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Problem solving strategies in mathematics and computer science

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This presentation was placed on a course project of reading course in the university of texas, san Antonio. This is a group project and the project lead was Lishu Li

This presentation was placed on a course project of reading course in the university of texas, san Antonio. This is a group project and the project lead was Lishu Li

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  • 1. Problem Solving in mathematics and computer science
    Team 4
    Chapter 13
    Reading in Mathematics
    Team members:
    Lishu Liu
    Yun Zhang
    ProsunjitBiswas
    Tahmina Ahmed
  • 2. How ideas and relationships are expressed in mathematics?
    Ideas and relationships are expressed through notations, symbols, numbers and formulas.
    Symbol: =,<,>,+,-,*,/ etc.
    Number: 1,2,3,0.1,1/2,logn etc.
    Formula: ex. y = x+2
  • 3. Thought pattern in mathematics
    The three patterns are:
    Process
    Problem solving
    Comparison and contrast
  • 4. The kissing problem
  • 5. Problem solving in mathematics- step1
    Define the problem
    Everyone must kiss each other.
    We define one kiss as occurring when two people kiss each other, any number of times.
    Q: How many kisses will occur if we have n people? 
  • 6. Problem solving in mathematics- step2
    Try to solvethe problem for simple cases
  • 7. Problem solving in mathematics- step3
    Look for a pattern or clue
    n=2: 1 kiss
    n=1: 0 kiss
    3
    1
    2
    3
    1
    4
    2
    n=4: 3+2+1 kisses
    n=3: 2+1 kisses
  • 8. Problem solving in mathematics- step3 (continuing…)
    n = 5, kisses = 4 + 3 + 2 + 1
    n = 6, kisses = 5 + 4 + 3 + 2 +1
    n= 7, kisses = 6 + 5 + 4 + 3 + 2 + 1
    So, what can be the pattern for the kissing problem?
  • 9. Problem solving in mathematics- step4
    Guess and check
    What if we have n people?
    ?
  • 10. Problem solving in mathematics- step5
    Use knowledge to solve the problem and extend the solution
    Kisses = (n-1) + (n-2) + … + 1
  • 11. Problem solving in mathematics- step6
    Try to find a better solution
    Kisses = (n-1) + (n-2) + … + 1
    = (n + n + … + n) – (1 + 2 + … + (n-1))
    = n(n-1) – n(n-1)/2
    = n(n-1)/2
    (n-(n-1))
    (n-1) factors
    (n-1) factors
    (n-1) factors
  • 12. Summarizing steps in mathematics
    Flow chart
  • 13. Problem solving in computer science - step1
    Define the problem
    Everyone must kiss each other.
    We define one kiss as occurring when two people kiss each other, any number of times.
    Q: For N number of People how many kisses there will be ?
  • 14. Problem solving in computer science - step2
    Get sample input and output for simple cases
    Define input 1, 2, 3, 4 …
    | | | |
    Define output 0, 1, 3, 6 …
  • 15. Problem solving in computer science - step3
    Construct logic with the pattern
    For first two input
    So, We can assume that for n people n -1 kisses.
    n=1: 0 kiss n=2 : 1 kiss
  • 16. Problem solving in computer science - step3
    We consider more input & output to justify our guess(kiss=n-1).
    n=1: 0 kiss n=2: 1 kiss
    n=3: 2 kisses n=4: 3 kisses
    But this time we are indeed wrong. So, need to improve our guess.
  • 17. Problem solving in computer science - step4
    We will improve our solution through trial & error.
    what will happen if we cannot reach the exact solution ?
  • 18. Problem solving in computer science – step4
    So, we will construct & justify our logic using mathematical formula.
    Kisses = n (n-1) / 2
  • 19. Problem solving in computer science - step5
    Now we have the solution
    Now its time to code !
    FIND NO OF KISSES( N)
    KISS=N(N-1)/2
    RETURN KISS
  • 20. Problem solving in computer science - step6
    Problem solved!
    Why do we really need a computer to solve the problem?
  • 21. Summarizing steps in computer science
    Flow chart
  • 22. Mathematics vs. Computer Science
  • 23. Historical relation between mathematics & computer science
    Donald Knuth (Professor of Stanford)
    -- Father of Analysis of Algorithm
    Graduated in Mathematics (Case Institute of Tech.)
    PhD in Mathematics (Caltech)
  • 24. Acknowledgement
  • 25. Questions?