# 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.

**Interim Dean, Rick Hicks**

For more information contact:

The Division Office

MathSciOffice@gwc.cccd.edu**714-895-8990**

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

**Mathematics Associate In Arts Degree In Mathematics**

**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:**

1. State and interpret the definition of derivatives, and compute the derivatives of basic and transcendental functions of one or more variables.

2. Apply concepts of differential and integral calculus of one or more variables to solve problems involving rates, area, volume, and lengths of arcs.

3. State and interpret the definition of integrals, and calculate definite and indefinite integrals involving basic and transcendental functions.

4. Graph equations in the rectangular, polar, cylindrical, and spherical coordinate systems, curves defined parametrically, conic sections, vectors, and vector valued functions.

5. Solve first-order differential equations and compute partial derivatives.

6. Perform matrix operations, eigenvalue and eigenvector computations and applications.

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**

MATH G180 – Calculus 1 – **5 units**

MATH G185 – Calculus 2 – **5 units**

MATH G280 – Calculus 3 – **5 units**

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

MATH G282 – Ordinary Differential Equations – **4 units**

MATH G235 – Applied Linear Algebra – **4 units**

MATH G285 – Introduction to Linear Algebra and Differential Equations – **5 units**

**List B: Select one additional course from the following if not selected above**

MATH G282 – Ordinary Differential Equations 4 units

MATH G235 – Applied Linear Algebra– **4 units**

PHYS G185 – Calculus Based Physics: Mechanics – **4 units**

CS G175 – C++ Programming – **4 units**

MATH G160 – Introduction to Statistics – **4 units**

**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 units): 3-9 units**

**DEGREE TOTAL UNITS (maximum): 60 units**

**Mathematics Associate In Arts Degree In Mathematics**

**Program Level Learning Outcomes**

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

1. State and interpret the definition of derivatives, and compute the derivatives of basic and transcendental functions of one or more variables.

2. Apply concepts of differential and integral calculus of one or more variables to solve problems involving rates, area, volume, and lengths of arcs.

3. State and interpret the definition of integrals, and calculate definite and indefinite integrals involving basic and transcendental functions.

4. Graph equations in the rectangular, polar, cylindrical, and spherical coordinate systems, curves defined parametrically, conic sections, vectors, and vector valued functions.

5. Solve first-order differential equations and compute partial derivatives.

6. Perform matrix operations, eigenvalue and eigenvector computations and applications.

**Required courses**

MATH G180 – Calculus 1 – **5 units**

MATH G185 – Calculus 2 –** 5 units**

MATH G280 – Calculus 3 – **5 units**

**Select one of the following:**

MATH G235 – Applied Linear Algebra – **4 units**

MATH G282 – Ordinary Differential Equations – **4 units**

MATH G285 – Introduction to Linear Algebra and Differential Equations – **5 units**

**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**

**MATHEMATICS G010 – 4 Units**

**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**

**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. **Not transferable, AA/AS degree only.**

**MATHEMATICS G040 – 5 Units**

**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. **Not transferable, AA/AS degree only.**

**MATHEMATICS G080 – 5 Units**

**Pre-Statistics**

*Prerequisites: MATH G010*

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 G091 – 2 Units**

**Support for College Algebra**

*Corequisites: MATH G115*

This co-requisite course is intended for students that enroll into College Algebra, Math G115. It provides supplemental instruction in basic algebra skills and concepts needed for success in College Algebra computations and applications. Success in this course will be based on attendance and satisfactory completion of in-class assignments. Requires concurrent enrollment in specified sections of College Algebra, Math G115. Lecture. Pass/no pass only. **Not transferable, not degree applicable.**

**MATHEMATICS G092 – 2 Units**

**Support for Trigonometry**

*Corequisites: MATH G120*

This co-requisite course is intended for students that enroll into Trigonometry, Math G120. It provides supplemental instruction in basic algebra skills and concepts needed for success in Trigonometry computations and applications. Success in this course will be based on attendance and satisfactory completion of in-class assignments. Requires concurrent enrollment in specified sections of Trigonometry, Math G120. Lecture. Pass/no pass only. **Not transferable, not degree applicable.**

