2010-2011 CATALOG

This is an archived copy of the 2010-2011 catalog. To access the most recent version of the catalog, please visit http://catalog.miracosta.edu

Mathematics

Mathematics, the abstract study of pattern and structure, is the foundation of all science and technology programs, such as biological, physical, computer, behavioral, and social sciences as well as engineering. Areas of mathematics include arithmetic, algebra, geometry, calculus, and various other theoretical and applied subjects. Students take mathematics courses to prepare for a mathematics major, to meet prerequisites in related disciplines, or to fulfill general education requirements. A bachelor's degree in mathematics can lead to a career in a computer-related field or as an actuary, accountant, mathematician, statistician, or teacher.

Contact Information

Department Chair: Peter Avery

Dean: Ric Matthews

www.miracosta.edu/MATH

Department: Mathematics

Office: SAN 602, (760) 795-6874

Full-Time Faculty

Janeen Apalatea
Peter Avery
Angela Beltran
David Bonds
Carol Congleton
Keith Dunbar
Julie Harland
Mark Laurel

Lemee Nakamura
Victoria Noddings
Zikica Perovic
Brent Pickett
Beth Powell
Mohammed G. Rajah
John Towers

Associate Degree

Associate in Arts Degree

Mathematics

The Mathematics Program offers lower-division preparation for students who plan on transferring to pursue a bachelor's degree in mathematics. Students planning to transfer and/or earn this associate degree may also need to complete additional requirements or electives required by the transfer institution, as many CSUs and UCs have unique admissions and preparation-for-the-major requirements. Students should meet with a MiraCosta College counselor to identify required courses and to develop a written plan for their targeted university.

Required courses:
MATH 150	Calculus and Analytic Geometry I	5
MATH 155	Calculus and Analytic Geometry II	4
MATH 260	Calculus and Analytic Geometry III	4
Select at least three courses from the following:		9-12
CS 111	Introduction to Computer Science I: Java
CS 112	Introduction to Computer Science II: Java
CS 150	C++ Programming
MATH 103	Statistics
MATH 226	Discrete Mathematics
MATH 265	Differential Equations
MATH 270	Linear Algebra
PHYS 151	Principles of Physics I
PHYS 152	Principles of Physics II
PHYS 253	Principles of Physics III
Total Units		22-25

How to Read Course Descriptions

Courses listed in this catalog apply to the fall 2010, spring 2011, and summer 2011 terms. Courses are numbered numerically within alphabetically arranged subject areas.

The bolded first line indicates the official course number, a descriptive title, and the number of units. The next lines indicate prerequisites, corequisites, advisories, repeatability rules, enrollment limitations, UC/CSU credit acceptance, and lecture and lab hours followed by a Taxonomy of Program number in parentheses.

Prerequisites: This is a requirement that must be met before a student can enroll in the course.
Corequisites: This is a course the student must take in the same semester.
Advisories: This is recommended preparation the student is advised but not required to have before or in conjunction with the course.
Repeatability Rules: When a course belongs to a group of related courses, students can complete one course or a combination of courses within the group for a maximum of four completions.
Enrollment Limitations: Some courses place limitations on enrollment. These limitations prevent students from duplicating course work or from enrolling in two sections of the same course in any given semester.
Acceptable for Credit: CSU means the course is accepted for transfer at any California State University (CSU) campus; UC means it is accepted for transfer at any University of California (UC) campus. Some courses can be used to satisfy general education or major requirements while others transfer as elective credit. UC Credit Limitation means credit for the course may have UC transfer restrictions; these restrictions are identified at the end of the course description.
Lecture and Lab Hours: These are the number of hours the course meets for lecture and/or lab per week.
Taxonomy of Program (TOP) Number: The TOP number is identified in parentheses after the lecture and lab hours. This number serves an administrative purpose and is not intended for student use.

The course description summarizes the purpose and key topical areas of the course, and it includes special requirements if any exist. Some course descriptions end with information about whether the course was "formerly" another course, how many times the course may be repeated, if the course is offered pass/no pass, or what the UC credit limitation is.

