# Mathematics

Mathematics is the study of quantity, structure, space and change. It is developed through the use of abstraction and logical reasoning from counting, calculations, measurement, study of shapes & change. Mathematics is also used to refer to the insight gained by mathematicians by doing mathematics, also known as the body of mathematical knowledge. This latter meaning of mathematics includes the mathematics used to do calculations and is an indispensable tool in the natural sciences and engineering.

Career paths chosen by students pursuing undergraduate studies in mathematics commonly include teaching, actuary, computer science, statistics, physics and engineering. Careers in the discipline that generally require graduate-level degrees include mathematics, engineering and the natural sciences. Even students who choose not to major in mathematics find that coursework in the field can improve their ability to think critically, solve complex problems, perform research and analysis and improve their writing skills.

College of the Desert’s mathematics curriculum includes course offerings that provide a general overview of the discipline, as well as specific mathematical topics that can be applied to other areas like physics, chemistry, biology, computer science and engineering. The College offers an Associate of Science degree, as well as courses leading to transfer. Students earning an associate’s degree in mathematics may pursue (entry-level) positions as teacher’s aid or may choose to continue their study in the discipline toward a bachelor’s or graduate degree. COD has transfer agreements with California State Universities and University of California systems in this discipline/program. However, transfer requirements at four-year colleges and universities vary from institution to institution; students should consult with a counselor for specific information regarding the transfer requirements of their preferred college or university.

In addition, the Mathematics Department offers an extensive remedial mathematics curriculum to assist the large portion of students that enter the College and are not prepared for college-level mathematics. For more information please call (760) 773-2573.

**Advisors:**

**Dustin Culhan**

dculhan@collegeofthedesert.edu

(760) 776-7376

**Steve Dostal**

sdostal@collegeofthedesert.edu

(760) 776-7275

**Melissa Flora**

mflora@collegeofthedesert.edu

(760) 776-7392

**Laura Graff**

lgraff@collegeofthedesert.edu

(760) 862-1334

**Geoffrey Hagopian**

ghagopian@collegeofthedesert.edu

(760) 776-7223

**Leif Jordan**

ljordan@collegeofthedesert.edu

(760) 776-7389

**Daniel Kleinfelter**

dkleinfelter@collegeofthedesert.edu

(760) 776-7346

**Thang Le**

tle@collegeofthedesert.edu

(760) 862-1368

**John Learned**

jlearned@collegeofthedesert.edu

(760) 776-7328

**Felix Marhuenda-Donate**

fmarhuenda@collegeofthedesert.edu

(760) 773-2523

**James Matthews**

jmatthews@collegeofthedesert.edu

(760) 776-7375

**Michael McJilton**

mmcjilton@collegeofthedesert.edu

(760) 776-7314

**Jim Parvizi**

jparvizi@collegeofthedesert.edu

(760) 776-7313

**Bartlomiej Podlesny**

bpodlesny@collegeofthedesert.edu

(760) 776-7379

**MATH 001A Calculus Units: 4**

This course is a study of the meaning, computation and analysis of the derivative with an introduction to the integral. Topics include the definitions and analysis of limits, continuity, and differentiability; methods for differentiating polynomial, rational, exponential, logarithmic and trigonometric functions, together with functions represented numerically and graphically; applications of the derivative; and an introduction to the integral. (C-ID MATH 210)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-012

Advisory: ENG-071

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 001B Calculus Units: 4**

This course is a study of the meaning, methods and applications of integration and infinite series. Topics include the definition of the definite integral, the Fundamental Theorem of Calculus, techniques of integration, applications of integration, first order separable differential equations, modeling exponential growth and decay, infinite series and approximation of functions using Taylor series with remainder. (C-ID MATH 220)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-001A

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 002A Multivariate Calculus Units: 4**

This course extends the concepts of differentiation and integration introduced in the first two semesters of calculus to functions of several variables. Topics include solid Euclidean geometry, vector algebra in 3 dimensions, line and surface integrals, multiple integration in rectangular, cylindrical and spherical coordinates, extreme values, parameterized space curves and surfaces, divergence, directional derivatives, gradients, Gauss', Green's and Stokes' theorems. (C-ID MATH 230)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-001B

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 002B Linear Algebra Units: 4**

This course is a standard introductory course in linear algebra. Topics include vectors in Rn, matrices and systems of linear equations, determinants, vector spaces, linear independence, linear transformations, eigenvalues, eigenvectors, and diagonalization of certain quadratic forms. (C-ID MATH 250)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-001B

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 002C Ordinary Differential Equations Units: 4**

This is a standard introductory course in differential equations and their applications in modeling dynamic phenomena. Topics include first, second and higher order differential equations; systems of first order equations, linear, homogeneous and nonhomogeneous differential equations; solutions by power series; numerical methods, LaPlace transforms; and applications. (C-ID MATH 240)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-001B

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 005 Trigonometry Units: 5**

This course is the first of a two semester sequence preparing students for calculus. In this course, students will study functions with an emphasis on the trigonometric functions along with topics in analytic geometry. Topics will include a review of plane and coordinate geometry, functions including function notation, transformations and inverses, definitions and graphs of the trigonometric functions, modeling periodic behavior, solving triangle problems with the Law of Sines and Cosines, the conic sections, parametric equations and vectors.

