MATH 315
INTRODUCTION TO NUMBER SYSTEMS

1. Catalog Entry

MATH 315. Introduction to Number Systems.
Three hours lecture (3).

Prerequisite: Either MATH 155 or both MATH 103 and MATH 109.

Whole numbers, integers, modular arithmetics, rational numbers, and real numbers will be studied in terms of the mathematical structure of each system. Problem solving within each system will be emphasized.

2. Detailed Description of Content of Course

MATH 315 provides the mathematical foundations necessary for the development of number systems. Similarities and differences between number systems will be explored, and this will result in an understanding of the problem solving potentials of each system.

The following is an outline of the mathematical content in this course:

• System on the Whole Numbers
  Sets and their properties will be used to develop the structure of the whole numbers. This mathematical structure will then be used to justify computational algorithms.
• The System of Integers
  The structure of the integers will be developed by using the whole numbers. Contrasts will be made between the two systems.
• Modular Arithmetic
  Finite number systems will be examined by making use of the properties of the integers in the development of modular
  arithmetic. Problems involving linear equations will be solved.
• The System of Rational Numbers
  The development of the rationals will be seen as an extension of the integers. The properties of the rationals and the problem solving techniques will be examined.
• The Real Numbers
  The need for real numbers will be considered in terms of appropriate problems. Techniques for approximating real numbers will be examined.

3. Detailed Description of Conduct of Course

Most instructors will use the lecture - discussion method. Some may require students to work together in small groups. Models of number systems and their properties and operations will be utilized. Students will be asked to work problems assigned as homework. The use of graphing calculators and/or computers will be included.

4. Goals and Objectives of the Course

• To provide information and understanding of the commonly used number systems.
• To provide mathematical content especially useful to elementary school teacher trainees.
• Students are expected to be active learners who will in turn promote active learning as a strategy in their teaching. Manipulative laboratory materials are an example particularly appropriate for active learning.

5. Assessment Measures

Graded tasks may include tests, quizzes, homework exercises, class participation, and attendance.

6. Other Course Information

This course is intended for students who plan to teach in the elementary schools and majors and minors in mathematics.

7. Review and Approval

DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair