# Mathematics (MATH)

### Courses

MATH 552 INFINITE PROCESSES FOR THE ELEMENTARY TEACHER 3 Units

This course is primarily for pre-service elementary and middle school teachers. Students will be introduced to the concepts of calculus, which include infinite precesses, limits, and continuity. In addition, dirivatives and integrals, and their relationship to area and change will be covered.

PREREQ: MATH 152

MATH 575 DEVELOPMENT OF MATHEMATICS 3 Units

A study of the development of mathematical notation and ideas from prehistoric times to the present. Periods and topics will be chosen corresponding to the backgrounds and interests of the students.

PREREQ: MATH 152 OR EQUIVALENT PREPARATION AS DETERMINED BY THE MATH DEPARTMENT

MATH 616 GEOMETRY FOR THE ELEMENTARY TEACHER 3 Units

A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tessellations, transformations, problem solving, and symmetries of polygons and polyhedra and use of geometry computer software.

PREREQ: MATH 149 AND MATH 152

MATH 617 NUMBER THEORY 3 Units

A study of the properties of integers, representation of integers in a given base, properties of primes, arithmetic functions, modulo arithmetic. Diophantine equations and quadratic residues. Consideration is also given to some famous problems in number theory.

PREREQ: UNDERGRADUATE DEGREE IN MATHEMATICS OR CONSENT OF INSTRUCTOR

MATH 621 MATHEMATICS FOR HIGH SCHOOL TEACHERS I 3 Units

The course revisits the high school curriculum from an advanced perspective. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes number systems, functions, equations, integers, and polynomials. Connections to geometry are emphasized throughout the course.

PREREQ: MATH 280, MATH 301 AND AT LEAST AN ADDITIONAL 3 CREDITS IN UPPER LEVEL MATH

MATH 622 MATHEMATICS FOR HIGH SCHOOL TEACHERS II 3 Units

The course continues the exploration of the high school curriculum from an advanced perspective that was started in MATH 421. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes congruence, distance, similarity, trigonometry, area, and volume. Connections to algebra are emphasized throughout the course.

PREREQ: MATH 353 AND MATH 421

MATH 623 ADVANCED FUNCTION AND ALGEBRA CONCEPTS 3 Units

Concepts from high school mathematics are discussed from an advanced perspective using calculus, abstract and linear algebra, and some complex variables. The topics include number systems, equations, functions, polynomials and basic number theory. Challenging problems and projects help to develop deeper understanding, and highlight connections of different areas of mathematics.

PREREQ: UNDERGRADUATE DEGREE IN MATHEMATICS OR CONSENT OF INSTRUCTOR

MATH 624 ADVANCED TOPICS IN GEOMETRY AND TRIGONOMETRY 3 Units

The course material is centered around concepts in geometry and trigonometry including geometric transformations in 2 and 3 dimensions, their representations by matrices, and equations with complex numbers. Metric spaces, minimum distance problems, quadratic, arithmetic, geometric, harmonic means. Area, volume and geometric probability. Multiple representations of the trigonometric functions and their identities. An individual research project is to be completed.

PREREQ: UNDERGRADUATE DEGREE IN MATHEMATICS OR CONSENT OF INSTRUCTOR

MATH 649 PROBABILITY AND STATISTICAL INFERENCE 3 Units

Foundations associated with quantifying and modeling chance and randomness with a focus on the role probability plays in statistical inference. Topics include set theory, combinatorics, random variables, selected discrete and continuous probability distributions, probability distributions for commonly used statistics, and the logic and applied use of probability in formulating and conducting hypothesis tests.

PREREQ: UNDERGRADUATE DEGREE IN MATHEMATICS OR STATISTICS, OR CONSENT OF INSTRUCTOR

MATH 650 GRAPH THEORY 3 Units

This course will examine basic concepts and applications of graph theory. Topics covered will be selected from trees, connectivity, paths and cycles, coloring, matching and covering problems, digraphs, and network flows.

PREREQ: UNDERGRADUATE DEGREE IN MATHEMATICS OR CONSENT OF INSTRUCTOR

MATH 690 WORKSHOP *Repeatable* 1-3 Units

Variable topics. Group activity oriented presentations emphasizing `hands on` and participatory instructional techniques.

MATH 694 SEMINAR *Repeatable* 2 Units

Variable topics. Group activity. An advanced course of study in a defined subject matter area emphasizing a small group in intense study with a faculty member.

MATH 696 SPECIAL STUDIES *Repeatable* 1-3 Units

Variable topics. Group activity. Not offered regularly in the curriculum but offered on topics selected on the basis of timeliness, need, and interest, and generally in the format of regularly scheduled Catalog offerings.

MATH 790 WORKSHOP 1-6 Units

Variable topics. Group activity oriented presentations emphasizing `hands on` and participatory instructional techniques.

MATH 794 SEMINAR 1-3 Units

Variable topics. Group activity. An advanced course of study in a defined subject matter area emphasizing a small group in intense study with a faculty member.

MATH 796 SPECIAL STUDIES 1-3 Units

Variable topics. Group activity. Not offered regularly in the curriculum but offered on topics selected on the basis of timeliness, need, and interest, and generally in the format of regularly scheduled Catalog offerings.

MATH 798 INDIVIDUAL STUDIES *Repeatable* 1-3 Units

In addition to allowing students to carry on independent studies in a wide variety of graduate level topics, students may take many of the department¿s upper level undergraduate courses supplemented with graduate components. These courses include advanced calculus, complex variables, differential equations, abstract algebra, number theory, probability, statistics, and more.

MATH 799 THESIS RESEARCH *Repeatable* 1-6 Units

Students must complete a Thesis Proposal Form in the Graduate Studies Office before registering for this course.