| Topic | Readings | |
| 1/16 | Introduction; events & probability |
MU Sections 1.1-1.2 |
| 1/18 | Verifying matrix multiplication; Karger's algorithm |
MU Sections 1.3-1.4 |
| 1/23 | Random variables and expectation |
MU Section 2.1 |
| 1/25 | Binomial and geometric distributions; coupon collecting; Quicksort |
MU Sections 2.2, 2.4-5 |
| 1/30 | Branching processes; conditional expectation; Markov's inequality; variance |
MU Sections 2.3, 3.1-2 |
| 2/1 | Chebyshev's inequality; random sampling; randomized algorithm for median finding |
MU Sections 3.3-4 |
| 2/6 | Randomized median finding (cont.) |
MU Section 3.4 |
| 2/8 | Chernoff bounds; set balancing |
MU Sections 4.2-4 |
| 2/13 | Proof of Chernoff bounds; randomized routing |
MU Sections 4.2, 4.5 |
| 2/15 | Randomized routing; birthday problem |
MU Sections 4.5, 5.1 |
| 2/20 | Birthday problem; Poisson distribution and rare events |
MU Sections 5.1-5.3 |
| 2/22 | Poisson approximation for balls & bins; maximum load |
MU Section 5.4 |
| 2/27 | Review Session (Hoeteck) |
Sample Midterm 1 |
| 3/1 | Hashing; Bloom filters |
MU Section 5.5 |
| 3/6 | Random graphs; connectivity; probabilistic method |
MU Sections 5.6.1, 6.1 |
| 3/8 | Probabilistic method; method of conditional expectations |
MU Sections 6.2, 6.3 |
| 3/13 | More on the probabilistic method; thresholds in random graphs |
MU Section 6.4, 6.5 |
| 3/15 | Property testing (Hoeteck) |
Pages 1-3 of this survey.
|
| 3/20 | Pairwise independence |
MU Sections 13.1-2
|
| 3/22 | Universal hash functions |
MU Section 13.3
|
| 4/3 | The power of two choices (Hoeteck) |
These notes.
|
| 4/5 | Markov chains; 2-SAT |
MU Section 7.1
|
| 4/10 | Markov chains: gambler's ruin, stationary distributions, fundamental theorem |
MU Sections 7.2-3
|
| 4/12 | Markov chains: examples; card shuffling, random walks, simple queue, cover time |
MU Sections 7.3-4
|
| 4/17 | Review Session (Hoeteck) |
Sample Midterm 2
|
| 4/19 | Markov chain Monte Carlo; Metropolis algorithm |
MU Sections 10.3 (no details), 10.4
|
| 4/24 | Mixing time; coupling |
MU Sections 11.1-2 (omit 11.2.3)
|
| 4/26 | No lecture (faculty retreat) |
|
| 5/1 | Sampling graph colorings; analysis of riffle shuffle |
MU Section 11.5
|
| 5/3 | Fingerprinting, pattern matching |
These notes.
|
| 5/8 | Primality testing |
These notes.
|
If you have a straightforward clarification question, your best option is to post a message to the newsgroup. We will check the newsgroup regularly, and if you use the newsgroup, other students will be able to help you too. When using the newsgroup, please avoid off-topic discussions, and please do not post answers to homework questions before the homework is due.
If your question is personal or not of interest to other students, you may send email to cs174@cory.eecs. Email to this address is forwarded to the instructor and the TA. We prefer that you use this address, rather than directly emailing the instructor and/or your TA. If you wish to talk with one of us individually, you are welcome to come to our office hours. If the office hours are not convenient, you may make an appointment with either of us by email. Please reserve email for the questions you can't get answered in office hours, in discussion sections, or through the newsgroup.
In any class, it can be challenging for the instructor to
gauge how smoothly the class is going. We always welcome any feedback
on what we could be doing better. If you would like to send anonymous
comments or criticisms, please feel free to use an anonymous remailer
like this
one to avoid revealing your identity.
Collaboration: You are encouraged to work on homework problems in study
groups of two to four people; however, you must write up the solutions
on your own, and you must never read or copy the solutions of other students.
Similarly, you may use books or online resources to help solve homework problems,
but you must credit all such sources in your writeup and you must
never copy material verbatim.
Warning: Your attention is drawn to the Department's
Policy on Academic Dishonesty.
In particular, you should be aware that
copying solutions, in whole or in part, from other
students in the class or any other source without acknowledgment
constitutes cheating. Any student found to be cheating risks automatically
failing the class and being referred to the Office of Student Conduct.
Regrading Policies:
Regrading of homeworks or exams will only be undertaken in cases where
you believe there has been a genuine error or misunderstanding.
Bear in mind that our primary aim in grading is consistency, so that
all students are treated the same; for this reason, we will not adjust
the score of one student on an issue of partial credit unless the score
allocated clearly deviates from the grading policy we adopted for that
problem. If you wish to request a regrading of a homework or exam, you
must return it to the instructor or the TA with a written note on a separate piece
of paper explaining the problem. The entire assignment may be regraded,
so be sure to check the solutions to confirm that your overall score will
go up after regrading. All such requests must be received within one
week from the date on which the homework or exam was made available for
return.
1. Don't fall behind! In a conceptual class such as this, it is particularly important to maintain a steady effort throughout the semester, rather than hope to cram just before homework deadlines or exams. This is because it takes time and practice for the ideas to sink in. Make sure you allocate a sufficient number of hours every week to the class, including enough time for reading and understanding the material as well as for doing assignments. (As a rough guide, you should expect to do at least one hour of reading and two hours of problem solving for each hour of lecture.) Even though this class does not have any major projects, you should plan to spend as much time on it as on any of your other Upper Division technical classes.
2. Take the homeworks seriously! The homeworks are explicitly designed to help you to learn the material as you go along. Although the numerical weight of the homeworks is not huge, there is usually a strong correlation between homework scores and final grades in the class. Also, regardless of how well you did on the homework, read the sample solutions, even for the problems you got right. You may well learn a different way of looking at the problem, and you may also benefit from emulating the style of the solutions. (In science people learn a lot from emulating the approach of more experienced scientists.)
3. Make use of office hours! The instructor and TA hold office hours expressly to help you. It is often surprising how many students do not take advantage of this service. You are free to attend as many office hours as you wish. You will also likely get more out of an office hour if you have spent a little time in advance thinking about the questions you have, and formulating them precisely. (In fact, this process can often lead you to a solution yourself!)
4. Take part in discussion sections! Discussion sections are not auxiliary lectures. They are an opportunity for interactive learning, through guided group problem solving and other activities. The success of a discussion section depends largely on the willingness of students to participate actively in it. As with office hours, the better prepared you are for the discussion, the more you are likely to get out of it.
5. Form study groups! As stated above, you are encouraged to form small groups (two to four people) to work together on homeworks and on understanding the class material on a regular basis. In addition to being fun, this can save you a lot of time by generating ideas quickly and preventing you from getting hung up on some point or other. Of course, it is your responsibility to ensure that you contribute actively to the group; passive listening will likely not help you much. And recall the caveat above that you must write up your solutions on your own.