mathematics required by their STEM degree program. Covering concepts from college algebra and trigonometry, students taking this course build, strengthen, and refine the requisite skills necessary for success in STEM Calculus and beyond.

**Concurrent Corequisite Support: **Our assortment of concurrent corequisite support courses are each designed to provide targeted, just-in-time skill development and additional support to students enrolled in the required math course of their program. We offer sections of corequisite support for Statistics and Liberal Arts Math, College Algebra, Calculus I for Biological Sciences and Business, STEM Calculus I and STEM Calculus II.

**Our Commitment**

We strive to have students from all backgrounds and perspectives be well-served and have their learning needs supported in all aspects of our program. The diversity that students bring to our class interactions is viewed as a resource, strength and benefit. We are committed to presenting materials and activities in both our in-person and online classrooms that are respectful of diversity: gender identity, sexuality, disability, age, socioeconomic status, ethnicity, race, nationality, religion, and culture, and build a positive learning community where all our students will grow and thrive.

**Planning a Program of Study**

Students are urged to enroll in a math class that meets a requirement of their degree program as soon as possible, preferably in their first semester; postponing may in some cases significantly delay transfer. Mathematics requirements vary by degree and transfer goal, so it is essential for students to consult with an academic counselor regularly to create and continue to update their personalized Student Education Plan (SEP) and ensure they maintain progress to achieving their goals.

Please visit sbcc.edu/mathematics/ to view all of our course descriptions and curriculum outlines of record by course, details of the various instructional methods/modalities offered by the SBCC Math department, contact information for our faculty, information about our Math Tutorial Lab, and other resources. To view sample program maps by degree and view your program of study’s mathematics requirement/recommendation, visit sbcc.edu/assessmentcenter/placementguides.php.

**Course Placement and Eligibility**

SBCC uses Multiple Measures, which primarily consists of the high school coursework and grades data collected in the student’s SBCC application, to establish eligibility for math courses. Students will receive a placement for both the Statistics and Liberal Arts Math (SLAM) and Business and Science, Technology, Engineering, Math (B-STEM) tracks through the Assessment Center, (805) 730-4149 or sbcc.edu/assessmentcenter; this information can be viewed by students in their Pipeline account. For some courses, it may be either required or recommended to concurrently enroll in a corequisite support course. For those questioning their placement, or for transfer students who have successfully completed an equivalent mathematics course at another college, please visit sbcc.edu/teo for pre/corequisite clearance and coursework/transcript evaluation procedures.

## Mathematics (MATH)

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: 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. Review topics include skills developed in pre-algebra and elementary algebra, operations on integers and fractions, simplifying and manipulating algebraic expressions, solving simple linear equations, applying basic geometric formulas, translation from English to algebra, and using the vocabulary/language of arithmetic and pre-algebra.

Transfer Information: Extrnl - Not Degree Applicable

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 095 Elementary Algebra (5 Units)

Prerequisites: MATH 004 or MATH 041 or equivalent based on SBCC's Assessment Center placement via multiple measures.

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 107 Intermediate Algebra (5 Units)

Prerequisites: MATH 095 or MATH 007C or or equivalent based on SBCC's Assessment Center placement via multiple measures.

Hours: 90 (90 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 108 Mathematical Concepts for Elementary School Teachers-Number Systems (4 Units)

Prerequisites: MATH 107 or equivalent, based on SBCC's Assessment Center placement via multiple measures.

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.

SBCC General Education: SBCCGE Area D2, SBCCGE Area E1

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

C-ID: Math 120.

MATH 110C Support for Statistics and Liberal Arts Math (2 Units)

Prerequisites: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures.

Corequisites: MATH 117 or MATH 114 or MATH 108.

Hours: 36 (36 lecture)

Concurrent A review of core prerequisite skills, competencies and concepts for elementary statistics and liberal arts mathematics. Intended for students who are concurrently enrolled in Math 117 Elementary Statistics, Math 114 Mathematics for Liberal Arts Majors, or Math 108 Mathematics for Elementary Teachers at Santa Barbara City College. Review topics include skills developed in elementary algebra and intermediate algebra, translation from English to algebra, evaluation of literal expressions, solving and graphing linear equations and calculator skills.

SBCC General Education: SBCCGE Area E1

MATH 114 Mathematics for Liberal Arts Majors (4 Units)

Prerequisites: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures.

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 equivalent based on SBCC's Assessment Center placement via multiple measures.

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 ANOVA, 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, MATH 117A and MATH 117B, PSY 150 and SOC 125 combined: maximum credit, 1 course or series.

C-ID: MATH 110.

MATH 117A Elementary Statistics A (2 Units)

Hours: 36 (36 lecture)

MATH 117A is the first part of a two course sequence of a general education mathematics course in statistics. Taken together, MATH 117A and MATH 117B are collectively equivalent to MATH 117, Elementary Statistics. Topics in this course include introduction to design of experiments, descriptive statistics, types of data, introductory probability and sampling distributions. Emphasis is placed on the application of statistical concepts to real world data, development of statistical literacy and reasoning, and the interpretation of results.

SBCC General Education: SBCCGE Area E1

Transfer Information: CSU Transferable, UC Transferable

UC Transfer Limit: MATH 117, MATH 117A and MATH 117B, PSY 150 and SOC 125 combined: maximum credit, 1 course or series.

MATH 117B Elementary Statistics B (2 Units)

Prerequisites: MATH 117A.

Hours: 36 (36 lecture)

MATH 117B is the second part of a two course sequence of a general education mathematics course in statistics. Taken together, MATH 117A and MATH 117B are collectively equivalent to MATH 117, Elementary Statistics. Topics include sampling distributions, Central Limit Theorem, statistical inference, confidence interval estimation, tests of hypotheses, correlation and linear regression, Chi-square, one-way ANOVA, and multiple comparisons procedure. Emphasis is placed on the application of statistical concepts to real world data, development of statistical literacy and reasoning, and the interpretation of results.

SBCC General Education: SBCCGE Area E1

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

MATH 118 Data Science for All (4 Units)

Same as: CS 118

Hours: 108 (54 lecture, 54 lab)

Introduction to data science using real-world data sets from a variety of disciplines while also presenting inherent uncertainties and issues associated with exploring data. Exposes students to foundational statistical concepts and inferential thinking by learning computation methods in a commonly used programming language such as Python.

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

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

Prerequisites: College algebra or equivalent or SBCC's Assessment Center placement via multiple measures.

Corequisites: MATH 130C based on SBCC's Assessment Center placement via multiple measures.

Hours: 90 (90 lecture)

Concurrent A first course in Calculus, the study of change-how to measure, model, and predict changes in quantities we observe in our universe. An investigation of functions, relations, and mathematical models arising in business, biological sciences, and social sciences, through the concepts of limit, differentiation, and integration. Applications of the derivative such as linear approximation, related rates, and optimization. Applications of integration such as area, and total change. Understanding the connection between differential calculus/rate of change and integral calculus/accumulation through the Fundamental Theorem of Calculus. This course is intended for Business and/or Biology majors who have successfully completed precalculus in high school, or SBCC's Math 137:College Algebra, or the equivalent. Students enrolling in Math 130 are eligible to concurrently enroll in Math 130C: Support for Calculus for the Biological Sciences, Social Sciences, and Business I; students with limited experience with college algebra/precalculus are especially encouraged, or may be required to do so. Students in Math 130 will demonstrate their learning of course outcomes through multiple methods of assessment, including at least 5 hours of controlled assessments in the form of in-person proctored exams/project presentations and a cumulative in-person proctored final exam.

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 130C Support for Calculus for Biological Sciences, Social Sciences and Business I (2 Units)

Corequisites: MATH 130.

Hours: 36 (36 lecture)

Concurrent A comprehensive supplemental course designed to support students who are concurrently enrolled in Math 130: Calculus for Biological Sciences, Social Sciences, and Business I at SBCC. Topics and learning activities for college algebra skills development and strengthening incorporated throughout, with an emphasis on refining skills necessary for success in Math 130, including algebraic manipulation, knowledge of functions and graphing, geometry, and applications, as well as problem-solving, study skills, and growth mindset in mathematics.

Transfer Information: CSU Transferable

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

Prerequisites: MATH 130.

Course Advisories: ENG 098 or ENG 103.

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 College Algebra (5 Units)

Hours: 90 (90 lecture)

Extensive treatment of functions and graphing techniques, including translations, symmetries, reflections, and graphs of inverse functions. Analysis and applications of polynomial, rational, absolute value, exponential and logarithmic functions. Systems of equations and inequalities, conics, and sequences and series.

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 137 and MATH 138 combined: maximum credit, 5 semester/7.5 quarter units. No credit for MATH 137 or H 138 if taken after MATH 130 or MATH 150.

MATH 137C Support for College Algebra (2 Units)

Corequisites: MATH 137.

Hours: 36 (36 lecture)

Concurrent A review of core prerequisite skills, competencies, and concepts for college algebra. Intended for students who are concurrently enrolled in Math 137 College Algebra at Santa Barbara City College. Review topics include skills developed in elementary algebra and intermediate algebra, with an emphasis on refining skills in algebraic manipulation and simplification of linear, quadratic, polynomial, radical, and rational expressions, functions and graphing.

SBCC General Education: SBCCGE Area E1

MATH 138 Precalculus - College Algebra and Trigonometry (4 Units)

Prerequisites: MATH 137 or equivalent based on SBCC's Assessment Center placement via multiple measures.

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 matrix algebra, logic and structure of proof, 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 137 and MATH 138 combined: maximum credit, 5 semester/7.5 quarter units; No credit for MATH 137 or MATH 138 if taken after MATH 130 or MATH 150.

