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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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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

CSci 2011

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

slide15
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…

CSci 2011

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 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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