MAT 523 Theory of Functions for Teachers
This is a sample syllabus only. Ask your instructor for the
official syllabus for your course.
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.
MAT 543, graduate standing and one year of full time secondary
After completing MAT 523 the student should be able to
- represent functions numerically, graphically, and
- 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
- demonstrate knowledge of current research on teaching and
learning about functions
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.
Functions, Modeling Change, by the Shell
Outline of contents
- representing functions and other relations numerically,
- examples of relations which are 1-1, many-1, 1-many, and
- identifying basic properties of functions given in each
of the different representations, for example:
- domain and range
- x- and y-intercepts
- intervals on which the function is
- comparison of slope for linear functions and variable
rates of change for nonlinear functions
- intervals on which the function is concave
- whether the function is one-to-one or
- 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
- existence of and properties of inverse functions
- introduction to the concepts, language and notation of
- the study of representatives of classic families of
- 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
- the relationship between functions of a discrete
variable, sequences, and functions of a continuous variable,
- 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
- 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
- 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
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 policy is set by the instructor.
Policy on Due Dates and Make-Up Work
Due dates and policy regarding make-up work are set by
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.
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
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) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.
Prepared by J. Barab 4/3/00. Revised 7/7/01, 7/25/06 (G. Jennings).