CATALOG DESCRIPTION:

Math 01.201  Structures of Mathematics I                                                              3 s.h.

Prerequisites: Basic Algebra II

This course concerns the development of number systems and algebraic structures, including the natural numbers, the integers, rational numbers, real and complex numbers.  Concrete examples of selected algebraic structures such as modular arithmetic and matrices are also included.  Students will be required to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality, using a variety of representations of mathematical concepts and procedures.  Use of calculators is required. (Students are expected to have completed the equilvalent of Intermediate Algebra)
 

OBJECTIVES:

This course is intended to provide students with the opportunity to develop their knowledge of the content and discourse of mathematics, including:

- mathematical concepts and procedures and the connections among them;

- multiple representations of mathematical concepts and procedures;

- ways to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality;

- the nature of mathematics, the contributions of different cultures toward the development of mathematics, and the role of mathematics in culture and society;

- the changes in the nature of mathematics and the way we teach, learn, and do mathematics resulting from the availability of technology;

- the place of "school mathematics" (what students have learned in elementary school and high school) within the discipline of mathematics;

- the relationship of mathematics to other subjects and its applications in society.
 

Students in the course will use physical materials and models to explore fundamental properties of number systems, to describe real-world relationships, and to explore selected algebraic structures, such as groups, rings, fields, and vector spaces.  They will also develop conjectures and intuitive proofs of number theoretic properties.  This course is especially appropriate for those students preparing to be elementary or special education teachers.
 

CONTENT:

1.  Nature and Use of Number

 1.1  Role of numbers as a logical, predictable system for
   expressing and relating quantities

 1.2  Features and basic computational techniques in selected
  numeration systems in use today and in the past

 1.3  Operations, properties, and uses of whole numbers,
  fractions, and decimals

 1.4  Estimation and mental arithmetic, calculators, computers,
  paper-and-pencil algorithms, and manipulative materials
  as tools for use in solving problems
 

2.  Patterns and Functions

 2.1  Pattern as an underlying, fundamental theme in
  mathematics

 2.2  Creating and using pictures, charts, graphs, variables,
  equations, inequalities, and other algebraic notation to
  recognize and describe mathematical relationships

 2.3  Functional relationships which arise from diverse problem
  situations

 2.4  Number sequences, patterns, and functional relationships

 2.5  Concrete examples of finite and infinite sequences and
  series, approximation of nonterminating decimals and
  approximation of functions
 

3.  Number Concepts and Relationships

 3.1  Fundamental properties of number systems

 3.2  Elementary number theory

 3.3  Infinity and its role in the study and historical
  development of mathematics
 

4.  Algebraic Structures

 4.1  Examples of functions arising from a variety of problem
  situations

 4.2  Properties of functions

 4.3  Properties of the integers, rational numbers, real and
  complex numbers (including order, denseness, and
  completeness)

 4.4  Concrete examples of selected algebraic structures such
  as groups, rings, fields, and vector spaces
 

POSSIBLE TEXT:

Bennette, Albert, & Nelson Ted. Mathematics for Elementary Teachers: Conceptual Approach & Activity Approach., McGraw-Hill, 7th edition