Participants study topics tested on the California Subject Examination for Teachers (CSET Mathematics Subtest 1: Algebra; Number Theory) that are related to algebraic structures, linear algebra, and number theory from an advanced perspective. Topics include: rings and fields, properties of real and complex numbers, vectors and matrices, properties of natural numbers, and Mathematical Induction. Prerequisite: Intermediate Algebra and Math X461A (Topics from High School Mathematics 1A) (recommended)

MATRIX OPERATIONS (MTX1)
Participants review methods for solving linear systems of equations (such as by graphing, substitution, and by elimination.) Participants learn what is a matrix and perform some basic matrix operations. Participants then apply elementary row operations and the Gaussian elimination method to solve linear systems of equations.

SOLVING SYSTEMS USING MATRICES (MTX2)
Participants learn what is a matrix and perform some basic matrix operations. Participants evaluate the determinant and use it to find the inverse of a matrix. Participants then use matrices to solve linear systems of equations.

INTRODUCTION TO VECTORS (VECT1)
Participants use the polar and rectangular form of a vector. Participants add vectors, and use them to find map distance and direction.

VECTOR MULTIPLICATION (VECT2)
Participants examine three types of vector multiplication: scalar product, cross product, and dot product in polar and rectangular form. They use the magnitude of the cross product to find the area of polygons. Finally, participants connect scalar product to the slope of perpendicular lines.

MATHEMATICAL INDUCTION (IND)
Participants review the difference recursive and explicit rules and practice deriving them for number sequences. Participants use summation notation to represent and find the sum of the terms of a series. Participants will learn what mathematical induction means. They will set up the required steps for a proof by the method of Mathematical Induction and apply the process to number sequences and contextual problems.

GROUPS, RINGS, AND FIELDS (GRF)
Participants learn to perform modular arithmetic and use it to investigate the properties of groups, rings and fields. Participants determine whether various number sets such as integers, and rational, irrational, and real numbers, along with their operations, meet the criteria of groups, rings, or fields.

NUMBER THEORY (NUMTH)
Participants review and test various rules for divisibility. Participants use a visual model to understand and the Euclidean algorithm to find the greatest common factors of numbers. They use mathematical induction to prove the divisibility rule for 6, and they use proof by contradiction to show that the square root of 2 is irrational.

RATIONAL FUNCTIONS (RAT)
Participants review computation skills with rational expressions. Participants investigate intercepts and asymptotes for graphs of rational functions. Then, participants investigate a fixed area problem that leads to a rational function. Finally, participants apply their knowledge to explore the effect of parameter changes on rational functions.

ABSOLUTE VALUE AND POWER FUNCTIONS (APF)
Participants graph power functions and absolute value functions, and they examine the effect of parameter changes on the graphs of these functions.

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