CS 174
Combinatorics and Discrete Probability

Announcements

• Announcements will be put on the piazza website: piazza.com

Topics

• Random variables, mean, variance
• Tail bounds: Markov, Chebyshev, Chernoff/Hoeffding
• Balls, bins and permutations
• Random graphs
• The probabilistic method
• The Lovasz local lemma
• Markov chains
• Entropy, information and coding
• Markov chain Monte Carlo
• Coupling
• Martingales

Prerequisites

• An upper division course on algorithms (CS 170 or equivalent).
• A course on discrete mathematics including basic probability (CS 70, Math 55 or equivalent).

Required Text

• Michael Mitzenmacher and Eli Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis, Cambridge University Press, 2005.
  See here for errata in the first and second printing of the book.

Reading Assignments

• [Jan 23]: Mitzenmacher and Upfal (MU) Sections 1.1 and 1.2
• [Jan 28]: Mitzenmacher and Upfal (MU) Sections 1.3 and 1.4
• [Jan 30]: Mitzenmacher and Upfal (MU) Sections 1.4, 2.1 and 2.2
• [Feb 2]: Mitzenmacher and Upfal (MU) Sections 2.3, 2.4 and 2.5
• [Feb 4]: Mitzenmacher and Upfal (MU) Sections 3.1, 3.2 and 3.3
• [Feb 6]: Mitzenmacher and Upfal (MU) Sections 3.2 and 3.3
• [Feb 9]: Mitzenmacher and Upfal (MU) Sections 3.3 and 3.4
• [Feb 11]: Mitzenmacher and Upfal (MU) Section 3.4
• [Feb 13]: Mitzenmacher and Upfal (MU) Sections 4.1 and 4.2
• [Feb 18]: Mitzenmacher and Upfal (MU) Sections 4.2 and 4.3
• [Feb 20]: Mitzenmacher and Upfal (MU) Sections 4.3 and 4.4
• [Feb 23]: Mitzenmacher and Upfal (MU) Sections 5.1, 5.2 and 5.3
• [Feb 25]: Mitzenmacher and Upfal (MU) Section 5.3
• [Feb 27]: Mitzenmacher and Upfal (MU) Section 5.4
• [Mar 2]: Mitzenmacher and Upfal (MU) Section 5.4
• [Mar 4]: Mitzenmacher and Upfal (MU) Section 5.5
• [Mar 6]: Mitzenmacher and Upfal (MU) Section 6.1, 6.2 and 6.3
• [Mar 9]: Mitzenmacher and Upfal (MU) Section 6.3
• [Mar 11]: Mitzenmacher and Upfal (MU) Section 6.4
• [Mar 13]: Mitzenmacher and Upfal (MU) Sections 6.5 and 6.6
• [Mar 18]: Mitzenmacher and Upfal (MU) Sections 6.6 and 6.7
• [Mar 20]: Mitzenmacher and Upfal (MU) Section 6.7
• [Mar 30]: Mitzenmacher and Upfal (MU) Sections 12.1, 12.2 and 12.3
• [Apr 1]: Mitzenmacher and Upfal (MU) Sections 12.2 and 12.3
• [Apr 3]: Mitzenmacher and Upfal (MU) Sections 12.4 and 12.5
• [Apr 6]: Mitzenmacher and Upfal (MU) Sections 7.1 and 7.2
• [Apr 8]: Mitzenmacher and Upfal (MU) Sections 7.2, 7.3 and 7.4
• [Apr 10]: Mitzenmacher and Upfal (MU) Sections 10.1
• [Apr 13]: Mitzenmacher and Upfal (MU) Sections 10.2 and 10.3
• [Apr 15]: Mitzenmacher and Upfal (MU) Sections 10.3 and 10.4
• [Apr 17]: Mitzenmacher and Upfal (MU) Sections 10.3 and 10.4
• [Apr 20]: Mitzenmacher and Upfal (MU) Section 11.1
• [Apr 22]: Mitzenmacher and Upfal (MU) Sections 11.1 and 11.2
• [Apr 27]: Mitzenmacher and Upfal (MU) Sections 11.2 and 11.4
• [Apr 29]: Mitzenmacher and Upfal (MU) Section 11.3
• [May 1]: Mitzenmacher and Upfal (MU) Section 11.5

Homeworks, Exams and Grading

• There will be weekly homeworks. Homeworks will be passed out on Fridays and due the following Friday at noon, by uploading to the bCourse website. Homeworks must be turned in on time to receive credit.
• There will be one midterm exam and a final exam.
• The homeworks will count for 35% of the grade, the midterm will count for 20% and the final exam will count for 45% of the grade.
• 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 one of the TAs 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.

Academic Dishonesty

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 constitutes cheating. Any student found to be cheating risks automatically failing the class and being referred to the Office of Student Conduct.

Staff Office Hours and Locations

• Professor: Michael Jordan (jordan@cs.berkeley.edu)
  Weds 2:00-3:00 and Fri 2:00-3:00 in 427 Evans
  

• GSIs: Ahmed El Alaoui (elalaoui@berkeley.edu) and Robert Nishihara (robertnishihara@gmail.com)
  Mon 10-11am in 611 Soda
  Mon 11-12pm in 411 Soda
  Tue 11-12pm in 411 Soda
  Tue 1-2pm in 651 Soda
  

Some Helpful Hints

The following tips are offered based on our experience with Upper Division classes in CS Theory. If you follow these guidelines, you will make life much easier for yourself in this class.


• 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.
• Take the homeworks seriously! The homeworks are explicitly designed to help you to learn the material as you go along. There is usually a strong correlation between homework scores and final grades in the class. 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.
• Use Piazza! If you have a straightforward clarification question, your best option is to post a message to Piazza. There is a good chance that this will be answered by your classmates or one of the TAs or the instructor, very quickly. Please do not post any solutions or obvious hints to the homework questions on Piazza.
• 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. The better prepared you are for the discussion, the more you are likely to get out of it.
• Make use of office hours! The instructor and TAs hold office hours expressly to help you. 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!)