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CS55 - Spring 2004
TR 9:35-11 in Andrew 257
Prof. Chen

1/2/2005: I've archived all of the notes and problem sets 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.

News

Please check here regularly for general announcements
  • 04-05-03: Here are the questions that people submitted for problem 6 of problem set 12: <pdf>.
  • 04-04-27: If you were not in lecture today and are planning on doing problem set 12, you need to choose a topic for problem 6. The remaining topics are:
  • proof techniques (not including induction)
  • compression
  • RSA
  • error correction
  • If you want to do one of these topics, you must send me email telling me this so that I can remove it from the list of available topics.
  • 04-04-06: I'm giving anyone who wants it an extension until Thursday morning (9:30) on problem set 9.
  • 04-03-11: A modified version of problem set 7 (due the Tuesday after spring break) has been posted.
  • 04-02-22: Just a reminder that the first midterm is this coming Tuesday, from 9:30 until 11AM. You are allowed 1 double-sided 8.5x11" sheet of notes, which must be in your own handwriting.
  • 04-02-17: Either I or a grutor will be around the 2nd floor of Andrew Monday evenings from 7-8PM.
  • 04-02-12: Problem set 4 has been modified so that problems 15-17 are optional. However there are now new problems 18 and 19:
  • 18: Problem 18 on page 279 of the textbook
  • 19: Problem 22 on page 279 of the textbook
  • An updated version has been posted below.
  • 04-02-10: The second midterm has been moved to Thursday, April 8th. (The administrivia had it originally scheduled for Tuesday, April 6th.)
  • 04-02-03: The version of problem set 3 that I handed out in class has an option in the coding problem that suggests breaking up a string into "8 bit chunks for encoding (and 12 bit chunks for decoding)". That should be "11 bit chunks" and "15 bit chunks", following the preceeding description of the problem. The version on the web site is correct.
  • 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.

    CS55 satisfies the PAC 3 requirement.

    The spring 2004 version of CS55 meets on Tuesday and Thursdays from 9:35-10:50AM in Andrew 257.

  • Administrivia <pdf>
  • Tentative Syllabus: <pdf>
  • Lectures and Labs

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

    Week Tuesday Thursday
    1/19 Introduction, motivation, background
    Sets, direct proofs
    1/26 Direct proofs, functions, relations
    Relations, computer representations
    2/2 Working with data (I) - error detection/correction
    Counting
    2/9 Counting and discrete probability
    Discrete probability (basic, conditional)
    2/16 Discrete probability (Bayes, expected values)
    Discrete probability (expected values), Review
    2/23 *** Midterm I ***
    Working with data (II) - compression
    3/1 Introduction to logic
    (tutoring session run by TA)
    3/8 Logic
    Basic number theory and proof techniques
    3/15 No class - spring break
    No class - spring break
    3/22 More number theory and proof techniques
    Even more number theory and proof techniques
    3/29 Induction
    Induction, proof writing
    4/5 Working with data (III) - cryptography
    *** Midterm II ***
    4/12 Asymptotics, algorithms, and recurrence relations
    Recurrence relations and an introduction to graphs
    4/19 Lots of graph terminology
    Euler circuits, Hamilton cycles, NP
    4/26 NP, planar graphs, chromatic number
    graphs in the "real world"
    5/3 wrap-up, evaluations
    No class - end of semester

    The comprehensive final exam is at 9AM on Monday, May 10.

    Problem Sets

    Because some of the problems are variations of ones from on-line sources, I've chosen to not always put complete citations on the problem sets themselves (to hopefully make looking up the solution less tempting). However, they will be either on the solution sets or available from me after the relevant due date.

  • Problem Set 1, due 9:35AM on 1/27. <pdf>
  • Problem Set 2, due 9:35AM on 2/3. <pdf>
  • Problem Set 3, due 9:35AM on 2/10. <pdf>
  • Problem Set 4, due 9:35AM on 2/17. Revised: <pdf> (original <pdf>)
  • Problem Set 5, due 9:35AM on 3/2. <pdf>
  • Problem Set 6, due 9:35AM on 3/9. <pdf>
  • Problem Set 7, due 9:35AM on 3/23. Revised: <pdf> (original <pdf>)
  • Problem Set 8, due 9:35AM on 3/30. <pdf>
  • Problem Set 9, due 9:35AM on 4/6. <pdf>
  • Problem Set 10, due 9:35AM on 4/20. <pdf>
  • Problem Set 11, due 9:35AM on 4/27. <pdf>
  • Problem Set 12, due 9:35AM on 5/4. <pdf>
  • See 04-04-27 note above.
  • Links

  • Official page for the textbook. Note the list of errata.

  • MathWorld: collection of information related to mathematics
  • Cut The Knot: mathematics miscellany and puzzles

  • --Laurent Gasser