Csci 2011 discrete mathematics lecture 1 introduction
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CSci 2011 Discrete Mathematics Lecture 1 Introduction. Yongdae Kim. Instructor, TA, Office Hours. Instructor Yongdae Kim ( Fourth time teaching 2011) Email:   kyd(at)cs. umn. edu Please include 2011 in the subject of your mail

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CSci 2011 Discrete Mathematics Lecture 1 Introduction

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Csci 2011 discrete mathematics lecture 1 introduction

CSci 2011 Discrete MathematicsLecture 1Introduction

Yongdae Kim

CSci 2011


Instructor ta office hours

Instructor, TA, Office Hours

  • Instructor

    • Yongdae Kim (Fourth time teaching 2011)

    • Email:   kyd(at)cs. umn. edu

      • Please include 2011 in the subject of your mail

    • Office: 200 Union St. SE, EECS Building (Keller Hall), room 4-225E

    • Office Hours: T 11:00 ~ 12:00, Th 10:00 ~ 11:00 (Also by appointment)

  • Teaching Assistants

    • Ben Dischinger, disch029(at)umn.edu, MW 9:45 AM - 10:45 AM

    • Abedelaziz Mohaisen (Aziz), mohaisen(at)cs.umn.edu, Th 11:30 AM - 1:30 PM

    • Jeremy Iverson, jiverson(at)cs.umn.edu, Tu 2:30 PM - 3:30 PM

    • Shaun Goss, goss0063(at)umn.edu, Th 2:30 PM - 3:30 PM

    • Nathan Fox, foxxx340(at)umn.edu, Th 1:30 PM - 2:30 PM

    • Katie Wolf, wolfx265(at)umn.edu, W 1:30 PM - 2:30 PM

  • Recitation

    • Section 001: Ben (Lead), Katie, Shaun

    • Section 002: Ben (Lead), Aziz, Katie

    • Section 003: Aziz (Lead), Ben, Nathan

    • Section 004: Aziz (Lead), Jeremy, Shaun

    • Section 005: Jeremy (Lead), Shaun, Nathan

CSci 2011


Class web page e mail

Class web page, e-mail

  • http://www-users.itlabs.umn.edu/classes/Fall-2010/csci2011/

    • Reading the page carefully and regularly!

    • Read the Syllabus carefully.

    • Check calendar.

  • E-mail policy

    • Include [2011] in the subject of your e-mail

    • Use TA as much as possible :-)

CSci 2011


Textbook

Textbook

  • Discrete Mathematics and Its Applications,

    • Rosen

    • 6th Edition

    • McGraw Hill

    • 2006

CSci 2011


Overview

Overview

  • Much of the basic mathematical machinery useful in computer science will be presented, with applications.

  • Students will learn actively the art of creating real-world proofs in these areas,

    • preparing them for diverse regions of computer science such as architecture, algorithms, automata, programming languages, cryptography, and

    • increasing their general problem-solving abilities in all areas.

CSci 2011


Problems solved using discrete math

Problems solved using Discrete Math

  • How many secure passwords?

  • Probability of winning Texas Hold’em?

  • How can I encrypt a message?

  • Shortest paths between two cities using public transportation?

  • How many steps required to sort 10,000 numbers? Is this algorithm correct?

  • How to design a circuit that multiply two integers?

CSci 2011


Why study discrete maths

Why study Discrete Maths?

  • Proof

    • Ability to understand and create mathematical argument

  • Gateway to more advanced CS courses

    • Data structures, algorithms, automata theory, formal languages

    • Database, networks, operating system, security

CSci 2011


Guide for successful study

Guide for Successful Study

  • No minimalist approach

    • Homework would be sufficient! NOPE!!!

    • Read relevant sections before coming to class

    • Do the homework (of course!!!)

    • Solve much more problems (odd numbered)

  • Work regularly

    • Most chapters are building blocks for other chapters

      • So you cannot catch up 2 week lectures in 2 days

    • On average 10 hours EVERY week!

  • Creativity

    • No questions will require you to put just numbers to formula.

    • Need to know how to apply! This can be improved by practice!

  • Learning  Book, class, note, homework

    • It is combination of everything!

  • Think yourself, discuss with your friends, write your own answer!