**MATHEMATICS G096 – 2 Units**

**Support for Introduction to Statistics**

*Corequisites: MATH G160*

This co-requisite course is intended for students that enroll into Introduction to Statistics G160. It provides supplemental instruction in basic algebra skills and concepts needed for success in Introduction to Statistics computations and applications. Success in this course will be based on attendance and satisfactory completion of in-class assignments. Requires concurrent enrollment in specified sections of Introduction to Statistics G160. Lecture. Pass/no pass only. **Not transferable, not degree applicable.**

**MATHEMATICS G100 – 3 Units**

**Liberal Arts Mathematics**

*Prerequisites: Math G030, or Math G040, Math G080, or Math 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. Letter grade only. **Transferable to CSU; UC.**

**MATHEMATICS G103 – 3 Units**

**Statistics for Elementary Teachers**

*(Formerly known as: Elem. Teachers Math. 3-Probability & Statistics)*

*Prerequisites: GWC Math placement level of 50 or higher or MATH G030 or MATH G040, or MATH G080*

This course is designed for prospective teachers. This course is an activity-based exploration of statistics aligned with the California State Mathematics Standards. Topics include data representation and analysis, randomization and sampling, measures of central tendency and variability, hypothesizing and statistical inference. UC Credit Limitations: Math G103, G104 and G106 combined—maximum credit, one course; no credit for G103 if taken after G160/G160H. Lecture & lab. Letter grade only. * Transferable to CSU; UC*. Offered spring semester only.

**MATHEMATICS G104 – 3 Units**

**Mathematics for Elementary Teachers**

*(Formerly known as: Mathematics for Elementary Teachers 1)*

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

This course is designed for the prospective elementary school teacher. Topics include problem-solving, structure and arithmetic of the real numbers and other numerical systems, set theory, and manipulatives. This course is designed to develop and reinforce conceptual understanding of the national and state curriculum standards for elementary school mathematics, including the common core. C-ID MATH 120. Lecture. Letter grade only. **Transferable to CSU; UC.**

**MATHEMATICS G115 – 4 Units**

**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**

**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. C-ID 851. Lecture. Letter grade only. **Transferable to CSU.**

**MATHEMATICS G140 – 4 Units**

**Business Calculus**

*(Formerly known as: Math130 Survey of Calculus)*

*Prerequisites: Mathematics G115 or Mathematics 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**

**Introduction to Statistics**

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

This course includes 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**

**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**

**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**

**Calculus 2**

*Prerequisites: Mathematics G180 or Mathematics 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**

**Applied Linear Algebra**

*(Formerly known as: Math 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**

**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**

**Ordinary Differential Equations**

*Prerequisites: Math 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**

**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

**All instructors possess at minimum a Master’s Degree in Mathematics.*

**Gita Alemansour** – *Program Chair and Full-time Faculty*

B.S. in Engineering from UCI & M.A. in Mathematics from CSUF

Office: MS – 221; Ext. 51090

galemansour@gwc.cccd.edu

**Pete Bouzar** – *Professor*

B.A. & M.A. in Mathematics from CSUF

Office: MS – 226; Ext. 52247

pbouzar@gwc.cccd.edu

**Antony Hoang** – *Professor*

B.S. & M.S. in Mathematics from UCI

Office: MS – 225; Ext. 51042

ahoang@gwc.cccd.edu

**Maryam Khakbazan** – *Full-time Faculty*

M.S. & M.A. in Engineering and Mathematics from CSUF

Office: LRC – 326; Ext. 52296

mkhakbazan@gwc.cccd.edu

**Gary Kirby** – *Full-time Faculty*

B.A. & M.A. in Mathematics from UCSC

Office: MS – 223; Ext.51100

gkirbyjr@gwc.cccd.edu

**Natalie Koch** – *Full-time Faculty*

B.A. Mathematics from UCSB, M.S. Mathematics CSULB

Office: MS – 223; Ext. 51122

nkoch2@gwc.cccd.edu

**Lindsay Lewis** – *Full-time Faculty*

B.S. & M.S. in Mathematics from CSUF

Office: MS – 225; Ext. 51108

llewis@gwc.cccd.edu

**Annette Park** – *Full-time Faculty*

B.S. in Mathematics from UC Irvine; M.A. in Mathematics from CSUF

Office: MS – 222; Ext. 51068

apark52@gwc.cccd.edu