# MATHEMATICS

The Golden West College Mathematics Department offers a number of programs to satisfy the diverse needs of its students:

**The Developmental Mathematics Program**

The Developmental Program is designed for students who desire to improve their mathematics skills in Arithmetic, Prealgebra, Algebra, and Geometry.**The K-8 Teacher Preparation Program**

This Program is designed for students who desire to become K-8 Teachers**The General Education Transfer Program**

This Program is designed for students planning to transfer to four -year colleges or universities but are not committed to a major in Mathematics, the Physical or the Social Sciences.

**The Natural Science Transfer Program**

This Program is designed for students majoring in Mathematics, Physical Sciences (i.e. Astronomy, Chemistry, Engineering, Geology, Physics), Life Sciences (i.e. Pre-medicine, Biology, Botany, Microbiology) In addition to these programs the department also offers free tutoring for students enrolled in mathematics courses at Golden West College.

**Program Highlights**

The department offers a comprehensive sequence of mathematics at the two-year college level from arithmetic through differential equations.

- All instructors possess Masters degrees in mathematics
- Tutoring is available for any GWC math student
- The department maintains two fully equipped computer labs with staff to assist GWC students in developmental/remedial math classes.

Link to: **DEVELOPMENTAL MATH PROGRAM **web pages.

**Jeff Courchaine, Dean**

For more information contact:

The Division Office

MathSciOffice@gwc.cccd.edu

**714-895-8990**

**Associate In Science Degree In Mathematics For Transfer**

Required courses | Semester at a Glance

**Mathematics Associate In Arts Degree In Mathematics**

Required courses | Semester at a Glance

**Associate In Science Degree In Mathematics For Transfer**

By successfully completing the courses for an AS-T in Mathematics at Golden West College, the student will gain a practical and theoretical understanding for future studies in mathematics. Students satisfying requirements for the Associate in Science in Mathematics for Transfer are guaranteed transfer into a bachelor’s program in mathematics at a California State University campus. Students intending to transfer to a particular CSU campus or to a university or college that is not part of the California State University system should consult with a counselor when planning to complete the degree to verify that a particular college acknowledges and accepts the AS-T in Mathematics conferred by Golden West College.

**Program Level Learning Outcomes**

**Upon completion of this program, students will be able to:**

- State and interpret the definition of derivatives, and compute the derivatives of basic and transcendental functions of one or more variables. (Math 180, Math 185, Math 280)
- Apply concepts of differential and integral calculus of one or more variables to solve problems involving rates, area, volume, and lengths of arcs. (Math 180, Math 185, Math 280)
- State and interpret the definition of integrals, and calculate definite and indefinite integrals involving basic and transcendental functions. (Math 180, Math 185)
- Graph equations in the rectangular, polar, cylindrical, and spherical coordinate systems, curves defined parametrically, conic sections, vectors, and vector valued functions. (Math 280)
- Solve first-order differential equations and compute partial derivatives. (Math 185, Math 280, Math 282)
- Perform matrix operations, eigenvalue and eigenvector computations and applications. (Math 235)

This is the major pattern for students planning to transfer to a CSU. It is strongly recommended that students contact a GWC counselor to develop an official Student Educational Plan to discuss non-CSU universities, or if they have questions about the AA in Mathematics for CSU Transfer.

**Required courses**

**Core
**Mathematics G180 – Calculus 1 –

**5 units**

Mathematics G185 – Calculus 2 –

**5 units**

Mathematics G280 – Calculus 3 –

**5 units**

**List A: Select one course from the following**

Mathematics G282 – Ordinary Differential Equations – **4 units
**Mathematics G235 – Linear Algebra –

