Introduction to Structures

CSLU 1100.Lo3Fall 2007

Cameron McInallycameron.mcinally@nyu.edu

Fordham University

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• 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

Introduction

• About the instructor– Name: Cameron McInally– Office Hours: TF 2:15 – 3:15 or by appointment– Office: LL 819d– Phone: +16092876806– Email: cameron.mcinally@nyu.edu

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Objective:To provide students with the skills to solve analytical

and algorithmic problems.

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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

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Resources available to you:• Textbook: Discrete Mathematics:

Mathematical Reasoning and Proof with Puzzles, Patterns and games by Douglas Ensley and Winston Crawley

• Blackboard: All course materials will be accessible via fordham.blackboard.com

• Instructor: That’s me

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• 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.

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• 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, October 17 @ 6:00pm and Wednesday, December 19 @ 6:00 pm. Exams cannot be made up.

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• 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.

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• 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.

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• 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.

Now onto the course

“Would you like to play a game?”

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).

Directions

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

Directions

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

Directions

4. Turn over the top two cards in one chunk

Directions

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

Directions

6. Turn over the top two cards in one chunk

Directions

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

Directions

8. Either turn over the entire stack or do not

Directions

9. Turn over the top card

Directions

10. Turn over the top two cards in one chunk

Directions

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

What is the only card facing the opposite way of the others?

It’s a club!

The Josephus Game

• Get into a circle. Every 7th 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?

Play it on your own

Josephus Game

Drawing Puzzles

Try out the Drawing Game

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.

What can happen on my first throw?

• I could hit the target• I could miss the target.

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.

What will happen is I make 3 throws?

Throw 1 Throw 2 Throw 3

Option #1 Hit Hit Hit

Option #2 Hit Hit Miss

Option #3 Hit Miss Hit

Option #4 Hit Miss Miss

Option #5 Miss Hit Hit

Option #6 Miss Hit Miss

Option #7 Miss Miss Hit

Option #8 Miss Miss Miss

Tables can be very useful another option to represent possibilities is

a game tree.

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.

Homework(Always Due in One WeekAlways Due in One Week)

• Complete Online Survey on the course website.

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