# Mathematics

### Courses

**MAT 1510. Independent Study. 1-5 Unit.**

**MAT 1900A. Calculus. 4 Units.**

The course aims to apply and extend what students have learned in previous mathematics courses through the study of limits, derivatives, along with basic differentiating and integrating techniques. The course starts with five major problems that introduce the big ideas of calculus: limits, exponential functions, the relationship between distance and velocity, piece wise functions, and the Fundamental Theorem of Calculus. Each of these five major problems is revisited again later in Math 1900B for students to solve using new calculus knowledge. Students in Calculus will continue to use problem solving strategies, questioning, investigating, and explaining in conjunction with their knowledge of the connections among algebra, geometry and functions to analyze problems and formulate solutions. Throughout, they will also use these strategies to extend their current knowledge by making new connections.

**MAT 1900B. Calculus. 4 Units.**

The course aims to apply and extend what students have learned in previous mathematics courses through the study of limits, derivatives, along with basic differentiating and integrating techniques. The course starts with five major problems that introduce the big ideas of calculus: optimization, limits, differential equations, exponential functions, the relationship between distance and velocity, piece wise functions, volumes of revolution, volumes by slicing, and the Fundamental Theorem of Calculus. Each of these five major problems is revisited again later in the course for students to solve using new calculus knowledge. Students in Calculus will continue to use problem solving strategies, questioning, investigating, and explaining in conjunction with their knowledge of the connections among algebra, geometry and functions to analyze problems and formulate solutions. Throughout, they will also use these strategies to extend their current knowledge by making new connections.

**MAT 1910. Calculus I. 4 Units.**

The course aims to apply and extend what students have learned in previous mathematics courses through the study of limits, derivatives, and integrals, along with basic differentiating and integrating techniques. The course starts with five major problems that introduce the big ideas of calculus: limits, exponential functions, the relationship between distance and velocity, piecewise functions, and the Fundamental Theorem of Calculus. Derivative techniques and applications will include related rates, implicit differentiation, optimization, and the Mean Value Theorem. Integration techniques and applications will include areas between curves, u-substitution, and volumes. Each of these five major problems is revisited again later in Math 1920 for students to solve using new calculus knowledge. Students in Calculus will continue to use problem solving strategies, questioning, investigating, and explaining in conjunction with their knowledge of the connections among algebra, geometry and functions to analyze problems and formulate solutions. Throughout, they will also use these strategies to extend their current knowledge by making new connections. The course is a college level course and requires a significant amount of preparation for every class on the part of the student.

**MAT 1920. Calculus II. 4 Units.**

The course aims to apply and extend what students have learned in previous mathematics courses through the study of more derivative techniques and application, integration techniques and applications, derivatives and integrals of transcendental functions, polar and parametric functions, and sequences and series. The course begins with a wrapping up of derivative techniques from Math 1910 and L'Hopital's rule. Students then work on integration applications like volumes and arc length. The course continues to integration techniques like integration by parts, partial fractions, and improper integrals. Students learn to work with, graph, differentiate, and integrate polar and parametric functions. The last part of the course includes a thorough treatment of sequences and series, including finding the sum of an infinite series and utilizing tests for convergence. Students in this course will continue to use problem solving strategies, questioning, investigating, and explaining in conjunction with their knowledge of the connections among algebra, geometry and functions to analyze problems and formulate solutions. Throughout, they will also use these strategies to extend their current knowledge by making new connections. The course is a college level course and requires a significant amount of preparation for every class on the part of the student.

**MAT 2500. Prior Learning: Mathematics. 0 Units.**

**MAT 2510. Independent Study. 1-5 Unit.**

**MAT 3210. Math in the Real World. 3-4 Unit.**

Through a three-pronged approach, students develop an analytical and inquisitive point of view as it relates to the mathematics they encounter in their daily lives. Students are challenged in their critical thinking and verbal reasoning through class discussions, with self-directed projects and by developing a much stronger and innate understanding of foundational math skills. By working in-depth in the student's area of interest, students will follow a natural development of understanding of math concepts and how they relate to their personal interest topics.

**MAT 3500. Prior Learning: Mathematics. 0 Units.**

**MAT 3510. Independent Study. 1-5 Unit.**

**MAT 3530. Internship. 1-5 Unit.**

**MAT 3700. Quantitative Thought. 3-4 Unit.**

The goal of this course is to improve the student's analytical thinking skills, increasing the student's ability to analyze and solve mathematical and logical problems. Students not only examine the thought processes and techniques that lead to correct answers but also carefully explore the thought processes that lead to errors, learning to avoid making similar mistakes in the future. Students review and build upon basic knowledge in algebra and geometry, applying their learning to practical applications of mathematics, logic and reasoning.

**MAT 3810. Mathematical Thinking: Personal Financial Management. 3-4 Unit.**

This course addresses such issues as budgeting, planning for retirement, long term health care, investments, stocks, mortgages, and other areas applicable to understanding the finance of everyday life.

**MAT 4020. Research Design and Methodology. 4-5 Unit.**

The course introduces students to experimental and non-experimental designs used in psychological research. Class time is divided between discussion of the reading material and laboratory work. Students discuss commonly used designs, the elements of these designs, and the benefits of each type of design. Students get hands-on experience with several studies, serving as subjects in these studies, analyzing the data, and writing reports on the research using an APA-style format. Students are involved in designing their own studies, gathering data, analyzing the data, and presenting this information both in oral and written form. Prerequisite: MAT 403/PSY 414 Descriptive and Inferential Statistics.

**MAT 4030. Descriptive and Inferential Statistics. 4 Units.**

This course concentrates on the application of statistical methods to research problems. Statistical methods such as correlation analysis, t-tests, and analysis of variance are applied to research designs. In addition, students learn how to utilize computer programs to solve statistical problems.

**MAT 4130. Chaos Theory: the Geometry of Nature. 3-4 Unit.**

This course explores the origins and current state of chaos theory from a conceptual perspective. Topics discussed include the butterfly effect, bifurcation and wildlife populations, Mandelbrot sets, the geometry of nature, strange attractors, Feigenbaum sequences, fractals, biological rhythms, and pattern formation. The inescapable relationship between chaos and complexity is also discussed.

**MAT 4510. Independent Study. 1-5 Unit.**

**MAT X2000. Mathematics / Quantitative Domain. 1-9 Unit.**

General Education Transfer Credit Equivalency: Do not make any sections from this course.

**MAT X2001. Mathematics & Bus / Quantitative Domain. 1-9 Unit.**

General Education Transfer Credit Equivalency: Do not make any sections from this course.

**MAT X4000. Mathematics / Quantitative Domain. 1-9 Unit.**

General Education Transfer Credit Equivalency: Do not make any sections from this course.

**MAT X4001. Mathematics & Bus / Quant Domain. 1-9 Unit.**

General Education Transfer Credit Equivalency: Do not make any sections from this course.