**4 units**

Mathematics G285 – Introduction to Linear Algebra and Differential Equations –

**5 units**

**List B: Select one additional course from the following
**Mathematics G282 or Mathematics G235 if not selected above

Physics G185 – Calculus Based Physics: Mechanics –

**4 units**

Computer Science G175 C++ Programming –

**4 units**

Mathematics G160 – Introduction to Statistics –

**4 units**

Total units: **23-24**

**Semester at a Glance – Associate In Science Degree In Mathematics For Transfer**

**Semester 1
**Math G180 (Core) – Calculus 1 –

**5 units**

General Education –

**TBD**

**Semester 2
**Math G185 (Core) – Calculus 2 –

**5 units**

General Education –

**TBD**

**Semester 3
**Math G280 (Core) – Calculus 3 –

**5 units**

General Education –

**TBD**

**Semester 4
One courses from: (List A)
**Math G282 (Fall Only) – Ordinary Differential Equations –

**4 units**

Math G235 (Spring Only) – Applied Linear Algebra –

**4 units**

Math G285 – Intro to Linear Algebra and Differential Equations –

**5 units**

**One course from: (List B)
**Math G160 – Introduction to Statistics –

**4 units**

Physics G185 – Calculus based Physics: Mechanics – 4 units

Computer Science G175 – C++ Programming –

**4 units**

General Education –

**TBD**

Major total: **23-24 units
**CSU General Education Breadth or IGETC Pattern:

**37-39 units**

Total units that may be double-counted:

**6 units**

Transferable Electives (as needed to reach 60 transferable units):

**3-9 units**

DEGREE TOTAL UNITS (maximum):

**60 units**

( ) Description in parentheses indicates credit earned in AST.

**Mathematics Associate In Arts Degree In Mathematics**

**Program Level Learning Outcomes:**

**Upon completion of this program, students will be able to:**

- State and interpret the definition of derivatives, and compute the derivatives of basic and transcendental functions of one or more variables.
- Apply concepts of differential and integral calculus of one or more variables to solve problems involving rates, area, volume, and lengths of arcs.
- State and interpret the definition of integrals, and calculate definite and indefinite integrals involving basic and transcendental functions.
- Graph equations in the rectangular, polar, cylindrical, and spherical coordinate systems, curves defined parametrically, conic sections, vectors, and vector valued functions.
- Solve first-order differential equations and compute partial derivatives.
- Perform matrix operations, eigenvalue and eigenvector computations and applications.

**Required courses**

Mathematics G180 – Calculus 1 – **5 units**

Mathematics G185 – Calculus 2 –** 5 units**

Mathematics G280 – Calculus 3 – **5 units**

**Select one of the following:
**Mathematics G235 – Applied Linear Algebra –

**4 units**

Mathematics G282 – Ordinary Differential Equations – 4 units

Mathematics G285 – Introduction to Linear Algebra and Differential Equations –

**5 units**

Total units: **19 – 20**

**Semester at a Glance – Mathematics Associate In Arts Degree In Mathematics**

**Semester 1
**Math G180 – Calculus 1 –

**5 units**

General Education –

**TBD**

**Semester 2
**Math G185 – Calculus 2 –

**5 units**

General Education –

**TBD**

**Semester 3
**Math G280 – Calculus 3 –

**5 units**

General Education –

**TBD**

**Semester 4
**

**One course from:**

Math G282 (Fall Only) – Ordinary Differential Equations –

**4 units**

Math G235 (Spring Only) – Applied Linear Algebra –

**4 units**

Math G285 – Intro to Linear Algebra and Differential Equation –

**5 units**

General Education –

**TBD**

Major Total: **19-20 units
**GE Pattern: GWC AA, , CSU General Education Breadth or IGETC Pattern:

**21-39 units**

DEGREE TOTAL UNITS (maximum):

**60 units**

To view all courses (opens new window)

**MATHEMATICS G009 – 1 Unit
**Course Outline (opens new window)

**Medication Calculations for Nurses**

This course presents a review of decimals, fractions and percents as utilized by medical professionals to calculate drug dosages. Dosage calculations are presented using ‘dimensional analysis.’ Additional applications include conversion between the metric, apothecary and household systems, dosage calculations based upon body weight, intravenous calculations, and preparation of dilutions. Lecture. Optional pass/no pass grade.

**Not transferable, not degree applicable**.

**MATHEMATICS G010 – 4 Units
**Course Outline (opens new window)

**Elementary Algebra**

Properties of real numbers; simplifying polynomial, rational, and radical expressions; solving linear, quadratic, rational, and radical equations in one variable; the rectangular coordinate system; graphing linear equations in two variables; and solving systems of linear equations in two variables. Applications of mathematical concepts. Equivalent to a first-year high school algebra course. Taught in a combined large lecture and laboratory format. Software used requires access to a computer with Windows operating system. Lecture & lab. Letter grade only.

