introduction comp283 – discrete structures. joohwi lee dr. lee or mr. lee abd student working with...
TRANSCRIPT
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Introduction
COMP283 – Discrete Structures
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JOOHWI LEEDr. Lee or Mr. LeeABD Student working with Dr. Styner
Email: [email protected]://www.cs.unc.edu/~joohwi/COMP283
Class Information
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Office HoursMW 12:15PM ~ 01:15PM SN014MW 01:30PM ~ 02:30PM FB008Appointment via Email or after classes
Office Hours
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Discrete Mathematics with Applications
Textbook
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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
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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
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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
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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
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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?
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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
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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
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Need your own practicesRead the textbook!Lectures will guide you!Study Groups and DiscussionsDo quizzes and assignments by yourself
Hints for Success
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Introduction to Formal LogicElementary Number TheorySequence and Mathematical InductionSet TheoryFunctionsCounting and Discrete ProbabilitiesGraphs and Trees
A List of Topics
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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
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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
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Elementary Number TheoryProperties of NumbersNatural numbersIntegersReal Numbers
ProofProve that there is no integer that both even and odd
Example Contents
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Example Contents
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Example Contents
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Example Contents
Find a walk through the city that would cross each bridge once and only once
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Example Contents
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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
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Doubling the number and adding 3 gives the same result as squaring the number?
Mathematical Sentences