Computer Science 70 - Discrete Mathematics and Probability Theory - Spring 2011

Time and Location

  • MWF 10-11 in 10 Evans
  • The first class meeting will be lecture on Wednesday Jan 19. There will be no sections on Tuesday Jan 18.
  • Announcements

  • (May 1) This week Terry Filiba will be holding office hours on Wednesday right after the review session, from 10am-12pm in 711 Soda Hall, instead of her usual Monday and Wednesday office hours.
  • (Apr 29) There will be 3 (optional) review lectures during RRR week, MWF in 10 Evans from 9-10am (same room as the usual lectures, but one hour earlier). We will review the entire semester, which will also be covered by the final exam.
  • (Apr 1) Office hours today are postponed 1 hour until 12-1pm.
  • (Mar 27) A new version of Homework 9 has been posted, with a correction to Problem 6.
  • (Mar 26) There was an error in the version of Homework 9 posted 3/26, we will post a corrected version 3/27.
  • (Mar 9) Prof. Demmel's office hours today are moved to 2-3pm.
  • (Mar 8) Midterm 1 questions and answers are now posted on bspace.
  • (Mar 4) Prof. Demmel's office hours are cancelled today.
  • (Feb 26) HKN will offer a review session for Midterm 1 on Sunday, Feb 27, 3-5pm in 306 Soda Hall.
  • (Feb 23) Prof. Demmel's office hours today will be 1-2pm instead of 12-1pm.
  • (Feb 2) See below under "Homework" for a hint for Question 1 on Homework 2.
  • (Jan 31) Terry Filiba's office hours have changed, as well as the location of Fares Hedayati's office hours.
  • (Jan 30) Correction to Homework 2, Question 4, claim 1, posted Jan 30, 5:45am
  • (Jan 30) Times and locations for midterm review sessions posted below.
  • (Jan 28) Note change of office hours for Fares Hedayati.
  • (Jan 28) Podcasts (records audio) of lectures are available at webcast.berkeley.edu
  • (Jan 28) Since some students may not have access to Soda Hall in the evening to turn in homework in 283 Soda Hall, we are changing the times homework is due:
  • The first homework will be due by 8am Friday Jan 28; Soda Hall is open to everyone starting at 7:30am.
  • The second and subsequent homeworks will be due Thursdays by 6:30pm, when Soda Hall closes to the public.
  • bSpace

  • The primary website for this course is on bSpace. This webpage gives an overview of the course content and organization.
  • Overview

    The goal of this course is to introduce students to ideas and techniques from discrete mathematics and probability that are widely used in EECS. The course aims to present these ideas "in action"; each one will be geared towards a specific significant application. Thus, students will see the purpose of the techniques at the same time as learning about them. Math55 and CS70 cover overlapping material; Math55, however, typically covers a wider range of topics in less depth and with fewer applications, and is less closely tailored to EECS. L&S Computer Science majors, and EECS students admitted in Fall 2010 or later, must take CS70. Double majors in Math and EECS may take either CS70 or Math55.

    Instructor

  • Prof: Jim Demmel
  • Office hours: W 12-1 and F 11-12 (subject to change) in 564 Soda Hall ("Virginia," in the ParLab), 643-5386
  • (send email)
  • Administrative Assistants:
  • Tammy Johnson, 565 Soda Hall, 643-4816 (send email)
  • Roxana Infante, 563 Soda Hall, 643-1455 (send email)
  • Teaching Assistants and Sections

  • Nick Knight, Head GSI (responsible for enrollment questions),
  • Office Hours Th 11-1 in 751 Soda Hall
  • (send email)
  • Section 105, T 3-4, New Room starting Feb 1: 4 Evans
  • Terry Filiba
  • Office Hours M and W 11-12 in 711 Soda Hall (changed Jan 31)
  • (send email)
  • Section 101, T 10-11 and Section 102, T 11-12, both in 75 Evans
  • Fares Hedayati
  • Office Hours F 12-2 in 651 Soda Hall (note change, as of Jan 31)
  • (send email)
  • Section 103, T 12-1, in 85 Evans, and Section 104, T 1-2, in 75 Evans
  • Sayak Ray
  • Office Hours W 3-4 in 611 Soda Hall
  • (send email)
  • Section 106, T 4-5, in 3107 Etcheverry
  • Enrollment Questions

    Head GSI Nick Knight is responsible for implementing enrollment changes. If you want to switch to another discussion section, you must first contact the GSI for the section you wish to switch to, to request approval. You may only switch with the approval of the GSI for the section to which you want to switch. We will not approve switches into sections that are full.