**Not transferable, not degree applicable.**

**MATHEMATICS G030 – 4 Units
**Course Outline (opens new window)

**Intermediate Algebra**

*Prerequisites: Mathematics G010 or Mathematics Placement Assessment*

This course is equivalent to a second-year high school algebra course. Topics include absolute value, rational exponents, radicals, linear equations and inequalities, quadratic equations and inequalities, functional notation, linear and quadratic functions, conic sections, logarithms, exponential and logarithmic functions, linear systems in two and three variables, sequences, and series. Lecture. Letter grade only.

**MATHEMATICS G040 – 5 Units**

Course Outline (open new window)

**Accelerated Elementary and Intermediate Algebra
**Equivalent to a first and second year high school algebra course accelerated into one semester. Taught in a combined large lecture and laboratory format. Software used requires access to a computer. It is taught using group lectures in conjunction with computer assignments and laboratory work. Topics include: properties of real numbers; simplifying polynomial, rational, and radical expressions; solving linear, quadratic, rational, and radical equations in one variable; graphing and solving systems of linear equations in two variables, absolute value, rational exponents, quadratic equations and inequalities, linear and quadratic functions, conic sections, exponential and logarithmic functions, sequences, and series. A scientific calculator will be required. Lecture & lab. Letter grade only.

**MATHEMATICS G080 – 5 Units**

Course Outline (open new window)

**Pre-Statistics
**This course is designed for students whose education plan calls for Math G160: Introduction to Statistics. It may not be suitable for students on a STEM degree pathway. Please see a counselor for more information. The course covers requisite topics from Intermediate Algebra including linear equations and inequalities, linear regression analysis, exponential functions, exponential equations, descriptive statistics, probability, sampling distributions including the Normal distribution, and the use of graphing calculators and/or computer software. Lecture & lab. Letter grade only.

**Not transferable, not degree applicable**.

**MATHEMATICS G100 – 3 Units
**Course Outline (opens new window)

**Liberal Arts Mathematics**

*Prerequisites: Mathematics G030 or Mathematics Placement Assessment*

Using and expanding upon the skills gained from intermediate algebra, this course offers the liberal arts student an applications-oriented, problem-solving exploration into a variety of mathematical fields including geometry, trigonometry, statistics, and business mathematics. This course is designed not only to meet college general education requirements but to help generate a positive attitude toward and an interest in mathematics. Lecture & lab. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G104 – 3 Units
**Course Outline (opens new window)

**Mathematics for Elementary Teachers**

*(Formerly known*as:

*Mathematics for Elementary Teachers 1)*

Prerequisites: Math G030, or Math G040, or Math Placement Assessment

Topics include problem solving skills, structure and arithmetic of the real number system, other numeration systems, set theory, and manipulatives. This course is designed for students planning to be elementary teachers. Student should complete Mathematics G020 (high school geometry) before taking the CBEST test, or the second math course for elementary teachers at a four-year school. UC Credit Limitations: Math G103, G104 and G106 combined—maximum credit, one course. Lecture & lab. Letter grade only.

Prerequisites: Math G030, or Math G040, or Math Placement Assessment

**Transferable to CSU; UC.**

**MATHEMATICS G115 – 4 Units
**Course Outline (opens new window)

**College Algebra**

*Prerequisites: Math G030, or Math G040, or Math Placement Assessment*

This course is designed for students needing to improve algebra skills necessary for success in Math G140 and Math G180. Topics include linear and quadratic functions and their graphs, polynomial and rational functions and their graphs, exponential and logarithmic functions and their graphs, conic sections, sequence and series, solving systems of equations, matrices and determinants, counting and probability. UC Credit Limitations: Math G115 and G170 combined——maximum credit, one course. Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G120 – 3 Units
**Course Outline (opens new window)

**Trigonometry**

*Prerequisites: Math G030, or Math G040 or Math Placement Assessment*

This course is a study of the circular and trigonometric functions. The topics include inverses, graphs, solutions of triangles, conditional equations, identities, vectors, complex numbers, polar coordinates, parametric equations, and applications of these concepts. A scientific calculator is recommended. Lecture. Letter grade only.

