Introduction

COMP283 – Discrete Structures

JOOHWI LEEDr. Lee or Mr. LeeABD Student working with Dr. Styner

Email: joohwi@cs.unc.eduhttp://www.cs.unc.edu/~joohwi/COMP283

Class Information

Office HoursMW 12:15PM ~ 01:15PM SN014MW 01:30PM ~ 02:30PM FB008Appointment via Email or after classes

Office Hours

Discrete Mathematics with Applications

Textbook

Four categories10 Quizzes (20 pts)3 Assignments (30 pts)Midterm and Final exams (20 pts and 30 pts)Office hour meeting (extra 3 pts)

Evaluation

Quizzes6 In-class quizzes • will be announced at a previous class• may take up to 15 minutes

4 Take-home quizzes• may take up to 45 minutes

No discussionMostly from the textbook

Quizzes

Assignments

will be take-homeadvised to cooperate with classmates but write your own solutionswill have two weeks for submissionwill not be graded if submitted over due dates

Assignments and Exams

ExamsThe mid-term date will be 2nd March, Monday at the class (50 minutes)The final date will be discussed later

Curved Grading Scale90% A75%-89% B60%-74 % C50%-59 % D

Exams and Grading

I do reserve the right to be more lenient or strict

A very fundamental course

• Basis for Computer Programming• Basis for Algorithms and Data Structures• Basis for Database System• …• Helpful to prepare interviews for IT companies

What is Discrete Mathematics?

This is a really helpful and useful class.This class contains one of the most basic (and even beautiful) math you will ever learn.This class should be fun if you really learn.

Good News

Several TopicsLogics, Sets, Functions, Graphs, …

Definitions and ConceptsThere are many you have to memorize

Mathematical Proof and AnalysisA painful processes with heavy concentrationThis will tease our brains

Could be boring if you are smartThis is a required course.

Bad News

Need your own practicesRead the textbook!Lectures will guide you!Study Groups and DiscussionsDo quizzes and assignments by yourself

Hints for Success

Introduction to Formal LogicElementary Number TheorySequence and Mathematical InductionSet TheoryFunctionsCounting and Discrete ProbabilitiesGraphs and Trees

A List of Topics

Formal LogicsLearning rules of logical deduction regardless of its content

Example: SyllogismIf Socrates is a man, then Socrates is mortalSocrates is a manTherefore, Socrates is mortal

Replace sentences with symbols

Example Contents

In an island, two types of people live

Knights always tell the truthKnaves always tell lie

A says: B is a knight.B says: A and I are of opposite types.

What are A and B?

Example Contents

A B

Elementary Number TheoryProperties of NumbersNatural numbersIntegersReal Numbers

ProofProve that there is no integer that both even and odd

Example Contents

Example Contents

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Find a walk through the city that would cross each bridge once and only once

Example Contents

Sum up every natural number between 1 and 100

1 + 2 + 3 + 4 + … + 97 + 98 + 99 + 100 = ?

How do you prove the equation?

Example Contents

Doubling the number and adding 3 gives the same result as squaring the number?

Mathematical Sentences