Department of Mathematics

Syllabus

**Math 01.201 - Structures of Mathematics I**

**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