### Associate of Science in Mathematics

Santa Barbara, USA

DURATION

2 Years

LANGUAGES

English

PACE

Full time

APPLICATION DEADLINE

Request application deadline

EARLIEST START DATE

Request earliest startdate

TUITION FEES

USD 419 / per credit

STUDY FORMAT

On-Campus

### Introduction

The Mathematics department strives to provide our students with the educational background necessary to pursue a successful career and to successfully transition into a baccalaureate institution. Each year, the list of careers demanding familiarity with basic mathematical skills grows. Environmental sciences, architecture, business management, nursing, dentistry, computer programming, electronics, forestry management, psychology and photography represent only a small sample from this list.

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, linear algebra, and differential equations for 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.
- A complete precalculus program, including elementary algebra, intermediate algebra, college algebra and trigonometry to review old or gain new mathematical skills.

SBCC offers a Transfer Agreement Guarantee (TAG). A TAG is a contractual agreement between the student, SBCC, and specific four-year colleges or universities. This includes six University of California ( *UC) institutions, six California State Institutions (CSU), seven California private institutions, nine out-of-state institutions, as well as Honors Transfer Agreements with ten institutions and 8 CSUs without campus impaction. Students must enroll in the TAG program and work with a TAG advisor. Please click here to learn more on the TAG program website.

### Admissions

### Scholarships and Funding

Enrolled students may apply one time per year in February. If awarded, the money is disbursed for the following academic year in two parts: half in the fall semester and half in the spring semester. The amounts range from very small: $100-750 and larger $1000-2500 with some variations in between.

### Curriculum

### Mathematics (MATH)

MATH 007C Support for Intermediate Algebra (2 Units)

Same as: MATH 077

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

Corequisites: MATH 107.

Hours: 36 (36 lectures)

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.

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

Hours: 90 (90 lectures)

Foundational course, including language development, place value; definitions, concepts, and operations on whole numbers, fractions, decimals, ratios, proportions, percentages, 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 lectures)

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. The 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 lectures)

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 080 Elementary Algebra Refresher (1 Unit)

Hours: 18 (18 lectures)

For students who assessed into Math 95 and wish to improve their assessment level or who unsuccessfully attempted Math 107 and need a 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 lectures)

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. The 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 lectures)

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

Hours: 90 (90 lectures)

The second course is in algebra, including algebraic manipulation of polynomials, rational expressions, exponents, radicals, linear equations, ratio and proportion, inequalities, word problems, quadratic equations, and 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 lectures)

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 lectures)

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 lectures)

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 lectures)

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, PSY 150, and SOC 125 combined: maximum credit, one course.

C-ID: MATH 110.

MATH 118 Data Science for All (4 Units)

Same as: CS 118

Hours: 108 (54 lectures, 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: CSU Transferable, UC Transferable

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

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

Hours: 90 (90 lectures)

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

Prerequisites: Placement by SBCC assessment through multiple measures or.

Corequisites: MATH 130.

Hours: 36 (36 lectures)

Concurrent A review of core prerequisite skills, competencies, and advanced algebra concepts for calculus. Intended for students who are concurrently enrolled in Math 130 Calculus for Biological Sciences, Social Sciences, and Business I 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 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 lectures)

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 lectures)

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, 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 lectures)

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 lectures)

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.

C-ID: MATH 120.

MATH 138C Support for Precalculus (2 Units)

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

Corequisites: MATH 138.

Hours: 36 (36 lectures)

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 150 Calculus with Analytic Geometry I (5 Units)

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

Hours: 90 (90 lectures)

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

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)

Prerequisites: placement by SBCC assessment through multiple measures or MATH 138.

Corequisites: MATH 150.

Hours: 36 (36 lectures)

Concurrent A review of core prerequisite skills, competencies, and advanced algebra concepts for calculus. Intended for students who have concurrently enrolled in Math 150 Calculus with Analytic Geometry I at Santa Barbara City College. Review topics include skills developed in college algebra and precalculus, with an emphasis on refining skills in algebraic manipulation, functions, trigonometry, and geometry.

Transfer Information: CSU Transferable

MATH 160 Calculus with Analytic Geometry II (5 Units)

Prerequisites: MATH 150.

Hours: 90 (90 lectures)

Techniques of integration; applications of definite integrals; polar and parametric equations; sequences and infinite series; introduction to differential equations and 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 160C Support Course for Calculus with Analytic Geometry II (2 Units)

Corequisites: MATH 160.

Hours: 36 (36 lectures)

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 lectures)

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 are covered.

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

MATH 188 Trigonometry Refresher (1 Unit)

Hours: 18 (18 lectures)

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 lectures)

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 lectures)

Finite dimensional vector spaces, linear independence, basis, systems of linear equations, linear transformations, matrices, LU factorization, change of basis, the 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 lectures)

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.

### Program Outcome

### Learning Outcomes

- Use symbolic, graphical, numerical, and written representations to describe mathematical ideas.
- Use mathematical reasoning to solve problems and apply a variety of problem-solving approaches to find and interpret solutions.
- Use mathematics to model and solve problems in the sciences.
- Use appropriate technology to enhance mathematical thinking and understanding, solve mathematical problems, and interpret their results.
- Use the language and notation of differential and integral calculus correctly and use the appropriate style and format in written work.
- Recognize the roles of definitions, axioms, and theorems, and identify and construct valid deductive arguments.