# Certificate Programs

Certificates may be earned by regularly matriculated or extended learning students and denote successful completion of a prescribed program of study designed a) to impart specified professional/vocational/career competencies; or b) to produce mastery of the content of a sub-field of an academic major (discipline); or c) to provide exposure to the range of materials in a traditional or emerging interdisciplinary field. Candidates must receive two-thirds of their certificate-applicable credit from the university. The transferring of credit or the substitution of courses may occur only after application to the appropriate campus authority. See Page 60 in the 2012-2014 Bulletin of Courses for additional certificate information.

## Certificate in Introductory Actuarial Science

This program is designed to prepare students for the preliminary examinations given by the Society of Actuaries. Completion of those exams is normally considered the prerequisite for internships and entry-level positions in the field of actuarial science. For more information contact the Department of Mathematics.

### Certificate Requirements (50 units)

Lower-division requirements (30 units)

- ECON 200. Principles of Microeconomics (4)
- ECON 202. Principles of Macroeconomics (4)
- MATH 211. Basic Concepts of Calculus (4)
- MATH 212. Calculus II (4)
- MATH 213. Calculus III (4)
- MATH 241. Problem Solving in Calculus (2)
- MATH 251. Multivariable Calculus I (4)
- MATH 252. Multivariable Calculus II (4)

Upper-division requirements (20 units)

- ECON 300. Intermediate Macroeconomics (4)
- ECON 302. Intermediate Microeconomics (4)
- MATH 320. Mathematical Interest Theory (4)
- MATH 372. Combinatorics (4)
- MATH 465. Probability Theory (4)

## Certificate in Introductory Mathematics

The Certificate in Introductory Mathematics has been approved by the California Commission on Teaching Credentialing to meet the required components for the Subject Matter Authorization: Introductory Mathematics. Completion of this program allows students to apply for the Subject Matter Authorization: Introductory Mathematics for teaching the content matter up through the ninth grade mathematics.

Holders of a valid California teaching credential who satisfy the following requirements in algebra, geometry, and development of the real number system and who complete at least thirty units of this certificate may apply to the California Commission on Teacher Credentialing for a supplementary authorization in mathematics.

### Certificate Requirements (48 units)

Courses must be completed with a grade of "C" or better.

### Component Areas (20 units)

- Select at least one course from each of the following five areas, with no course used to satisfy more than one area:
**A1: Algebra**- MATH 110. College Algebra (4)
- May choose only one of the following two courses:
- MATH 192. Methods of Calculus (4)
- MATH 211. Basic Calculus (4)
- MATH 212. Calculus II (4)
**A2: Advanced Algebra**- MATH 120. Precalculus (4)
- May choose only one of the following two courses:
- MATH 192. Methods of Calculus (4)
- MATH 211. Basic Calculus (4)
- MATH 212. Calculus II (4)
- MATH 272. Discrete Mathematics (4)
**A3: Geometry**- May choose only one of the following two courses:
- MATH 192. Methods of Calculus (4)
- MATH 211. Basic Calculus (4)
- MATH 212. Calculus II (4)
- MATH 229. Geometry in Two and Three Dimension (4)
**A4: Probability and Statistics**- MATH 115. Ideas of Math (4)
- May choose only one of the following two courses:
- MATH 262: Applied Statistics (4)
- MATH 305. Statistics: Hypotheses Testing and Estimation (4)
**A5: Development of the Real Number System**- May choose only one of the following two courses:
- MATH 192. Methods of Calculus (4)
- MATH 211. Basic Calculus (4)
- MATH 212. Calculus II (4)
- MATH 301A. Fundamental Concepts of Mathematics for Educators A: Fundamental Concepts of Arithmetic and Geometry (4)
- Electives (28 units)
- Select an additional 28 units from other courses listed above not already taken (unless restricted between two courses), or from the following courses:
- MATH 180. Critical Thinking Through Applications of Mathematical Logic (4)
- MATH 199. Technology in Math Education Through Problem Solving (3)
- MATH 301B. Fundamental Concepts of Mathematics for Educators B: Transition from Concrete to Abstract in Algebra and Geometry (4)
- MATH 301C. Fundamental Concepts of Mathematics for Educators C: Further Developments in Algebra and Geometry (4)
- MATH 308. Problem Solving Through Theory and Practice (2)

For more information please visit our website. Department of Mathematics.

*For official information please refer to the university catalog.*