Courses

This course is designed to introduce students to the basic skills necessary for academic success in the discipline of Mathematics and to provide students with an overview of professions in which that major may be applied.

This course will include instruction in the following areas covering the K-8 California Standards: critical thinking, sets, systems of numeration, number theory, the real number system, two- and three-dimensional geometry, representational systems, methods for determining measurement, statistics, data analysis, and probability. Students will analyze complex problems, apply logical reasoning techniques, evaluate the truth of mathematical statements, and apply different solution strategies.

This course is designed to prepare a student for Calculus I. It will include instruction in the following areas: review of systems of equations and inequalities, functions and their graphs, sequences, induction, counting, probability, trigonometry, analytical geometry, and pre-calculus material.

Basic concepts of analytical geometry, limits and derivatives, differentials and rates, integration, definite and indefinite integrals, differentiation of logarithmic and exponential functions.

The study of symbolic languages, such as Mathematics, Maple, and MATLAB, for the use and application in Calculus and modeling courses.

Continued study and applications of integration: volumes, lengths, surface of revolution; derivatives and integrals involving trigonometric functions, infinite series, expansion of functions, hyperbolic functions, law of the mean, partial fractions, polar coordinates, and conic sections.

This course will equip candidates with the theories and practices connected to working with diverse student populations. Candidates will examine the manner in which societal and cultural forces have impacted current perspectives of equity especially as they relate to special needs and English language learning students. The role of assessment in determining student needs and designing appropriate pedagogical strategies will also be emphasized. This course will solidify understanding of the strengths-based approach to making adaptations required in the TPA process.

The nature, determinants, adjustments, and problems of persons with intellectual gifts, intellectual disabilities, physical disabilities, learning disabilities, health problems, and emotional problems will be studied in conjunction with appropriate educational interventions in the general education Middle and High School classroom setting.

A study of various methods of proofs and mathematical structures covering logic, universal and existential quantifiers, sets, functions, and selected topics in discrete mathematics, linear algebra, abstract algebra, and real analysis. This is a bridge course to abstract mathematics and should be taken prior to or concurrently with courses in linear or abstract algebra, and real or complex analysis.

A calculus based course covering discrete and continuous distributions, expectations, the normal distribution, the central limit theorem, the binomial distribution, and various topics in statistical theory such as point estimation, hypothesis testing, and linear regression.

A study of the History of Mathematics from ancient to modern times: Elementary topics in number theory, linear congruencies, Fermat and Wilson theorems, quadratic reciprocity laws.

Vector spaces; matrices, rank and systems of linear equations; linear transformation; similarity and diagonalization theorems; eigenvectors and eigenvalues.

An advanced study of concepts of Euclidean geometry and an introduction to non-Euclidean geometry. Theorems and proofs are emphasized.

The course is designed to be a culminating experience for senior students who are preparing to teach mathematics at the junior/senior high school level. The course provides students an opportunity to reflect on the critical assignments that have been completed throughout their coursework and relate these lessons to the career of teaching.

Study and applications of vector analysis, partial differentiation, multiple integration, Jacobians, theorems of Green and Stokes, and divergence theorem.

An introduction to real analysis and topology covering the completeness of the real numbers, sequences, limits, continuity, uniform continuity, Riemann integrability, topology of the real numbers, topological spaces, connectedness, compactness, and metric spaces.

The focus of this class is an independent research project that the student undertakes under the direction of a faculty member who acts as a research advisor. Content varies from year to year and is determined by both instructor's and students' interests.

The first course in a 2-semester calculus-based physics sequence for science and mathematics majors. A study of mechanics, heat and thermodynamics, waves, sound, and the mathematical methods of physics. Should be taken with PHY 214L - Physics for Scientists I Lab and PHY 214D - Physics for Scientists I Discussion.

This laboratory course, designed to be taken concurrently with PHY 214 - Physics for Scientists I, emphasizes scientific measuring and reporting techniques. Observational laboratories will reinforce topics in mechanics, including kinematics, Newton's Laws, momentum, energy, waves, sound, and thermodynamics.

The second course in a 2-semester calculus-based physics sequence for science and mathematics majors. Includes a study of electricity, magnetism, electromagnetic waves, optics, and modern physics topics. Should be taken with PHY 224L - Physics for Scientists II Lab and PHY 224D - Physics for Scientists II Discussion.

This laboratory course, designed to be taken concurrently with PHY224 - Physics for Scientists II, emphasizes scientific measuring and reporting techniques. Observational laboratories will reinforce topics in electricity, magnetism, optics, and modern physics.