CSci 2011


Course content

Course content

very approximately in temporal order

  • Ch. 1: Logic and Proofs

  • Ch. 2: Sets, Functions, Sequences and Sums

  • Ch. 3: Algorithms, the Integers, and Matrices

  • Ch. 4: Induction and Recursion

  • Ch. 5: Counting

  • Ch. 6: Discrete Probability

  • Ch. 8: Relations

  • Ch. 12: Modeling Computation

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Typical schedule

Typical Schedule

  • Tuesday

    • Lecture: 75 minutes

    • Group Work Due (Given in recitation section, every week)

  • Thursday

    • Lecture: 75 minutes

    • Assignment due (Every other week)

      • Posted on Sunday (1.5 week is given)

      • Topics covered until the Tuesday in the same week

    • Quiz: Every other Wednesday (50 min)

  • Wednesday

    • Recitation: 50 minutes

      • Group assignment. (Formed by instructor)

      • Due: next Tuesday

CSci 2011


Evaluation important

Evaluation (IMPORTANT!)

  • The following rules will be strictly enforced.

  • Evaluation:

    • Assignments (6), group assignments (12), quizzes (6), and a Final exam.

    • You must pass every quiz individually by attaining at least 50% of the available points on each

    • Students who fail more than once will receive an F for the course.

    • All quizzes and examinations are closed book and closed notes. (One page cheat sheet is OK.)

    • Do not schedule any absence (especially on Thursday) during the semester - there are no make-up quizzes.

CSci 2011


Due dates and submission

Due dates and Submission

  • Due dates for all assignments are strict

  • All assignments must be received at the very start of the class to receive credit.

    • No late assignment will be graded.

  • Keep a copy of each of your submissions as evidence that you have indeed submitted each assignment.

  • Do not ever put your assignment under the instructor’s office door.

CSci 2011


Grading

Grading

  • Absolute (i.e. not on a curve).

  • The overall grade will be based upon

    • 3% for each homework, 1% for each group assignment, 7% for each quiz, and 28% for the final.

    • A minimum of 60% is necessary for an S or C- grade.

  • Grading will be as follows

    • 95.0% or above yields an A, 90.0% an A-

    • 85% = B+, 80% = B, 75% = B-

    • 70% = C+, 65% = C, 60% = C-

    • 55% = D+, 50% = D, and less than 50% yields an F.

  • Percentages are not rounded when using this scheme.

  • Extra credit questions will be always available.

CSci 2011


Grading questions and complaints

Grading questions and Complaints

  • Grading is performed by the TAs.

  • If you have a question about grading, talk to TAs.

    • Only if something unreasonable has occurred will the instructor intervene.

  • Furthermore, there is a limit of ten days from when an assignment or quiz is returned in recitation (whether you are there to receive it or not) for grading problems to be dealt with.

    • After that period, such will not be considered.

    • The sole exception to this rule is the final examination.

CSci 2011


Csci 2011 discrete mathematics lecture 1 introduction

And…

  • Incompletes (or make up exams) will in general not be given.

    • Exception: a provably serious family or personal emergency arises with proof and the student has already completed all but a small portion of the work.

  • Scholastic conduct must be acceptable. Specifically, you must do your assignments, quizzes and examinations yourself, on your own.

CSci 2011


Survey

Survey

  • Office Hour

  • Network and computer security research

  • Math, math, math…

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Propositions

Propositions

  • A proposition is a statement that can be either true or false

    • “Yongdae has an Apple laptop.”

    • “Yongdae is a professor.”

    • “3 = 2 + 1”

    • “3 = 2 + 2”

  • Not propositions:

    • “Are you Bob?”

    • “x = 7”

    • “I am heavy.”

CSci 2011


Propositional variables

Propositional variables

  • We use propositional variables to refer to propositions

    • Usually are lower case letters starting with p (i.e. p, q, r, s, etc.)