How to Read Course Descriptions

Courses

MATH 101: Intermediate Algebra

Units: 4
Prerequisites: MATH 830 or MATH 830B or qualification through the Math Competency Exam or approved equivalent.
Repeatability Rule: Students may earn a maximum of 4 units in any combination of MATH 101, MATH 101A, MATH 101B.
Lecture 4 hours. (1701.00)

Topics include a study of radicals, exponents, rational expressions, concepts of relations and functions, exponential and logarithmic functions, linear and quadratic functions; and the solutions of equations from these topics. This course is offered in both traditional and self-paced formats.

MATH 101A: Intermediate Algebra Part 1

Units: 2
Prerequisites: MATH 830 or MATH 830B with a C or better, or qualification through the Math Competency Exam or approved equivalent.
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 101, MATH 101A, and MATH 101B.
Lecture 2 hours. (1701.00)

This course covers radicals, exponents, rational expressions, concepts of relations and functions, and linear and quadratic functions. Students analyze verbal problems, model with appropriate functions, substitute the unknown values, and solve the resulting equations. Students may be required to take proctored exams.

MATH 101B: Intermediate Algebra Part 2

Units: 2
Prerequisites: MATH 101A with a grade of C or better.
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 101, MATH 101A, and MATH 101B.
Lecture 2 hours. (1701.00)

This algebra course covers rational expressions, relations and functions, and exponential and logarithmic functions. Students may be required to take proctored exams.

MATH 103: Statistics

Units: 4
Prerequisites: MATH 101 or MATH 101B with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Acceptable for Credit: CSU, UC Credit limitation
Lecture 4 hours. (1701.00)

This course introduces data analysis. Topics include design of experiments, descriptive statistics, correlation and regression, probability, sampling, estimation, and significance testing. Students use appropriate technology to analyze real-world data. Students may be required to take proctored exams. UC CREDIT LIMITATION: Credit for MATH 103, BIO/BTEC 180, or PSYC/SOC 104.

MATH 105: Concepts and Structures of Elementary Mathematics I

Units: 3
Prerequisites: MATH 101 or MATH 101B with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Acceptable for Credit: CSU, UC Credit limitation
Lecture 3 hours. (1701.00)

Subjects include set theory, problem solving, systems of numeration, elementary number theory, numerical operations and arithmetic algorithms. Emphasis throughout is on cognitive learning and developing problem solving strategies and techniques. Students may work collaboratively in groups and/or independently using manipulatives and models to explore the structures and formulate concepts. UC CREDIT LIMITATION: Credit for MATH 105 or MATH 106.

MATH 106: Concepts and Structures of Elementary Mathematics II

Units: 3
Prerequisites: MATH 105 with a grade of C or better or approved equivalent.
Acceptable for Credit: CSU, UC Credit limitation
Lecture 3 hours. (1701.00)

This course, which is a continuation of MATH 105, is a study of the mathematical concepts needed for teaching elementary school mathematics. Core topics include the real number system, geometry, Pythagorean theorem, measurement in both the English and Metric systems, transformations, and symmetry. Students are required to demonstrate their understanding of the concepts and structures of elementary mathematics using critical thinking. Analytical reading, writing, problem solving, and the ability to do constructive geometry are required for success in this course. UC CREDIT LIMITATION: Credit for MATH 105 or MATH 106.

MATH 115: Calculus with Applications

This course relates calculus to real-world applications in social science, economics, and business. Topics include an algebra review, graphing, limits, derivatives of logarithmic and exponential functions, development of integration techniques, and an introduction to multi-variable calculus, and their applications to problems. This course is designed primarily for students majoring in social science, economics, and business who require calculus and is not recommended for mathematics, physical science, engineering, or biological science majors. UC CREDIT LIMITATION: Credit for MATH 115 or MATH 150.

MATH 125: College Algebra

Topics include a review of techniques for solving algebraic equations and inequalities; definitions and properties of functions and inverse functions; graphs of linear, quadratic, and other polynomial functions and of rational functions; translations and combinations of functions; zeros of polynomial functions; definitions, graphs, and properties of exponential and logarithmic functions; techniques for solving exponential and logarithmic equations; and techniques for solving systems of equations. UC CREDIT LIMITATION: Credit for MATH 125 or MATH 135.

