[ news |
problem sets |
CS55 - Spring 2004
TR 9:35-11 in Andrew 257
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.
Please check here regularly for general announcements
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.
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.
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.