Elementary Theory of Arithmetic I

Revised: July 2009 (Ralph Willis)

Course Description

Propositional and quantified logic, sets, relations, counting, numeration systems, mathematical systems, probability, statistics and geometry. Three semester hours.

Liberal Studies Objectives This course can satisfy the C2 (Mathematics) portion of the Liberal Studies Program. The learning goals of the Liberal Studies Program are for students to:

• Demonstrate the ability to locate, analyze, synthesize, and evaluate information;
• Demonstrate the ability to interpret and use numerical, written, oral and visual data;
• Demonstrate the ability to read with comprehension, and to write and speak clearly, coherently, and effectively as well as to adapt modes of communication appropriate to an audience;
• Demonstrate the ability to critically analyze arguments; demonstrate the ability to recognize behaviors and define choices that affect lifelong well-being;
• Demonstrate an understanding of
• Past human experiences and ability to relate them to the present;
• Different contemporary cultures and their interrelationships;
• Issues involving social institutions, interpersonal and group dynamics, human development and behavior, and cultural diversity; scientific concepts and methods as well as contemporary issues in science and technology;

Cultural heritage through its expressions of wisdom, literature and art and their roles in the process of self and social understanding.

C2: Mathematics Objectives (pending approval)

• Students will be introduced to applications of mathematics in daily experience.
• Student learning will be focused on the development of conceptual understanding rather than computational drill.
• An assignment in which students display an application of mathematics will be required. This assignment will address an application of mathematics, which may include statistics, optimization, linear regression, the mathematics of motion, or the mathematics of population growth.

Course Specific Objectives

1. Become acquainted with such ideas and basic principles of mathematics as the nature of mathematical thinking, use of mathematical models and machines, nature of proof, relation of mathematics to logical thought and knowledge of the world.
2. Understand the contributions of mathematics to man's social, economic, philosophic, and artistic heritage.
3. Learn to use words, symbols, and techniques of mathematics with precision so as to communicate concepts and ideas correctly and clearly.
4. Experience the satisfaction of mathematical discovery which stimulate curiosity, initiative, confidence, and interest in mathematics.
5. Develop understanding and appreciation of the structure of the number system, elementary number theory, and the use of algebra and geometry.
6. Develop patterns of reasoning which enable one to investigate unfamiliar situations.
7. Develop an ability to organize mathematical experiences as a means of discovery rather than presentations of a fixed set of facts and procedures.

Text

Billstein, Libeskind and Lott. A Problem Solving Approach to Mathematics for Elementary School Teachers, Tenth Edition, Pearson/Addison-Wesley, 2010.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

• Chapter 1: An Introduction to Problem Solving (8 days)
  Sections 1-3: Mathematics and Problem Solving; Explorations with Patterns; Reasoning and Logic: An Introduction.
• Chapter 2: Numeration Systems and Sets (5 days)
  Sections 2-3: Describing Sets; Other Set Operations and their Properties.
• Chapter 4: Algebraic Thinking (5 days)
  Sections 1-3: Variables; Equations; Functions.
• Chapter 2: Numerations Systems and Sets (6 days)
  Section 1: Numeration Systems.
• Supplement: Mathematical Systems (4 days)
  Finite Mathematical Systems; Rotations of Geometric Figures; Clock and Modular Arithmetic.
• Chapter 9: Probability (6 days)
  Sections 1-5: How Probabilities Are Determined; Multistage Experiments with Tree Diagrams and Geometric Probabilities; Using Simulations in Probabilities; Odds, Conditional Probability, and Expected Value; Using Permutations and Combinations in Probability.
• Chapter 10: Data Analysis/Statistics: An Introduction (6 days)
  Sections 1-4: Displaying Data: Part I; Displaying Data: Part II; Measures of Central Tendency and Variation; Abuses of Statistics.
• Chapter 11: Introductory Geometry (5 days)
  Sections 1-4: Basic Notations; Polygons; More About Angles; Geometry in Three Dimensions.