MAT 523 Theory of Functions for Teachers
This is a sample syllabus only. Ask your instructor for the
official syllabus for your course.
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Course Description
Topics from Function Theory including: mathematical models,
linear functions, nonlinear functions, transformations, limits,
continuity, functions of several variables.
MAT 523 meets for three hours of lecture per week.
Prerequisites
MAT 543, graduate standing and one year of full time secondary
teaching.
Objectives
After completing MAT 523 the student should be able to
 represent functions numerically, graphically, and
algebraically
 use a graphing calculator effectively in exploring
properties of functions
 state the relevant mathematical definitions and results
about functions and apply them to solving problems
 demonstrate understanding of the abstract concepts of
functions and be able to identify these concepts within
models of particular functions in context
 identify function concepts within the secondary
curriculum
 demonstrate knowledge of current research on teaching and
learning about functions
Expected outcomes
Students should be able to demonstrate through written
assignments, tests, and/or oral presentations, that they
have achieved the objectives of MAT 523.
Method of Evaluating Outcomes
Evaluations are based on homework, class participation,
short tests and scheduled examinations covering students'
understanding of topics covered in MAT 523 and a project to be
written and presented to the class.
Text
Functions, Modeling Change, by the Shell
Centre.
Outline of contents
 representing functions and other relations numerically,
graphically, algebraically
 examples of relations which are 11, many1, 1many, and
manymany
 identifying basic properties of functions given in each
of the different representations, for example:

 domain and range
 x and yintercepts
 intervals on which the function is
increasing/decreasing
 comparison of slope for linear functions and variable
rates of change for nonlinear functions
 intervals on which the function is concave
up/down
 whether the function is onetoone or
manytoone
 given x, find f(x)
 given b, solve for x such that f(x) = b, f(x) < b,
f(x) > b.
 identify horizontal and vertical asymptotes
 intervals on which the function is
continuous/smooth
 existence of and properties of inverse functions
 introduction to the concepts, language and notation of
calculus
 the study of representatives of classic families of
functions:

 linear functions
 quadratic functions
 other polynomial functions
 exponential functions
 logarithmic functions
 rational functions
 trigonometric functions
 modeling given situations with functions and identifying
basic concepts associated with functions in particular
contexts
 the relationship between functions of a discrete
variable, sequences, and functions of a continuous variable,
for example:

 connection with patterns
 when to connect the dots on a graph
 progression of exponents from whole numbers to
integers to rationals to reals
 extension of the domain of trigonometric functions
from basic angles in a right triangle to their full
domain within the real numbers
 using line/curve of best fit to analyze data
 identifying functions and relations throughout the
secondary mathematics curriculum, for example:

 the need for inverse functions in solving
equations
 the expression on each side of an equation or an
inequality as a function (particularly when an expression
= or < or > a constant)
 the number of elements as a function of the subsets
of a given set
 the probability of an event as a function of the
subsets of a sample space
 the number of vertices, the measure of the largest
angle, the area, the perimeter each as a function of the
set of polygons
 the number of factors as a function of the counting
numbers
 the correspondence between a fraction representation
and a decimal representation of rational numbers
 selected topics regarding current research on both
teachers and students understanding of functions
Grading Policy
Students' grades are based on homework, class participation,
short tests, and scheduled examinations covering students'
understanding of the topics covered in MAT 523. The instructor
determines the relative weights of these factors.
Attendance Requirements
Attendance policy is set by the instructor.
Policy on Due Dates and MakeUp Work
Due dates and policy regarding makeup work are set by
the instructor.
Schedule of Examinations
The instructor sets all test dates except the date of the
final exam. The final exam is given at the date and time
announced in the Schedule of Classes.
Academic Integrity
The mathematics department does not tolerate cheating.
Students who have questions or concerns about academic
integrity should ask their professors or the counselors in the
Student Development Office, or refer to the University Catalog
for more information. (Look in the index under "academic
integrity".)
Accomodations for Students with Disabilities
Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 2433660 or to use telecommunications Device for the Deaf, call (310) 2432028.
Revision history:
Prepared by J. Barab 4/3/00. Revised 7/7/01, 7/25/06 (G. Jennings).