    • A propositional variable can have one of two values: true (T) or false (F)

  • A proposition can be…

    • A single variable: p

    • An operation of multiple variables: p(qr)

CSci 2011


Introduction to logical operators

Introduction to Logical Operators

  • About a dozen logical operators

    • Similar to algebraic operators + * - /

  • In the following examples,

    • p = “Today is Friday”

    • q = “Today is my birthday”

CSci 2011


Logical operators not

Logical operators: Not

  • A “not” operation switches (negates) the truth value

  • Symbol:  or ~

  • p = “Today is not Friday”

CSci 2011


Logical operators and

Logical operators: And

  • An “and” operation is true if both operands are true

  • Symbol: 

    • It’s like the ‘A’ in And

  • pq = “Today is Friday and today is my birthday”

CSci 2011


Logical operators or

Logical operators: Or

  • An “or” operation is true if either operands are true

  • Symbol: 

  • pq = “Today is Friday or today is my birthday (or possibly both)”

CSci 2011


Logical operators conditional 1

Logical operators: Conditional 1

  • A conditional means “if p then q”

  • Symbol: 

  • pq = “If today is Friday, then today is my birthday”

  • p→q=¬pq

the

antecedent

the

consequence

CSci 2011


Logical operators conditional 2

Logical operators: Conditional 2

  • Let p = “I am elected” and q = “I will lower taxes”

  • I state: p  q = “If I am elected, then I will lower taxes”

  • Consider all possibilities

  • Note that if p is false, then the conditional is true regardless of whether q is true or false

CSci 2011


Logical operators conditional 3

Logical operators: Conditional 3

  • Alternate ways of stating a conditional:

    • p implies q

    • If p, q

    • p only if q

    • p is sufficient for q

    • q if p

    • q whenever p

    • q is necessary for p

CSci 2011


Logical operators conditional 4

Logical operators: Conditional 4

CSci 2011


Logical operators bi conditional 1

Logical operators: Bi-conditional 1

  • A bi-conditional means “p if and only if q”

  • Symbol: 

  • Alternatively, it means “(if p then q) and (if q then p)”

  • Note that a bi-conditional has the opposite truth values of the exclusive or

CSci 2011


Logical operators bi conditional 2

Logical operators: Bi-conditional 2

  • Let p = “You take this class” and q = “You get a grade”

  • Then pq means “You take this class if and only if you get a grade”

  • Alternatively, it means “If you take this class, then you get a grade and if you get a grade then you take (took) this class”

CSci 2011


Boolean operators summary

Boolean operators summary

  • Learn what they mean, don’t just memorize the table!

CSci 2011


Precedence of operators

Precedence of operators

  • Just as in algebra, operators have precedence

    • 4+3*2 = 4+(3*2), not (4+3)*2

  • Precedence order (from highest to lowest):

    ¬   → ↔

    • The first three are the most important

  • This means that p  q  ¬r→s↔tyields: (p  (q  (¬r)) →s) ↔ (t)

  • Not is always performed before any other operation

CSci 2011


Translating english sentences

Translating English Sentences

  • Question 7 from Rosen, p. 17

    • p = “It is below freezing”

    • q = “It is snowing”

  • It is below freezing and it is snowing

  • It is below freezing but not snowing

  • It is not below freezing and it is not snowing

  • It is either snowing or below freezing (or both)

  • If it is below freezing, it is also snowing

  • It is either below freezing or it is snowing, but it is not snowing if it is below freezing

  • That it is below freezing is necessary and

    sufficient for it to be snowing

pq

p¬q

¬p¬q

pq

p→q

((pq)¬(pq))(p→¬q)

p↔q

CSci 2011


Translation example 2

Translation Example 2

  • Heard on the radio:

    • A study showed that there was a correlation between the more children ate dinners with their families and lower rate of substance abuse by those children

    • Announcer conclusions:

      • If children eat more meals with their family, they will have lower substance abuse

      • If they have a higher substance abuse rate, then they did not eat more meals with their family

CSci 2011


Translation example 3

Translation Example 3

  • “I have neither given nor received help on this exam”

  • Let p = “I have given help on this exam”

  • Let q = “I have received help on this exam”

  • ¬p¬q

CSci 2011


Translation example 4

Translation Example 4

  • You can access the Internet from campus only if you are a computer science major or you are not a freshman.

  • a  (c  f)

  • You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.

  • (f  s)  r

  • r  ( f  s)

CSci 2011


Boolean searches

Boolean Searches

(2011 OR 5471) AND yongdae AND “computer science”

  • Note that Google requires you to capitalize Boolean operators

  • Google defaults to AND; many others do not

CSci 2011


Bit operations

Bit Operations

  • Boolean values can be represented as 1 (true) and 0 (false)

  • A bit string is a series of Boolean values. Length of the string is the number of bits.

    • 10110100 is eight Boolean values in one string

  • We can then do operations on these Boolean strings

    • Each column is its ownBoolean operation

01011010

10110100

11101110

CSci 2011


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