Algorithms and Expressions

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• Misc
  • Sign up to grade lesson 1
• Questions?
• Algorithms
  • “What is an Algorithm” video
    • Algorithm = set of steps to always solve problem
      • Doable (effective)
      • Finite = doesn’t go on forever
      • Correct
      • Clear (definite)
    • Why?
      • Every program is an algorithm
      • Thinking about algorithm separate from program is really helpful in programming
• Variables and Expressions (Lesson 1)
  • Quadratic Equation
    • Ways of starting
      • Look for built-in function
        • roots
      • Use quadratic equation from handout
    • Roots you found for 3x² + x + 2
      • -1 ± 0.7993i
      • -0.1667 ± 0.7993i
      • -1.5 ± 7.19i
      • These can’t all be right. How do you test?
        • Try plugging them back into the polynomial and seeing if you get 0
          

          3 * (-0.1667+0.7993i)^2 + (-0.1667 + 0.7993i) + 2
          ans =
              2.5200e-05 - 1.5986e-04i

        • Note that this isn’t quite 0. This is because of “roundoff error” i.e., all computer calculations involving real numbers round them to some extent, so you have to use some judgement in deciding whether a result is correct. Here the numbers are actually close to 0, so this is probably a root, or very close to a root, of the polynomial.
      • Be careful about parentheses and precedence, e.g., x = ... / ( 2 * a )
• Next
  • Finish variables and expressions lesson
  • Watch video lectures re lottery math:
    • “The Multiplication Principle — Counting Techniques” at https://www.youtube.com/watch?v=sEul6TMYDY0
    • “Combinations — Counting Using Combinations” at https://www.youtube.com/watch?v=uATuM3ajhBw&list=PL4098211B87018422&index=1
    • “Expected Value” at http://www.youtube.com/watch?v=DAjVAEDil_Q

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