MATH 1711: WEEK 1

Topics for this week are:

• Venn Diagrams and Counting
• The Multiplication Principle

Objectives for this week:

• Use the set operations of union, intersection, and complement
• Draw and shade Venn Diagrams with two and three circles (subsets)
• Use Venn Diagrams to solve counting problems
• Apply the Multiplication Principle to counting problems

Text coverage:     Sections 5.1 - 5.4 of Goldstein, Schneider and Siegel.

Online resources:

• Week 1 Formula Sheet
• Week 1 Practice Problems
• Online notes
  • Notes on sets and set operations. Before we begin learning about counting and probability, we first must introduce the notion of a set. These notes explain the basic concepts of sets and some set operations, including unions, intersections, and complements.
  • Notes on how to count using Venn diagrams and trees.Venn diagrams are often very useful for solving counting problems involving unions or intersections of sets. Tree diagrams are also good visual aids for solving counting problems, and are most helpful with the multiplication principle and Bayes' theorem.
  • Notes and examples on the Multiplication and Addition principles.The multiplication and addition principles are the two most basic counting rules. Think of the multiplication principle as the "AND" rule, and the addition principle as the "OR" rule.
  • A history of John Venn, the inventor of the Venn Diagram. The Venn Diagram is a very important tool in set theory. A Venn diagram is to a set as a graph is to a function; i.e., a Venn diagram gives us a physical picture of the set in question. Here you can find a brief history on the creator of the Venn Diagram.
• Java Applets
  • A Java applet to graph functions, and an introduction to Maple commands. Follow this link to review the graphs of various functions using the Java applet. In addition, you can experiment with some introductory Maple commands and learn how to draw graphs in Maple.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.