Chap 1

• Mathematics is the scientific study of structure, order, and relationships emerged from elemental procedures of counting, measuring, and explaining the format of objects.
• Mathematics copes with logical reasoning and quantitative calculation.
• Mathematics classified into two categories: Continuous Mathematics and Discrete Mathematics
• Continuous Mathematics can be broken down into fractions or decimals
• Discrete Mathematics involves distinct values, that are a countable number of points
• Discrete - Counted
• Continuous - Measured
• Continuous

  • Weight range from 60 to 100 kilos
  • 10 to 20 CM
  • Age of pig
  • time
  • temperature
  • weight
  • distance

  Discrete

  • 4 family members
  • 5 books
  • Number of pig
  • purchasing tickets
  • number of students
  • text messages
• Continuous Mathematics is based upon continuous number line or the real numbers
• Continuous Mathematics is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers.
• Discrete Math is a description of a set of branches of math that all have in common the feature that they are "discrete" rather than "continuous"
• Discrete mathematics is math that makes use of discrete structures
• Discrete structures are structures that are used in describing discrete mathematics
• Discrete structure is set of discrete elements on which certain operations are defined
• Problem solving is an art and there are no universal approaches to solving problems
• The traditional “GUESS” method (Heller and Heller, Univ. of Minnesota)

  • Givens - Identify the “given” information
  • Unknown - Identify what is wanted
  • Equation - Select equation for solution
  • Solution - Solve equation for unknown
  • Survey - Make certain solution is realistic
• Framework for Problem Solving (Polya)

  Understanding the problem

  Devising a Solution Plan

  Carrying out the plan

  Looking back i.e. verifying