    Homework

    See the Announcements above for when homework is due. Turn in your homework in the boxes labeled "CS70" on the 2nd floor of Soda Hall. See the detailed instructions at the top of Homework 1 below on how to label and turn in your homework. Please begin your answer to each problem on a new sheet of paper, and make sure that each sheet is labeled with your name, section number, GSI name, the assignment number, the problem number, and "CS70--Spring 2011". Reason: Different problems may be graded in parallel by different readers. Warning: You risk receiving no credit, or losing points, for any homework that does not conform to the above regulations! Please take the time to write clear and concise solutions; we will not grade messy or unreadable submissions. No late homeworks will be accepted. We will drop the lowest two homework scores.
  • Homework #1, due Jan 27
  • Homework #2, due Feb 3
  • Hint for Question 1 (posted Feb 2, 3:55pm): For the induction step: Consider using a case argument, with 2 cases: m and n are either relatively prime, or they are not. If they are relatively prime, you are finished. If they are not, this means they have a common factor (not necessarily their greatest common divisor, which is what this question is trying to define!) which you can factor out, and reduce to a smaller pair of integers to which you can apply induction.
    For the base case: The base case is when m and n are relatively prime. In other words, there are infinitely pairs of (m,n) that constitute the base case. This is ok, since the algorithm handles this case immediately.
  • correction to Question 4, claim 1, posted Jan 30, 5:45am
  • Homework #3, due Feb 10
  • Homework #4, due Feb 18 (note change in due date)
  • Homework #5, due Feb 25
  • Homework #6, due Mar 4
  • Homework #7, due Mar 11
  • Homework #8, due Mar 18
  • Homework #9, due Apr 1 (no kidding)
  • correction to Question 6, posted Mar 27, 8:15am
  • Homework #10, due Apr 8
  • Homework #11, due Apr 15
  • Homework #12, due Apr 22
  • Homework #13, due Apr 29 (the last!)

  • Exams

    There will be two midterms (in the evening, not in class) and a final:
  • Midterm 1: Thursday March 3, 6-8pm in 2050 Valley Life Sciences Building (VLSB)
  • Midterm 1 questions and answers are now posted on bspace.
  • Midterm 1 will cover the material in Note 1 through Note 8.
  • Review session for Midterm 1: Monday February 28, 6-8pm in 120 Latimer
  • Review session for Midterm 1: Sunday February 27, 3-5pm in 306 Soda (organized by HKN)
  • Rules for Midterm 1:
  • Bring your student ID card.
  • This is a closed book, closed calculator, closed computer, closed network, open brain exam, but you are permitted a 1 page, double-sided set of notes, large enough to read without a magnifying glass.
  • Write all your answers on the exam. If you need scratch paper, ask for it, write your name on each sheet, and attach it when you turn it in (we have a stapler).
  • Midterm 2: Thursday April 7, 6-8pm, also in 2050 VLSB
  • Review session for Midterm 2: Monday April 4, 6-8pm in 120 Latimer
  • Review session for Midterm 2: Sunday April 3, 3-6pm in 306 Soda (organized by HKN)
  • Rules for Midterm 2 will be the same as for Midterm 1.
  • Final Exam: Tuesday, May 10, 3-6pm, 155 Dwinelle Hall
  • You are allowed 2 double-sided cheat-sheets, so 2 pieces of paper but you can write on all 4 sides. (Disregard anything we said about cheat-sheets in section/office hours - this is the correct policy).
  • There will be 3 (optional) review lectures during RRR week, MWF in 10 Evans from 9-10am (same room as the usual lectures, but one hour earlier). We will review the entire semester, which will also be covered by the final exam.

  • A makeup final will only be given for (1) unexpected circumstances beyond your control, documented by a signed note from a physician or equivalent, (2) conflict with another scheduled exam (3) a religious holiday. Contact us as soon as possible in cases (2) and (3).
    There will be no makeup midterms; instead your final exam grades will be used as described under Grading.
    You are required to a bring a student photo ID to all exams.

    Grading

    The grades will be computed as follows:
  • Homework: 20%
  • Midterms: 40%. Each midterm grade will be replaced by the maximum of the actual midterm grade and the final grade. This means that a missing midterm grade will be replaced by the final grade.
  • Final: 40%
  • Text Book

    You should purchase the course notes, Discrete Mathematics and Probability Theory at Copy Central on Hearst Ave near Euclid. We will cover most all of these notes in the order given. See below under Readings for other suggested references.

    Course Policies

    Prerequisites:

    Sophomore mathematical maturity, and programming experience equivalent to that gained in CS3 or the Advanced Placement Computer Science A course (e.g., CS 3, E 7, CS 61A). If you lack any of these prerequisites, you may only take the class with special permission from the instructor. The work in the class will be pencil-and-paper exercises.