Lecture Hours: 90 Lab Hours: None Repeatable: No

Grading: Letter

**Prerequisite:** MATH-030 and MATH-040

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: None

**MATH 009 Business Calculus Units: 4**

Presents a study of the techniques of calculus with emphasis placed on the application of these concepts to business and management related problems. The applications of derivatives and integrals of functions including polynomials, rational, exponential and logarithmic functions are studied. (C-ID MATH 140)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-010 or MATH-012

Advisory: ENG-071

Limitation on enrollment: None

Transfer Status: CSU Degree Applicable: AA/AS

COD GE: C4b CSU GE: None IGETC: None

**MATH 010 College Algebra Units: 4**

This is a function oriented course that includes an examination of the general concept of a function and function notation, as well as an in depth investigation of polynomial, rational, exponential, and logarithmic functions, particularly their equations, graphs, and behavior. Other topics include the binomial theorem, conic sections, and matrices as they apply to systems of linear equations. (C-ID MATH 150)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-040

Advisory: ENG-071

Limitation on enrollment: None

Transfer Status: CSU/UC* Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 011 Math Concepts For Elementary School Teachers-Number System Units: 4**

This course covers mathematical topics needed for elementary school teaching with a focus on quantitative reasoning, problem solving and communication. Topics include structure of the real number system, sets, numeration systems, computation algorithms, problem solving strategies, and elementary number theory. The course meets requirements for elementary school teacher certification. (C-ID MATH 120)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-040, or completion of two years of High School Algebra,and appropriate placement score.

Advisory: MATH-030 or one year High School Geometry and,ENG-061 or ENG-071

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: None

**MATH 012 Pre-calculus Units: 5**

This course is the second in a two semester sequence preparing students for Calculus. In this course, students will extend the concept of a function to polynomial, rational, exponential and logarithmic functions as well as studying analytic trigonometry. Topics include recognizing, graphing and solving equations and word problems involving polynomial, rational, exponential and logarithmic functions, trigonometric identities, inverse trigonometric functions, and solving trigonometric equations.

Lecture Hours: 90 Lab Hours: None Repeatable: No

Grading: Letter

**Prerequisite:** MATH-005

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC* Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 013 Liberal Arts Math Units: 4**

This course is designed for Social Science and Liberal Arts majors. It emphasizes applications of Mathematics in the areas of management science, probability and statistics, social choice and decision making, game theory, and consumer finance. Topics include sets, logic & counting, probability, linear systems, linear programming & scheduling, statistics, mathematics of finance and applications for Liberal Arts majors.

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-040 and ENG-071

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 014 Statistical Methods Units: 4**

This course is an introduction to descriptive and inferential statistics; how to use measures of central tendency and dispersion among population samples to draw inferences about a population and to compare two or more populations. Discrete and continuous probability density distributions are analyzed including the binomial, normal, Student-t, chi-squared, and F-distributions. Confidence intervals for population means, proportions and variance are set. Additional topics include regression and correlation analysis and techniques of hypothesis testing, including ANOVA, and use of calculator and software applications. (C-ID MATH 110)

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-040

Advisory: ENG-071

Limitation on enrollment: None

Transfer Status: CSU/UC* Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 015 Discrete Mathematics for Computers Units: 4**

This course is an introduction to discrete mathematics and its applications. Topics to be covered include logic and sets, relations and functions, combinatorics, probabilities, graph and tree theory, recurrence relations, Boolean algebra, Proofs, algorithms, and finite-state machines. Applications to computer studies and other related areas will be presented. discrete mathematical systems including methods of proof that shape the foundations of computer science. Includes propositional logic, set and number theory, Boolean Algebra, deductive and inductive proof, functions and relations, combinatorics, discrete probability, graph theory and network models, and efficiency of algorithms.

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-012

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU/UC Degree Applicable: AA/AS

COD GE: C4b CSU GE: B4 IGETC: 2A

**MATH 030 Plane Geometry Units: 3**

This course examines fundamentals of plane geometry, including topics in solid and coordinate geometry, developed by both inductive and deductive processes. This course is offered in the Fall semester.

Lecture Hours: 54 Lab Hours: None Repeatable: No

Grading: Letter

**Prerequisite:** MATH-054

Advisory: None

Limitation on enrollment: None

Transfer Status: None Degree Applicable: NAA

COD GE: None CSU GE: None IGETC: None

**MATH 031 Undergraduate Research Experience Units: 2**

Under the supervision of STEM faculty, students will select a project to be completed during the semester. Topics will include information retrieval, computer skills applied to laboratory research, time management and organizational skills, application of modern research methods, experimental design, data collection and analysis, presentation skills (written and oral), and applying for summer internship opportunities. This course is intended for students pursuing a STEM degree and who have completed a minimum of 35 college level units.