MATH 138C Support for Precalculus (2 Units)

Prerequisites: Placement by SBCC assessment through multiple measures or MATH 120.

Corequisites: MATH 138.

Hours: 36 (36 lecture)

Concurrent A review of core prerequisite skills, competencies and advanced concepts for precalculus. Intended for students who are concurrently enrolled in Math 138 Precalculus II at Santa Barbara City College. Review topics include skills developed in college algebra, with an emphasis on refining skills in algebraic manipulation, functions and geometry.

Transfer Information: CSU Transferable

MATH 149 Precalculus for STEM Majors (6 Units)

Hours: 108 (108 lecture)

Preparation for SBCC's STEM Calculus sequence Math 150, followed by Math 160. Topics include the study of polynomial, absolute value, radical, rational, exponential, and logarithmic functions, analytic geometry, and polar coordinates. The study of trigonometric functions, their inverses and their graphs, identities, and proofs related to trigonometric expressions, solving trigonometric equations, solving right triangles, and solving triangles using the Law of Cosines and the Law of Sines will also be covered, as well as an introduction to 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: All College Algebra and Pre-Calculus courses limited to a single course with a maximum of 5 semester / 7.5 quarter units.

MATH 150 Calculus with Analytic Geometry I (5 Units)

Prerequisites: MATH 138 or MATH 149 or equivalent based on SBCC's Assessment Center placement via multiple measures.

Hours: 90 (90 lecture)

A first course in Calculus, the study of change-how to measure, model, and predict changes in quantities we observe in our universe. An investigation of functions, relations, and mathematical models from a variety of STEM disciplines, through the concepts of limit, differentiation, and integration. Applications of the derivative such as linear approximation, related rates, and optimization. Applications of integration such as area, net, and total change. Understanding the connection between differential calculus/rate of change and integral calculus/accumulation through the Fundamental Theorem of Calculus. This course is intended for STEM majors that have successfully completed the equivalent of one year of precalculus in high school, OR SBCC's Math 137: College Algebra and 138: College Algebra & Trigonometry precalculus sequence, OR Math 149: Precalculus for STEM Majors. Students enrolled in Math 150 are eligible to concurrently enroll in Math 150C: Support for Calculus w/ Analytic Geometry I. Students in Math 150 will demonstrate their learning of course outcomes through multiple methods of assessment, including at least 5 hours of controlled assessments in the form of in-person proctored exams/project presentations and a cumulative, in-person proctored final exam.

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 150C Support Course for Calculus with Analytic Geometry I (2 Units)

Corequisites: MATH 150.

Hours: 36 (36 lecture)

Concurrent A comprehensive supplemental course designed to support students who are concurrently enrolled in Math 150: Calculus with Analytic Geometry I at SBCC. Topics and learning activities for precalculus skills development and strengthening incorporated throughout, with an emphasis on refining skills necessary for success in Calculus I including algebraic manipulation, knowledge of functions and graphing, trigonometry, geometry, and applications, as well as problem-solving, study skills, and growth mindset in mathematics.

Transfer Information: CSU Transferable

MATH 160 Calculus with Analytic Geometry II (5 Units)

Prerequisites: MATH 150.

Hours: 90 (90 lecture)

A second course in Calculus, the study of accumulation-how to measure, model, and approximate quantities we observe in our universe. An investigation of techniques of integration and applications of the definite integral such as area, volume, arclength, surface area, and center of mass. Explore convergence of infinite series and applications of power series. Apply calculus to alternative descriptions of curves in the plane via polar functions and parametric equations. An introduction to differential equations and an introduction to vectors is also included. This course is intended for STEM majors who have successfully completed SBCC's Math 150: Calculus with Analytic Geometry I, OR the equivalent, OR scored 3 or higher on the AP Calculus AB exam. Students enrolled in Math 160 are eligible to concurrently enroll in Math 160C: Support for Calculus w/ Analytic Geometry II. Students in Math 160 will demonstrate their learning of course outcomes through multiple methods of assessment, including at least 5 hours of controlled assessments in the form of in-person proctored exams/project presentations and a cumulative, in-person proctored final exam.

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 160C Support Course for Calculus with Analytic Geometry II (2 Units)

Corequisites: MATH 160.

Hours: 36 (36 lecture)

Concurrent A review of core prerequisite skills, competencies, advanced algebra and beginning calculus concepts for second semester calculus. Intended for students who are concurrently enrolled in Math 160 Calculus with Analytic Geometry II at Santa Barbara City College. Review topics include skills developed in college algebra, precalculus, and first-semester calculus, with an emphasis on refining skills in algebraic manipulation, functions, trigonometry, proofs, limits and differentiation.

Transfer Information: CSU Transferable

MATH 180 Transition to Advanced Mathematics (4 Units)

Prerequisites: MATH 160.

Hours: 72 (72 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: CSUGE Area B4, IGETC Area 2A, CSU Transferable, UC 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, and 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.