problem solving strategies in mathematics and computer science
DESCRIPTION
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 LiTRANSCRIPT
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Problem Solving in mathematics and computer science
Team members:Lishu Liu
Yun ZhangProsunjit BiswasTahmina Ahmed
Team 4Chapter 13 Reading in Mathematics
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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
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Thought pattern in mathematics
The three patterns are: ProcessProblem solvingComparison and contrast
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The kissing problem
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Problem solving in mathematics- step1
Define the problemEveryone 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?
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Problem solving in mathematics- step2
Try to solve the problem for simple cases
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Problem solving in mathematics- step3
Look for a pattern or clue
n=1: 0 kiss
n=4: 3+2+1 kisses n=3: 2+1 kisses
n=2: 1 kiss
1 3
2
1
2
3
4
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Problem solving in mathematics- step3 (continuing…)
n = 5, kisses = 4 + 3 + 2 + 1n = 6, kisses = 5 + 4 + 3 + 2 +1n = 7, kisses = 6 + 5 + 4 + 3 + 2 + 1
So, what can be the pattern for the kissing problem?
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Problem solving in mathematics- step4
Guess and checkWhat if we have n people?
?
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Problem solving in mathematics- step5
Use knowledge to solve the problem and extend the solution Kisses = (n-1) + (n-2) + … + 1
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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-1) factors
(n-1) factors (n-1) factors
(n-(n-1))
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Summarizing steps in mathematics
Flow chart
Step 1
•Define the problem
Step 2
•Try some solution to the problem for simple cases
Step 3
•Look for a pattern or clue
Step 4
•Guess and check
Step 5
•Use knowledge to solve the problem and extend the solution
Step 6
•Try to find a better solution
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Problem solving in computer science - step1
Define the problemEveryone 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 ?
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Problem solving in computer science - step2
Get sample input and output for simple casesDefine input 1, 2, 3, 4 … | | | |Define output 0, 1, 3, 6 …
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Problem solving in computer science - step3
Construct logic with the patternFor first two input
So, We can assume that for n people n -1 kisses.
n=1: 0 kiss n=2 : 1 kiss
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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.
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Problem solving in computer science - step4
We will improve our solution through trial & error.
what will happen if we cannot reach the exact solution ?
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Problem solving in computer science – step4
So, we will construct & justify our logic using mathematical formula.
Kisses = n (n-1) / 2
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Problem solving in computer science - step5
Now we have the solutionNow its time to code !
FIND NO OF KISSES( N) KISS=N(N-1)/2RETURN KISS
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Problem solving in computer science - step6
Problem solved!
Why do we really need a computer to solve the problem?
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Summarizing steps in computer science
Flow chart
Step 1
•Problem Understanding
Step 2
•Get sample Input and Output
Step 3
•Construct logic with the pattern
Step 4
•Improve logic through Trial & Error
Step 5
•Finally solve the problem with mathematics
Step 6
•Fitting the mathematical solution in computer programming.
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Mathematics vs. Computer Science
Mathematics Computer ScienceStep 1 Define the problem Problem understandingStep 2 Try to solve the problem for
some simple cases Get sample input and output
Step 3 Look for a pattern or clue Construct logic with the pattern
Step 4 Guess and check Improve logic through trail & error
Step 5 Use knowledge to solve the problem and extend the solution
Finally get the solution
Step 6 Try to find a better solution Problem solved
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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)
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Acknowledgement
Contact Person Ahmed, TahminaHandout preparation Ahmed, Tahmina & Lishu LiuProof reading Zhang, YunSlide Customization Biswas, ProsunjitContent Preparation AllSlide Preparation All
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Questions?
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