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CS55 - Spring 2007
MW 2:45-4:00 in Lincoln 1135
Prof. Chen

11/21/2007: I've archived all of the notes and problem sets (ie, most of the links below don't work) and am only leaving up the syllabus for reference. If you're looking for the material, you may be able to find a link to a more recent offering of the class here or here.

News

Please check here regularly for assorted announcements. You are responsible for being aware of information posted here.
  • 07-04-26: The final (2-5PM on Monday 5/7 in Lincoln 1135) will be open textbook and open notes.
  • 07-04-25: The last problem set is due by noon on Friday May 4th.
  • 07-03-28: The second midterm will be in class on Wednesday April 11th. It is open textbook and open 1 double-sided 8.5"x11" page of handwritten notes.
  • 07-02-26: A "*" under the Readings column of the syllabus indicates that some of the material is not in the textbook.
  • 07-02-18: The midterm tomorrow is open textbook and open notes, but closed other things (eg, laptop, calculator). You should feel free to bookmark pages in the textbook.
  • 07-02-12: A hint for problem 3 on problem set 4: The problem with the set S' is similar to the problem with someone saying "I always lie."
  • 07-02-12: A reminder that you should feel free to talk to each other, America, or me about problems on the homework. You should also feel free to IM/email me questions about the problem set.
  • 07-01-29: On problem set 2, problem 1(d) should say "10.4 (c,g)" instead of "10.4 (c,k)" since there's no part (k) in problem 10.4
  • Information

    CS55 is an introduction to discrete mathematics for computer scientists. In particular, we will study finite mathematical structures and ways to build them, count them, and analyze them. The topics and examples will be chosen to relate to concepts of interest in the design and analysis of computer algorithms.

    No programming experience is required (or assumed). However, precalculus mathematics and an interest in applications of math to computer science is a prerequisite.

    The lectures are on Mondays and Wednesdays from 2:45-4:00 in Lincoln 1135

    The textbook is Mathematics: A Discrete Introduction, 2nd Edition by Scheinerman. The link takes you to the Amazon page, but the book should also be available at Huntley bookstore.

  • Administrivia <pdf>
  • Lectures

    Any topic that's listed for a date in the future should be taken as tentative. Any topic that's listed for a date at least 2 days in the past is what was actually covered in that lecture.

    Week Date In class Readings Assignments due
    1 (Wed) 1/17 introduction/motivation/background
    administrivia
    sample.tex, sample.pdf
    section 1
    2 (Mon) 1/22 basic concepts/definitions
    basic proof techniques
    2-5 ps1a
    (Wed) 1/24 boolean algebra
    knights and knaves, circuits
    6, * ps1b
    3 (Mon) 1/29 SR latch
    working with quantifiers
    basic counting principles
    7-8, 10, *
    (Wed) 1/31 sets
    combinatorial proofs
    9, 11-12 ps2
    4 (Mon) 2/5 relations, equivalence relations
    partitions
    13-15
    (Wed) 2/7 binomial coefficients
    multisets
    15-16 ps3
    5 (Mon) 2/12 even more counting
    more proof techniques
    17-19
    (Wed) 2/14 proof techniques
    review for midterm
    19 ps4
    6 (Mon) 2/19
    Midterm 1
    (Wed) 2/21 induction
    recurrence relations
    20-22
    7 (Mon) 2/26 more on induction and recurrences
    functions
    21, 23, * ps5 - part 1
    (Wed) 2/28 composing functions
    counting infinite sets, diagonalization
    algorithms
    25, *
    8 (Mon) 3/5 asymptotics
    guess-and-check
    28, * ps5 - part 2
    (Wed) 3/7 master method
    games
    *
    9 (Mon) 3/12
    *** No class - Spring Break ***
    (Wed) 3/14
    10 (Mon) 3/19 basic probability 29-30
    (Wed) 3/21 conditional probability
    random variables
    31-32 ps6
    11 (Mon) 3/26 expected value
    introduction to compression
    33, *
    (Wed) 3/28 a little more on compression
    introduction to number theory
    *, 34 ps7
    12 (Mon) 4/2 a little more number theory 35-36
    (Wed) 4/3 introduction to graphs 46-47 ps8
    13 (Mon) 4/9 review for midterm
    (Wed) 4/11
    Midterm 2
    14 (Mon) 4/16 graphs: representations,
    connectivity, Euler circuits
    *, 48, 50
    (Wed) 4/18 graphs: Hamiltonian cycles
    planarity
    *, 52 ps9
    15 (Mon) 4/23 trees, weighted graphs,
    MSTs
    49, *
    (Wed) 4/25 graph traversals * ps10
    16 (Mon) 4/30 applications of graphs
    course evaluations
    *
    (Wed) 5/2 review for final
    (Fri) 5/4 ps11 due by noon
    17 (Mon) 5/7
    Final exam at 2PM

    Problem Sets

  • ps1a, due 2:45PM on 1/22 <tex><pdf>
  • ps1b, due 2:45PM on 1/24 <tex><pdf>
  • ps2, due 2:45PM on 1/31 <tex><pdf>
  • ps3, due 2:45PM on 2/7 <tex><pdf>
  • ps4, due 2:45PM on 2/14 <tex><pdf>
  • ps5 (counting triangles) <tex><pdf>:
  • part 1 due 2:45PM on 2/26
  • part 2 due 2:45PM on 3/5
  • ps6, due 2:45PM on 3/21 <tex><pdf>
  • ps7, due 2:45PM on 3/28 <tex><pdf>
  • ps8, due 2:45PM on 4/4 <tex><pdf>
  • ps9, due 2:45PM on 4/18 <tex><pdf>
  • ps10, due 2:45PM on 4/25 <tex><pdf>
  • ps11, due noon on 5/4 <tex><pdf>
  • Links

  • some pages discussing LaTeX, the best way to format anything containing mathematical equations.
  • A simple latex document that creates the file <sample.pdf>
  • A fast introduction to LaTeX written by Tony Roberts.
  • The Not So Short Introduction to LaTeX2e, also known as LaTeX2e in 129 minutes by Oetiker, Partl, Hyna, and Schlegl. (This is an evolving document, at the moment they're on version 4.12, dated April 2003.)

  • "Computers do not solve problems, they execute solutions"
    --Laurent Gasser