    Readings:

    Lecture notes will be posted on bSpace on or before the day of the relevant class. For additional background and examples, it is recommended that students consult the books Discrete Mathematics and its Applications, by Kenneth Rosen (6th ed., McGraw-Hill, New York, 2007) and Introduction to Probability, by Bertsekas and Tsitsiklis (2nd ed., Athena Scientific, Massachusetts, 2002).
    Lecture Notes:
  • Lecture 1, January 19 (also read Note 1 in the class reader)
  • Lecture 2, January 21 (also read Note 2 in the class reader)
  • Lecture 3, January 24 (also read Note 2 in the class reader)
  • Lecture 4, January 26 (start reading Note 3 in the class reader)
  • Lecture 5, January 28 (finish reading Note 3 in the class reader, start Note 4)
  • Lecture 6, January 31 (continue reading Note 4)
  • Lecture 7, February 2 (continue reading Note 4)
  • Lecture 8, February 4 (Today's notes are a superset of Lecture 7, we will start where we left off last time.) (finish reading Note 4)
  • Lecture 9, February 7 (We will finish Lecture 8 - the proof of `male optimality' - and then start Lecture 9. Please read Note 5.)
  • Lecture 10, February 9 (Today's notes are a superset of Lecture 9, we will start where we left off last time. Please read Note 5.)
  • Lecture 11, February 11 (Please read Note 6.)
  • We will continue with Lecture 11 from last time.
  • Lecture 13, February 16 (Please read Note 7.)
  • We will continue with Lecture 13 from last time. (slides have been updated, Feb 18, 6:20am) (Please read Note 8.)
  • Lecture 15, February 23 (Please read Note 10; note that we are skipping Note 9).
  • February 25: continue with notes from last time
  • February 28: continue with notes from last time
  • Lecture 18, March 2 (Please read Note 11)
  • March 4: continue with notes from last time
  • Lecture 20, March 7 (Please read Note 12)
  • March 9: continue with notes from last time
  • March 11: complete notes from last time (updated), then begin Lecture 22, March 11 (Please read Note 13)
  • March 14: complete notes from last time, then begin Lecture 23, March 14 (Please read Note 14)
  • March 16: continue with notes from last time
  • March 18: continue with notes from last time
  • March 28: Lecture 26, March 28 (Please read Note 15)
  • March 30: continue with notes from last time
  • April 1: complete notes from last time, then begin Lecture 28, April 1 (Please read Note 16)
  • April 4: continue with notes from last time
  • April 6: complete notes from last time, then begin Lecture 30, April 6 (Please read Note 17, and start Note 18)
  • April 11: Lecture 32, April 11 (Please read Note 18)
  • April 13: complete notes from last time, then begin Lecture 33, April 13 (Please read Note 18)
  • April 18: complete notes from last time, then begin Lecture 35, April 18 (Please read Note 19)
  • April 20: continue with notes from last time (updated)
  • April 22: complete notes from last time, begin Lecture 38 (updated)
  • April 25: complete notes from last time (updated 4/24 at 7:15pm)
  • April 27: Lecture 39 (Please read Notes 21 and 22; we will skip Note 20)
  • April 29: complete notes from last time (and the semester!)
  • Contact Information:

    The instructor and GSIs will post announcements, clarifications, hints, etc. on bSpace. Hence you must check bSpace frequently throughout the semester. If you have a question, your best option is to post a message to the Forum on bspace. The staff (instructor and GSIs) will check the forum regularly, and if you use the forum, other students will be able to help you too. When using the forum, please avoid off-topic discussions, and please do not post answers to homework questions before the homework is due. For informal discussions with other students, you are also welcomed to use the chat room on bspace. The chat room will NOT be monitored on a regular basis by the staff.

    If your question is personal or not of interest to other students, you may send email to cs70@inst.eecs. Email to this address is forwarded to the instructor and all GSIs. We prefer that you use this address, rather than directly emailing the instructor and/or your GSI, as it will usually get a faster response and also helps to ensure consistency in our treatment of students. 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 any 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 a class this large, 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 no more than 3 people; however, you must always write up the solutions on your own, and you must never read or copy the solutions of other students. Please write the names of your collaborators on your homework. Similarly, you may use books or online resources to help solve homework problems, but you must always 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 your section GSI 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.

    Discussion sections

    If you want to switch to another discussion section, you must first contact the GSI for the section you wish to switch to, to request approval. You may only switch with the approval of the GSI for the section to which you want to switch. We will not approve switches into sections that are full.

    Helpful Hints

    The following tips are offered based on our experience with undergraduate classes in CS Theory. If you follow these guidelines, you will make life much easier for yourself in this class.
    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 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 GSIs 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 are not constrained just to use the office hours of your section GSI). 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 (no more than 3 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.