**Transferable to CSU**.

**MATHEMATICS G140 – 4 Units
**Course Outline (opens new window)

**Business Calculus**

*(Formerly known*as:

*Mathematics 130)*

*Prerequisites: Mathematics G115 or G170 or Mathematics Placement Assessment*

This course is designed for students of business, management, and social science who need only one semester of calculus that covers a variety of topics that usually span parts of three semesters of calculus. Topics include functions, limits and continuity, differentiation, integration, graphing, the calculus of two variables and applications of the derivative and integral. This course does not prepare a student to enter Mathematics G180 or G185. UC Credit Limitations: Math G140, G180 and G180H combined—maximum credit, one course. C-ID: MATH 140 Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G160 – 4 Units
**Course Outline (opens new window)

**Introduction to Statistics**

*Prerequisites: Math G030, or Math G040, or Math G080 or Math Placement Assessment*

Topics include concepts and procedures of descriptive and inferential statistics; collecting, classifying, tabulating, graphing univariate and bivariate data; measures of central tendencies, variation, percentiles, probability, binomial, normal, T, Chi-square and F distributions; making inferences, decisions and predictions. This course develops statistical thinking through the study of and applications to data sets in the social and behavioral sciences, business, and other disciplines. The use of a graphing calculator and/or statistical analysis computer programs is integrated into the course. UC Credit Limitations: Math G160 and G160H combined—maximum credit, one course. UC credit limitations. See counselor. C-ID: MATH 110 OR C-ID: SOCI 125 Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G170 – 5 Units
**Course Outline (opens new window)

**Precalculus**

*Prerequisites: Mathematics G120 or Mathematics Placement Assessment*

This course will cover topics required for studying calculus. Particular emphasis will be placed on the analysis of polynomial, rational, exponential, logarithmic, trigonometric and inverse functions. Other topics include vectors, analytic geometry, linear systems, matrices, elementary theory of equations, polar coordinates, sequences, series, and complex numbers. This course is essential for those students planning to study Mathematics G180 (Calculus 1). UC Credit Limitations: Math G115 and G170 combined—maximum credit, one course. Math G170 (maximum credit, 4 units.) Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G180 – 5 Units
**Course Outline (opens new window)

**Calculus 1**

*Prerequisites: Mathematics G170 or Mathematics Placement Assessment or Math G115 and Math G120*

This is the first course in a three-course sequence designed for mathematics, science and engineering majors. The topics covered in this course include limits and continuity, derivatives of algebraic and transcendental functions, applications of derivatives, indefinite integrals, definite integrals, the Fundamental Theorem of Calculus and applications of integration. UC credit limitations. See counselor. C-ID MATH 210 OR C-ID: MATH 211 Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G185 – 5 Units
**Course Outline (opens new window)

**Calculus 2**

*Prerequisites: Mathematics G180 or G180H*

This is the second course in a three-course sequence designed for mathematics, science and engineering majors. The topics covered in this course include methods of integration, applications of the definite integral, polar and parametric functions, improper integrals, convergence and divergence of sequences and series including power series, and conic sections. (The student should plan to complete the first three semesters of calculus at Golden West College to maintain continuity.) C-ID MATH 221 Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G235 – 4 Units
**Course Outline (opens new window)

**Applied Linear Algebra**

*(Formerly known*as:

*Mathematics 290)*

*Prerequisites: Mathematics G185*

Introduction to linear algebra, classical linear algebra problems, and applications to computer science and related technologies including matrices, determinants, linear spaces, linear transformations, and eigenvalues. C-ID: MATH 250 Lecture. Letter grade only.

**Transferable to CSU; UC. Offered spring semester only.**

**MATHEMATICS G280 – 5 Units
**Course Outline (opens new window)

**Calculus 3**

*Prerequisites: Mathematics G185*

This is the third course in a three-course sequence, designed for mathematics, science and engineering majors. Topics include vectors in three-dimensional space, curves and surfaces, functions of several variables, partial differentiation, the gradient, the curl, the divergence, multiple integration, Green’s Theorem, Gauss’ (Divergence) Theorem and Stokes’ Theorem. The student should plan to complete the first three semesters of calculus at Golden West College to maintain continuity. C-ID MATH 230 Lecture. Letter grade only.

