1. Introduction to Structures CSLU 1100.Lo3 Fall 2007 Cameron McInally cameron.mcinally@nyu.edu Fordham University

2. Introduction A Discrete Math Course from a Computer Science perspective. Counts towards the mathematical reasoning requirement of the Fordham Core Curriculum. Also used periodically as a liberal arts course or transfer credit

3. Introduction About the instructor – Name: Cameron McInally – Office Hours: M 6:30-9:00pm and W 4:00-6:00pm. – Office: LL 819d – Phone: +16092876806 – Email: mcinally@fordham.edu

4. Introduction Objective: To provide students with the skills to solve analytical and algorithmic problems.

5. Introduction Desired Outcomes: Be able to analyze and understand common math notation Be able to develop solutions to mathematical problems Be able to use a well-defined methodology to reason about math Be able to develop solution to multi-step reasoning problems

6. Introduction Resources available to you: Textbook: Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games Douglas E. Ensley, J. Winston Crawley Wiley, ISBN 0-471-47602-1 Website: All course materials will be accessible via: http://www.dsm.fordham.edu/~mcinally/courses/Spring2008/CS1100/CS1100.Lo3/ http://www.dsm.fordham.edu/~mcinally/courses/Spring2008/CS1100/CS1100.Lo3/ Instructor: That’s me

7. Introduction Attendance: Just short of mandatory. We are all busy people but I need to have you here for all 15 sessions. Unexcused absences or missing more than 2 classes will lower your course grade Homework: Expect to spend approximately 6 hours each week on work. You should work on it everyday but I will expect it done by Tuesday classes.

8. Introduction Computer Projects: Are designed to be challenging. Don’t give up, I don’t expect you to know how to do it already. By the end of the project, you will have mastered the skill. Exams: Keep these dates in mind Wednesday, February 27 @ 6:00pm and Wednesday, May 7 @ 6:00 pm. Exams cannot be made up.

9. Introduction Cheating: Don’t Cheat. The formal school policy is more extensive and you should read about it to know your rights and the rules. The work you do should be your own. You are only allowed help from authorized sources or when I explicitly permit it.

10. Introduction So, what is this course about? – This is a Discrete Math course that will teach you about CS reasoning. What is CS? – CS could stand for Computer Science here, but it does not. CS stands for Common Sense.

11. Introduction Why could CS stand for Computer Science? – These mathematical problems are fundamental to Computer Scientists. Why does CS stand for Common Sense? –Any math problem in this course can be completed with a basic pocket calculator. The problems require more thinking than formal mathematical skill.

12. Now onto the course “ Would you like to play a game?”

13. Directions 1.Place the cards face up in this order heart, club, diamond and spade (the heart should be on the bottom and the spade should be visible).

14. Directions 2.Turn the top card (the spade) face down)

15. Directions 3.Move any number of cards (one at a time) from the top to the bottom

16. Directions 4.Turn over the top two cards in one chunk

17. Directions 5.Move any number of cards (one at a time) from the top to the bottom

18. Directions 6.Turn over the top two cards in one chunk

19. Directions 7.Move any number of cards (one at a time) from the top to the bottom

20. Directions 8.Either turn over the entire stack or do not

21. Directions 9.Turn over the top card

22. Directions 10.Turn over the top two cards in one chunk

23. Directions 11.Turn over the top three cards in one chunk.

24. What is the only card facing the opposite way of the others? It’s a club!

25. The Josephus Game Get into a circle. Every 7 th person will be executed. We will continue until everyone has died. The last person alive win’s and gets to continue living. Where do you want to stand?

26. Play it on your own Josephus Game

27. Drawing Puzzles Try out the Drawing Game

28. Keeping Track of What Happened In some puzzles it is important to keep track of all the possibilities something can have. Suppose I am at the fair throwing balls at the dunk tank.

29. What can happen on my first throw? I could hit the target I could miss the target.

30. What if I make two throws? What could happen? I could hit the first throw, and hit the second throw I could hit the first throw and miss the second throw I could miss the first throw and hit the second throw I could miss the first throw and miss the second throw.

31. What will happen is I make 3 throws? Throw 1Throw 2Throw 3 Option #1Hit Option #2Hit Miss Option #3HitMissHit Option #4HitMiss Option #5MissHit Option #6MissHitMiss Option #7Miss Hit Option #8Miss

32. Tables can be very useful another option to represent possibilities is a game tree.

33. What can we learn from puzzles? Puzzles capture and illustrate the essential points of many mathematical reasoning tasks They can give us a concrete foundation on which to attach and understand a problem They are in fact the inspiration for many important mathematical and computer science breakthroughs.

34. Always Due in One Week Homework (Always Due in One Week) Complete Online Survey on the course website. Introduction