MATH 130: Trigonometry

Units: 3
Prerequisites: MATH 101 or MATH 101B with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Acceptable for Credit: CSU
Lecture 3 hours. (1701.00)

Topics include definitions and properties of trigonometric functions; solutions of applied problems involving right triangles; graphs of trigonometric functions including period changes, amplitude changes, and phase shifts; trigonometric identities; trigonometric equation solving; and evaluation of inverse trigonometric functions.

MATH 135: Pre-Calculus Mathematics

Units: 5
Prerequisites: MATH 130 with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Corequisite: MATH 130 if prerequisite not met.
Acceptable for Credit: CSU, UC Credit limitation
Lecture 5 hours. (1701.00)

A study of functions and their properties. Topics include linear, quadratic, polynomial, rational, trigonometric, exponential, and logarithmic functions; systems of equations and inequalities; and conics. NOTE: A graphics calculator is required. Please attend the first class meeting before purchasing. UC CREDIT LIMITATION: Credit for MATH 125 or MATH 135.

MATH 150: Calculus and Analytic Geometry I

Units: 5
Prerequisites: MATH 130 and MATH 135 with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Acceptable for Credit: CSU, UC Credit limitation
Lecture 5 hours. (1701.00)

This course is the first in a three-semester calculus sequence designed for mathematics, science, and engineering majors. Topics include limits and continuity; differentiation of algebraic, trigonometric, and exponential functions and their universe; integration and the Fundamental Theorem of Calculus; and applications of differentiation and integration. NOTE: A graphics calculator is required. Please attend the first class meeting before purchasing. UC CREDIT LIMITATION: Credit for MATH 115 or MATH 150.

MATH 155: Calculus and Analytic Geometry II

Units: 4
Prerequisites: MATH 150 with a grade of C or better or approved equivalent.
Acceptable for Credit: CSU, UC
Lecture 4 hours. (1701.00)

This second course in a three-semester calculus sequence covers advanced integration techniques, improper integrals, infinite series, conic sections, parametric equations, and polar coordinates. This course is designed for mathematics, science, and engineering majors. NOTE: A graphics calculator is required. Please attend the first class meeting before purchasing.

MATH 226: Discrete Mathematics

Units: 3
Prerequisites: MATH 135 with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Acceptable for Credit: CSU, UC
Lecture 3 hours. (1701.00)

Designed for students majoring in mathematics or computer science, this introduces discrete mathematics including logic, methods of proof, number theory, sets, counting, relations, recursion, recurrence relations, and Boolean algebra. Topics will be illustrated with applications to computer science, including design and analysis of algorithms, undecidability, program correctness, digital logic design, and others.

MATH 260: Calculus and Analytic Geometry III

Units: 4
Prerequisites: MATH 155 with a grade of C or better or approved equivalent.
Acceptable for Credit: CSU, UC
Lecture 4 hours. (1701.00)

This third course in a three-semester calculus sequence covers vectors in two and three space, graphs of quadric surfaces, vector-valued functions of several variables, partial differentiation and multiple integration, vector fields, and line integrals and conservative fields. The course is designed for mathematics, science, and engineering majors.

MATH 265: Differential Equations

Units: 3
Prerequisites: MATH 155 with a grade of C or better or approved equivalent.
Acceptable for Credit: CSU, UC
Lecture 3 hours. (1701.00)

This course introduces the theory and applications of ordinary differential equations of first and higher (mostly second) order as well as systems of linear differential equations. It includes both quantitative and qualitative methods. The course deals with theoretical aspects of existence and uniqueness of solutions as well as techniques for finding these solutions: analytical, numerical, power-series. The course is designed for the transfer student planning to major in mathematics, engineering, computer science, or physical sciences.

MATH 270: Linear Algebra

Units: 3
Prerequisites: MATH 260 with a grade of C or better or approved equivalent.
Corequisite: MATH 260 if prerequisite not met.
Acceptable for Credit: CSU, UC
Lecture 3 hours. (1701.00)

This course introduces students to the concepts of linear algebra. Topics include matrix algebra, Gaussian elimination, determinants of a matrix, properties of determinants, vector spaces and their properties with an introduction to proofs, linear transformations, orthogonality, and eigenvalues and eigenvectors.

