Participants study topics tested on the California Subject Examination for Teachers (CSET Mathematics Subtest 1: Algebra; Number Theory) that are related to algebra and functions from an advanced perspective. Topics include: analysis of polynomial, rational, and exponential functions; and computation with complex numbers. Prerequisite: Intermediate Algebra and Math X464A (recommended)

RELATIONS AND FUNCTIONS (RAF)
Participants use vocabulary associated with relations and functions to describe two-variable equations. Participants practice graphing linear, quadratic, and absolute value relations and functions.

INEQUALITIES (INEQ)
Participants solve and graph linear and non-linear systems of inequalities. Participants apply their knowledge to analyze real-world application problems.

THE QUADRATIC EQUATION (QEQ)
Participants apply the zero product property and the square root property to solve equations and practice solving quadratic equations by completing the square. Participants derive the quadratic formula and analyze the discriminant to determine the nature of the roots.

QUADRATIC FUNCTIONS (QFN)
Participants solve a packaging problem, and use it to analyze characteristics of the quadratic function. Participants write quadratic functions in standard form, vertex form, and factored form (when possible). Participants solve problems that require analysis of the quadratic function. 

AN INTRODUCTION TO COMPLEX NUMBERS (CPX)
Participants explore solutions to quadratic equations with complex roots. Participants learn to compute with complex numbers as they explore some interesting properties of them.

POLYNOMIAL EQUATIONS (PEQ)
Participants review basic factoring techniques. Then they learn to use synthetic division, the factor theorem, rational root theorem, conjugate root theorem, and fundamental theorem of algebra to factor higher order polynomials and to find roots of polynomial equations. Participants examine a proof of the factor theorem and rational root theorem.

POLYNOMIAL FUNCTIONS (PFN)
Participants explore parent graphs of polynomial functions to determine the trends in their behavior. Participants sketch graphs of polynomials. Participants use various theorems to assist finding zeroes of polynomial functions.

COMPOSITE FUNCTIONS (CPFN)
Participants are introduced to the concept of composite functions two contexts. Participants discuss common notation, look at concerns about domain and range, explore some properties of composition, and examine how composition relates to inverse functions.

INVERSE FUNCTIONS (INV)
Participants are introduced to inverse functions through the conversion formulas for Celsius and Fahrenheit temperatures. Then, participants explore inverse functions through a hands-on activity, where they graphically find the reflection of a function along the y = x line. Finally, participants practice finding inverse relations for functions and determine if functions are invertible.

EXPONENTIAL FUNCTIONS (EXP)
Participants generate functions based on exponential growth and decay. They explore how compound interest is computed, and are introduced to the Euler constant. Participants solve problems that involve exponential functions.

LOGARITHMIC FUNCTIONS (LOG)
Participants explore the inverse of exponential functions as they learn about logarithmic notation and logarithm properties. They solve problems using exponents and logarithms.

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