**Transferable to CSU; UC.**

**MATHEMATICS G282 – 4 Units
**Course Outline (opens new window)

**Ordinary Differential Equations**

*Prerequisites: Mathematics G185*

This course provides students with an introduction to the theory, techniques and applications of ordinary differential equations. The topics covered include first-order differential equations, higher-order differential equations, power series solutions, Laplace transforms, systems of differential equations and numerical methods. C-ID: MATH 240 Lecture. Letter grade only.

**Transferable to CSU; UC**.

**MATHEMATICS G285 – 5 Units
**Course Outline (opens new window)

**Introduction to Linear Algebra and Differential Equations**

*(Formerly known*as:

*Ordinary Differential Equations)*

*Prerequisites: Mathematics G185*

This course is designed to introduce students to the fields of Linear Algebra and Differential Equations. Topics include matrices, determinants, vector spaces, linear systems of equations, inner product spaces, first and second order differential equations, systems of differential equations, and Laplace transforms. C-ID MATH 910S Lecture. Letter grade only.

**Transferable to CSU; UC. Offered fall semester only.**

The Associate in Arts Degree for Transfer (AA-T) in Mathematics will transfer to the following California State Universities:

CSU Bakersfield

CSU Channel Islands

CSU Chino

CSU Dominguez Hills

CSU East Bay

CSU Fresno

CSU Fullerton

CSU Humbolt

CSU Long Beach

CSU Los Angeles

CSU Monterey Bay

CSU Northridge

CSU Pomona

CSU Sacramento

CSU San Bernadino

CSU San Diego

CSU San Francisco

CSU San Jose

CSU San Luis Obispo

CSU San Marcos

CSU Sonoma

CSU Stanislaus

The list of CSU campuses for this major was provided by the California State University’s *A Degree with a Guarantee* website: http://adegreewithaguarantee.com/

**Most of the courses in this program also transfer to the University of California (UC) System and Private Universities. Please see your GWC Counselor early in your studies to choose the transfer option that is right for you.**

## Some Popular Career Choices:

#### Teaching

The teaching of mathematics at the K-12 level is a high-demand field and the need is expected to grow in the future. The place to go for explicit career information is the National Council of Teachers of Mathematics homepage.

#### Actuarial Science

Actuarial science takes mathematics and statistics and applies them to finance and insurance. Actuarial science includes a number of interrelating disciplines, including probability and statistics, finance, and economics. Check out Be An Actuary.

#### Computer Science

Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. Mathematicians, with their training in logical and precise thinking, are highly prized in this field. See the student section of the Association for Computing Machinery for career advice.

#### Operations Research

Operations research is an interdisciplinary branch of mathematics which uses mathematical methods to arrive at optimal decisions to problems in maximizing or minimizing things like costs or profits. The eventual intention behind using Operations Research is to elicit a best possible solution to a problem mathematically, which improves or optimizes the performance of the system. The group INFORMS is the world’s largest society devoted to operations research/management science.

#### Biomathematics

Mathematical biology or biomathematics is an interdisciplinary field of study. It models natural and biological processes using mathematical techniques and tools. Results have been applied to areas such as cellular neurobiology, epidemic modelling, and population genetics. The education page of the Society for Mathematical Biology links to schools offering biomath degrees along with a description of the coursework needed.

#### Cryptography

Cryptography is the practice and study of hiding information. Cryptography is considered to be a branch of both mathematics and computer science. Not just for spies anymore, cryptography applications include the security of ATM cards and computer passwords.

#### Finance

Finance is a field that studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. Mathematicians can build models to help explain and predict the behavior of financial markets. Several schools offer Master’s degrees in Financial Mathematics. A quick web search will take you to their web pages.

Source: Mathematical Association of America www.maa.org/careers

**Pete Bouzar
**

*Associate Professor, Mathematics*

B.A., M.A., California State University at Fullerton; further graduate study: Argosy University.

**Antony Hoang
**

*Professor, Mathematics*

B.S., M.S., University of California at Irvine.

**Lindsay Lewis
**

*Instructor, Mathematics*

B.A., M.A., California State University at Fullerton.