MATH321: Elementary Theory of Arithmetic I

Course Description

Liberal Studies Objectives

• 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;

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

Grading Procedure

Attendance Policy

Course Outline

• Chapter 1: Critical Thinking and Problem Solving (5 days)

  Sections 1-4: Critical Thinking; Critical Thinking and Inductive Reasoning; Introduction to Problem Solving; Strategies for Problem Solving.
  
  

• Chapter 2: The Language of Logic (6 days)

  Sections 1-4: An Introduction to Logic; Conditionals and Equivalent Statements; Making Use of Deductive Logic; Quantifiers, Venn Diagrams, and Valid Arguments.
  
  

• Chapter 3: Sets, Relations and Functions (6 days)

  Sections 1-4: An Introduction to Sets; Cartesian Product and Relations; The Number of Elements in a Set; Functions.
  
  

• Chapter 4: Numeration (7 days)

  Sections 3-4: History of Numeration Systems; Patterns for Numeration; Decimal and Nondecimal Bases.
  Supplement: Other Early Numeration Systems; The Hindu-Arabic Place-Value Numeration System.
  
  

• Supplement: Mathematics Systems (4 days)

  Finite Mathematical Systems; Rotations of Geometric Figures; Clock or Modular Systems.
  
  

• Chapter 9: Introduction To Probability Theory (6 days)

  Sections 1-5: The Language of Probability; Probability of Events and Properties of Probability; Multi-step Experiments, Expected Value and Simulation; The Fundamental Principle of Counting and Permutations; Counting and Combinations.
  
  

• Chapter 10: The Uses and Misuses of Statistics (5 days)

  Sections 1-3: Frequency Distributions and Graphical Representation; What Is Average; How to Measure Scattering.
  
  

• Chapter 11: Informal Geometry (6 days)

  Sections 1-3: An Introduction to Geometry; Lines, Planes and Angles; Simple Closed Curves.