Lecture, Date | Topic | Reading | Other |
Lecture 1, Tue. Jan. 17 | Admin; course overview; testing polynomial identities | This web page; MU Section 1.1 | |
Lecture 2, Thu. Jan. 19 | Basic probability | MU Section 1.2 | Fri. Jan. 20: HW 1 out |
Lecture 3, Tue. Jan. 24 | Testing matrix multiplication; Karger's min cut algorithm; random variables & expectation | MU Sections 1.3, 1.5, 2.1 | |
Lecture 4, Thu. Jan. 26 | Random variables & expectation; binomial & geometric distributions; Quicksort | MU Sections 2.1, 2.2, 2.4, 2.5 | Fri. Jan. 25: HW 1 due; HW 2 out |
Lecture 5, Tue. Jan. 31 | Jensen's inequality; moments; Markov and Chebyshev inequalities | MU Sections 2.1.2, 3.1, 3.2, 3.3 | |
Lecture 6, Thu. Feb. 2 | Randomized algorithm for computing the median | MU Sections 3.4, 3.5 | Fri. Feb. 3: HW 2 due; HW 3 out |
Lecture 7, Tue. Feb. 7 | Moment generating functions; Chernoff bounds | MU Sections 4.1, 4.2 | |
Lecture 8, Thu. Feb. 9 | Discrepancy/Set balancing; randomized routing on the hypercube | MU Section 4.4, Supplementary Note 1 | Fri. Feb. 10: HW 3 due; HW 4 out |
Lecture 9, Tue. Feb. 14 | Finish up randomized routing; birthday problem; balls & bins | Supp. Note 1; MU Sections 5.1,5.2 | |
Lecture 10, Thu. Feb. 16 | Poisson distribution; Poisson approximation | MU Sections 5.3, 5.4 | Fri. Feb. 17: HW 4 due; HW 5 out |
Lecture 11, Tue. Feb. 21 | Random graphs; Hamilton cycles | MU Section 5.6 | |
Lecture 12, Thu. Feb. 23 | The Probabilistic Method: Ramsey numbers, crossing number | MU Section 6.1 | Fri. Feb. 24: HW5 due. [No HW next week.] |
Lecture 13, Tue. Feb. 28 | Review session (Milind) | Sample midterm | |
Lecture 14, Thu. Mar. 2 | The Probabilistic Method: MaxCut, MaxSAT, Derandomization; Thresholds in random graphs | MU Sections 6.2, 6.3, 6.4, 6.5 | [No HW next week.] |
Lecture 15, Tue. Mar. 7 | Cancelled due to midterm | ||
Lecture 16, Thu. Mar. 9 | Pairwise independent random variables: constructions and applications | MU Sections 15.1, 15.2 | Fri. Mar. 10: HW6 out |
Lecture 17, Tue. Mar. 14 | Universal hash functions; perfect hashing; heavy hitters | MU Sections 15.3, 15.4 | |
Lecture 18, Thu. Mar. 16 | Finish up heavy hitters; Markov chain basics | MU Sections 7.1, 7.2 | Fri. Mar. 17: HW6 due; HW7 out |
Lecture 19, Tue. Mar. 21 | Lecture by Milind on Sampling Functional Proteins | See weekly bulletin | |
Lecture 20, Thu. Mar. 23 | Markov chains: stationary distributions, hitting and cover times | MU Sections 7.3, 7.4 | Fri. Mar. 24: HW7 due |
Tue. Mar. 28 | Spring Break | ||
Thu. Mar. 30 | Spring Break | ||
Lecture 21, Tue. Apr. 4 | Conclude hitting & cover times; preview of the MCMC method | MU Section 7.4 | |
Lecture 22, Thu. Apr. 6 | Mixing times; coupling; card shuffling; random walk on hypercube; graph colorings | MU Sections 12.1, 12.2, 12.3, 12.5 | Fri. Apr. 7: HW8 out |
Lecture 23, Tue. Apr. 11 | The Monte Carlo method | MU Chapter 11; also Q3 on HW4 | |
Lecture 24, Thu. Apr. 13 | Martingales: Stopping times; Optional Stopping Theorem | MU Sections 13.1, 13.2, 13.3 | Fri. Apr. 14: HW8 due; HW9 out |
Lecture 25, Tue. Apr. 18 | Martingales: Azuma's inequality and large deviations | MU Section 13.4 | |
Lecture 26, Thu. Apr. 20 | Azuma's inequality: Applications | MU Section 13.5 | Fri. Apr. 21: HW9 due; HW10 out |
Lecture 27, Tue. Apr. 25 | Fingerprinting | Supplementary Note 2 | |
Lecture 28, Thu. Apr. 27 | Primality testing | Supplementary Note 3 | Fri. Apr. 28: HW10 due |
If you have a more personal question that is not of interest to other students, you should instead send email to the instructor or TA. If your question requires more extensive discussion, please come to office hours or make an appointment with one of us over email. Please reserve email for questions you can't get answered in office hours, in discussion sections, or through the Ed forum.
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.
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.