While Loops

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• Misc
  • Today is the deadline for applying for math dept. scholarships
  • Colloquium
    • “Bodybuilding! ... for Mathematicians” + career thoughts
    • Monday March 30, 4:00-5:00 pm
    • Newton 201
    • Julie Croteau ’97, now at Corning Community College
    • Extra credit for summaries
• Questions?
• While Loops
  • Section 5.3
    • Loop that executes as long as condition is true
    • Can be infinite if condition is always true, so make sure condition eventually becomes false
    • Multiple conditions can be combined with or (||) or and (&&)
    • Uses
      • Error-checking...?
      • Counting...?
  • Idioms
    • Data validation, e.g., get 1-digit number from user
      • (We decided that a “1-digit number” is any integer between -9 and 9)
        

        >> n = input( 'Enter a 1-digit number ' );
        Enter a 1-digit number 17
        >> while n > 9
        + n = input( 'Too big! Try again ' );
        + end
        Too big! Try again 10
        Too big! Try again 236
        Too big! Try again 3
        n
        n =
            3
        >> round( 3.4 )
        ans =
            3
        >> round( 3 )
        ans =
            3
        >> while abs(n) > 10 && n ~= round(n)
        + n = input( 'Try again ' );
        + end
        % No prompt for more, this accepts 3 as 1-digit
        >> n = input( 'Enter a 1-digit number ' );
        Enter a 1-digit number -3.5
        >> while abs(n) > 10 && n ~= round(n)
        + n = input( 'Try again ' );
        + end
        % No prompt, so it also accepts -3.5 as 1-digit
        % correct number: abs(n) < 10 and n = round(n)
        % while "incorrect number"
        >> while abs(n) >= 10 || n ~= round(n)
        + n = input( 'Try again ' );
        + end
        Try again 1.5
        Try again 12
        Try again 10
        Try again 6
        % Seems to work
        % What if n is complex?
        >> n = 3+2i
        n =
            3.0000 + 2.0000i
        >> while abs(n) >= 10 || n ~= round(n)
        + n = input( 'Try again ' );
        + end
        % No prompt for more input, so Matlab apparently accepts 3 + 2i as a 1-digit number

      • Logic in while loops can be tricky
        • Often need to say “while what I want is not yet true”
        • de Morgan’s Laws
          • not( A and B ) = (not A) or (not B)
          • not( A or B ) = (not A) and (not B)
        • ... and “not <” is “≥”
• Next
  • Bisection and while
    • Hand out bisection lab
  • If statements

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