Lecture Hours: 18 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-001B

Advisory: LIS-001

Limitation on enrollment: None

Transfer Status: CSU Degree Applicable: AA/AS

COD GE: None CSU GE: None IGETC: None

**MATH 040 Intermediate Algebra Units: 4**

This course focuses on solving problems using linear, quadratic and exponential models with an introduction to the concept of a function. Topics include solving and graphing linear, quadratic and exponential equations, systems of linear equations, rational exponents, root equations, quadratic inequalities, circles and applications.

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-054

Advisory: RDG-051

Limitation on enrollment: None

Transfer Status: None Degree Applicable: AA/AS

COD GE: C4b CSU GE: None IGETC: None

**MATH 042 Beginning & Intermediate Algebra Units: 6**

This course starts with a review of the real number system and its properties. The focus then turns to the arithmetic of algebraic expressions, the solving of equations or systems of equations in one or more variables, and applications of these via mathematical modeling and problem solving. Topics include linear, quadratic, rational, radical, and exponential expressions, equations, and models, primarily in one or two variables. Significant emphasis is put on graphing in the Cartesian coordinate system and the use of graphing to assist in the problem solving process. (Equivalent to MATH-040.)

Lecture Hours: 81 Lab Hours: 81 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-060

Advisory: ENG-071

Limitation on enrollment: None

Transfer Status: None Degree Applicable: AA/AS

COD GE: C4b CSU GE: None IGETC: None

**MATH 044 College Geometry Units: 4**

This course includes fundamentals of plane geometry, including topics in coordinate geometry, developed by both inductive and deductive processes.

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-054

Advisory: None

Limitation on enrollment: None

Transfer Status: None Degree Applicable: AA/AS

COD GE: None CSU GE: None IGETC: None

**MATH 054 Beginning Algebra Units: 4**

This course is an introduction to the real number system and to the use of variable expressions and equations in problem solving. Topics include properties of the real numbers, square roots, arithmetic of variable expressions including polynomials and algebraic fractions, solving linear equations and inequalities in one variable, factoring, and an introduction to the Cartesian coordinate system and the equations and graphs of linear equations in two variables. Also, the proper use of math notation is emphasized along with an introduction to Pythagorean Theorem and basic geometric formulas, some dimensional analysis with modeling applications is included.

Lecture Hours: 54 Lab Hours: 54 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-060

Advisory: ENG-071

Limitation on enrollment: None

Transfer Status: None Degree Applicable: NAA

COD GE: None CSU GE: None IGETC: None

**MATH 060 A Preparation For The Study Of Algebra Units: 3**

This is a course in the elementary operations required for algebra. Topics include adding, subtracting, multiplying, and dividing whole numbers, decimals, and fractions with an introduction to the concept and uses of variables. Other topics include arithmetic with signed numbers, percents, ratios and proportions, the metric and American system of measurement, including the conversion of units, simplifying algebraic expressions and elementary geometry concepts such as perimeter, area, and volume.

Lecture Hours: 45 Lab Hours: 27 Repeatable: No

Grading: Letter

**Prerequisite:** MATH-070

Advisory: ENG-070

Limitation on enrollment: None

Transfer Status: None Degree Applicable: NAA

COD GE: None CSU GE: None IGETC: None

**MATH 070 Arithmetic Units: 2**

This is a course in the basic operations of arithmetic. Topics include adding, subtracting, multiplying, and dividing rational numbers, with an emphasis on whole numbers, integers, and rational numbers written in fraction form. Additional emphasis includes memorization of the basic number facts.

Lecture Hours: 27 Lab Hours: 27 Repeatable: No

Grading: Letter

**Prerequisite:** Advisory ENG-070

Advisory: None

Limitation on enrollment: None

Transfer Status: None Degree Applicable: NAA

COD GE: None CSU GE: None IGETC: None

**MATH 071 MESA CCCP Orientation Units: 1**

This course assists students in acquiring the knowledge and skills necessary to reach their educational objectives in engineering, mathematics, and science-related fields. Topics include career decisions and strategies, educational and personal enrichment, study skills and habits, time management, academic preparation, and success in college. Field trips may be required.

Lecture Hours: 18 Lab Hours: None Repeatable: No

Grading: Pass/No Pass

**Prerequisite:** None

Advisory: None

Limitation on enrollment: None

Transfer Status: None Degree Applicable: NAA

COD GE: None CSU GE: None IGETC: None

**MATH 095A Math Work Experience Units: 1**

This work experience course of supervised employment is designed to assist students to acquire desirable work habits, attitudes and skills so as to enable them to become productive employees. This course also provides students with career awareness for jobs. Credit may be accrued at the rate of one to 6 units per semester for a maximum of sixteen units (combined total of all Work Experience units). Additionally, students must work 75 paid hours or 60 non-paid hours per unit earned. This type of work experience is available to students whose job and educational or occupational goals are directly related to Math.

Lecture Hours: None Lab Hours: 75 Repeatable: Yes

Grading: Letter

**Prerequisite:** None

Advisory: None

Limitation on enrollment: None

Transfer Status: CSU Degree Applicable: AA/AS

COD GE: None CSU GE: None IGETC: None