MATH 292: Internship Studies

Units: 0.5-3
Prerequisites: Complete 6 units at MCC prior to internship; permission of instructor and department chair required.
Corequisite: Must currently be enrolled in 3 units and complete 60 hours of non-paid or 75 hours of paid work per unit of credit.
Acceptable for Credit: CSU
(1701.00)

Individualized study linking classroom learning to the workplace. Approval form must be signed by instructor and department chair before registration. (May be taken for a total of 12 units.)

MATH 293: Topics in Mathematics

Units: 1-3
Prerequisites: None
Repeatability Rule: Allow four completions in any combination of MATH 293, MATH 296.
Lecture 1 hour.
Lecture 2 hours.
Lecture 3 hours. (1701.00)

A study of relevant topics in the discipline not covered in the current selection of courses. Designed to meet special needs; content determined by participating faculty members in consultation with students and the community. Non-transfer topics only.

MATH 296: Topics in Mathematics

Units: 1-3
Prerequisites: MATH 135 or higher.
Acceptable for Credit: CSU
Lecture 1 hour or Laboratory 3 hours.
Lecture 2 hours or Lecture 1 hours, Laboratory 3 hours.
Lecture 3 hours or Lecture 2 hours, Laboratory 3 hours. (1701.00)

MATH 820: Pre-Algebra

Units: 4
Prerequisites: None
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 820, MATH 820A, and MATH 820B.
Lecture 4 hours. (1701.00)

This course prepares students for Elementary Algebra (MATH 830). Topics include operations on positive and negative numbers; fractions, decimals, and percents; perimeters, areas, and volumes of geometric figures; fundamental algebraic concepts; square roots; and applications. Students may be required to take proctored exams.

MATH 820A: Pre-Algebra Part 1

Units: 2
Prerequisites: None
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 820, MATH 820A, and MATH 820B.
Lecture 2 hours. (1701.00)

This course is designed as the first half of the Pre-Algebra course. Successful completion of this course together with MATH 820B is equivalent to MATH 820. Topics include operations on positive and negative numbers; review of fractions, decimals, and percents; and fundamental algebraic concepts. Students may be required to take proctored exams.

MATH 820B: Pre-Algebra Part 2

Units: 2
Prerequisites: MATH 820A with a grade of C or better.
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 820, MATH 820A, and MATH 820B.
Lecture 2 hours. (1701.00)

This successor course to MATH 820A prepares students for Elementary Algebra (MATH 830). Topics include perimeters, areas, and volumes of geometric figures, fundamental algebraic concepts, square roots, and applications. Students may be required to take proctored exams.

MATH 830: Elementary Algebra

Units: 4
Prerequisites: MATH 820 or MATH 820B or qualification through the Math Competency Exam or approved equivalent.
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 830, MATH 830A, MATH 830B.
Lecture 4 hours. (1701.00)

Designed to prepare students for Intermediate Algebra, Elementary Algebra teaches simplifying algebraic expressions involving polynomials and rational terms; factoring; solving linear equations; solving quadratic equations using factoring; analyzing graphs of linear equations; and solving applied problems. This course is offered in both traditional and self-paced formats. (Formerly MATH 100.)

MATH 830A: Elementary Algebra Part 1

Units: 2
Prerequisites: MATH 820 or MATH 820B with a grade of C or better or qualification through the Math Competency Exam or approved equivalent.
Enrollment Limitation: Students may earn a maximum of 4 units in any combination of MATH 830, MATH 830A/830B.
Lecture 2 hours. (1701.00)

This first half of Elementary Algebra covers simplifying algebraic expressions involving polynomials, solving linear equations, analyzing graphs of linear equations, and solving applied problems. Students may be required to take proctored exams. (Formerly MATH 100A.)

MATH 830B: Elementary Algebra Part 2

Units: 2
Prerequisites: MATH 830A with a grade of C or better.
Repeatability Rule: Repeatability: Students may earn a maximum of 4 units in any combination of MATH 830, MATH 830A, and MATH 830B.
Lecture 2 hours. (1701.00)

This second half of Elementary Algebra covers simplifying algebraic expressions involving rational expressions, factoring, solving quadratic equations using factoring, and solving applied problems. Students may be required to take proctored exams. (Formerly MATH 100B.)

MATH 896: Topics in Mathematics

Units: 0.5-3
Prerequisites: None
Lecture 3 hours. (1701.00)

A study of relevant topics in the discipline. Content will be determined by participating faculty members in consultation with students and the community.