Syllabus [ PDF ]

• Prerequisites
  
  An Upper Division course on algorithms (CS170 or equivalent)
  A course on discrete mathematics including basic probability (CS70, Math55, or equivalent)
  If you found those classes hard, then you will find this course harder and you should consider carefully whether it is the right class for you. It is also assumed that you have experience with programming in a standard imperative language such as C, C++ or Java. Although most homeworks will be pencil-and-paper exercises, you may also be expected to do some small programming assignments. If you have any doubts about your background, you should come and talk to me as soon as possible.
• Course Description
  This course will provide familiarity with basic tools in discrete probability and their applications to the design and analysis of randomized algorithms and data structures. You will learn how probabilistic ideas and techniques can lead to more efficient and conceptually simpler algorithms for many problems.
• Topics Covered
  
  • Events and probability
  • Random variables, expectation, conditional expectation
  • Bernoulli, binomial, geometric distributions
  • Program Checking/Polynomial Identities
  • Coupon collector's problem
  • Variance and moments
  • Markov's inequality, Chebyshev's inequality
  • Chernoff bounds, moment generating functions
  • Routing in sparse networks
  • Balls and bins
  • The Poisson distribution, the Poisson approximation
  • Hashing, Bloom filters
  • Random Graphs
  • The probabilistic method
  • Markov chains and random walks
  • Stationary distributions, classification of states
  • The Monte Carlo method, Markov chain Monte Carlo
  • Mixing time, coupling of Markov chains
  • Graph Algorithms: Minimum cut, independent sets, Hamiltonian cycles
• Textbooks
  
  Required text:

  • Probability and Computing: Randomized Algorithms and Probabilistic Analysis, by Michael Mitzenmacher and Eli Upfal, Cambridge University Press, 2005.
    It is essential that all students have regular access to this book. Pointers to the relevant sections of the book will be provided as we go along. (See here for errata in the first printing of the book, some of which were corrected in the second printing.)
  Recommended text:
  • Randomized Algorithms, by Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press, 1995.
    

Grading

• 20% Problem Sets (The lowest two problem set scores will be dropped)
• 40% Two Midterms (20% each)
• 40% Final Exam (Thursday, December 18, 2008, 12:30-3:30PM)

All homeworks are due Tuesday in class, unless otherwise stated. Please ensure that each sheet is labeled with your name, SID number, and "CS174--Fall 2008". You risk receiving no credit for any homework submitted without this information. Please take the time to write clear and concise solutions; we will not grade messy or unreadable submissions. No late homeworks will be accepted.

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.

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.

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. 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.)

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!)

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.

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.