DEPARTMENT OF MATHEMATICS
CLASS SYLLABUS
Course: Math 3003 Foundations of Number Systems
Instructor: Michael Keisler
Office: Corley 239
Office hours: see homepage for
current schedule
Phone: 968-0653
e-mail: dkeisler@atu.edu
Catalog Description: A brief review of elementary Set Theory,
followed by the construction of the natural numbers ,
the integers, the rational numbers, the real numbers and the complex numbers
accompanied by a development of the order and field properties.
Prerequisites: Math 2703
Text: Material developed in class.
Purpose: Math 3003 is a course intended to establish a
basic understanding of the axiomatic approach to mathematics and its benefits
when establishing the well known properties of mathematical systems through the
use of deductive logic. This will be
accomplished by having students construct some of these basic properties for
the familiar set of counting numbers.
Objectives: Students successfully completing this course
will be able to:
1. Understand
the concept of a set and recognize one of its important uses.
2. Understand
the essence of the concept of counting.
3. Understand
origin and utility of an axiomatic system.
4. Understand
the concept of number and recognize the challenge inherent in creating the set
of counting numbers.
5. Successfully
use basic properties to develop more advanced properties.
6. Understand and use the Principle of
Mathematical Induction.
7. Understand and create meaningful binary
operations.
Assessment Methods: Two tests of equal weight will be
given that constitute the objective and major component of your grade. An additional, subjective, component will be
my estimation of your participation in class activities, especially your
presentation of solutions to problems given in class.
Policies: Tests should be taken when
scheduled. In the event that a test
cannot be taken on time, you must contact me before or
as near to the time of the test as possible to determine if a makeup test is
possible.
absences: While absences are
not directly penalized, a lack of class participation can adversely affect your
final grade.
cheating/plagiarism: Will not be tolerated in any form.
Material Covered:
1 Definitions of set, subset, unions,
intersections and complements
2. Naïve
set theory properties, their motivation and statements
3. The
concept of number
4 The
construction of a finite set of basic counting numbers
5 The
construction of the infinite set of all counting numbers
6. Mathematical
Induction
7. Relations
and Functions
8. Products
of sets
9. Binary
operations between numbers
Edited