The document discusses the problem-solving processes in mathematics and computer science, using a 'kissing problem' as a case study. It outlines various steps involved in defining and resolving the problem, including identifying patterns, making guesses, and improving solutions through trial and error. It also touches on the historical relationship between mathematics and computer science, highlighting figures like Donald Knuth.

1. Problem Solving in mathematics and computer science Team 4 Chapter 13 Reading in MathematicsTeam members:Lishu LiuYun ZhangProsunjitBiswasTahmina 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 mathematicsThe three patterns are: ProcessProblem solvingComparison and contrast

4. The kissing problem

5. Problem solving in mathematics- step1Define 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?

6. Problem solving in mathematics- step2Try to solvethe problem for simple cases

7. Problem solving in mathematics- step3Look for a pattern or cluen=2: 1 kiss n=1: 0 kiss 3123142n=4: 3+2+1 kissesn=3: 2+1 kisses

8. 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 + 1So, what can be the pattern for the kissing problem?

9. Problem solving in mathematics- step4Guess and checkWhat if we have n people??

10. Problem solving in mathematics- step5Use knowledge to solve the problem and extend the solution Kisses = (n-1) + (n-2) + … + 1

11. Problem solving in mathematics- step6Try 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 mathematicsFlow chart

13. Problem solving in computer science - step1Define 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 ?

14. Problem solving in computer science - step2Get sample input and output for simple casesDefine input 1, 2, 3, 4 … | | | |Define output 0, 1, 3, 6 …

15. Problem solving in computer science - step3Construct logic with the patternFor first two inputSo, We can assume that for n people n -1 kisses.n=1: 0 kiss n=2 : 1 kiss

16. Problem solving in computer science - step3We 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 kissesBut this time we are indeed wrong. So, need to improve our guess.

17. Problem solving in computer science - step4We will improve our solution through trial & error.what will happen if we cannot reach the exact solution ?

18. Problem solving in computer science – step4So, we will construct & justify our logic using mathematical formula. Kisses = n (n-1) / 2

19. Problem solving in computer science - step5Now we have the solutionNow its time to code !FIND NO OF KISSES( N) KISS=N(N-1)/2RETURN KISS

20. Problem solving in computer science - step6Problem solved!Why do we really need a computer to solve the problem?

21. Summarizing steps in computer scienceFlow chart

22. Mathematics vs. Computer Science

23. Historical relation between mathematics & computer scienceDonald Knuth (Professor of Stanford)-- Father of Analysis of AlgorithmGraduated in Mathematics (Case Institute of Tech.)PhD in Mathematics (Caltech)

24. Acknowledgement

25. Questions?