CS 70, Fall 2003
Discrete Mathematics for Computer Science

  David Wagner (daw@cs, 765 Soda Hall, 642-2758)

  Amir Kamil (kamil@cs, 566 Soda Hall)

  Tu-Th, 3:30-5:00, 3106 Etcheverry

  101. F 9:00-10:00, 310 Soda
  102. F 10:00-11:00, 310 Soda
  Section notes are available.

Office Hours:
  Wagner: Mon 4:00-5:00, Tue 1:00-2:00 in 765 Soda.
  Kamil: Mon 3:00-4:00, Wed 2:30-4:30, at 751 Soda (alcove).


Course Overview

The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in Computer Science. 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.

Broadly speaking the material is similar to that in Math 55; however, Math 55 covers a wider range of topics in less depth and with fewer applications , and is less closely tailored to Computer Science. You should take this course as an alternative to Math 55 if you are intending to major in Computer Science and if you found the more conceptual parts of CS 61A enjoyable and relatively straightforward.

List of course topics:

Assignments and Exams

All homeworks are due on Thursday at 3:30 p.m. in the drop box labeled "CS 70" in 283 Soda. Deadlines will be enforced strictly. Late homework will be accepted only in extraordinary circumstances, and may in any case be penalized. The lowest homework grade will be dropped.


Old exams from previous semesters are available.


The following schedule is tentative and subject to change.

Topic Readings
1 August 26 Overview; intro to logic Notes [ps] [pdf].
[Rosen 1.1, 1.2]
2 August 28 Propositional logic; quantifiers [Rosen 1.3-1.5]
3September 2 Induction Notes [ps] [pdf].
[Rosen 3.3]
4September 4 Strong induction Notes [ps] [pdf].
[Rosen 3.3]
5September 9 Structural induction Notes [ps] [pdf].
[Rosen 3.4]
6September 11 Proofs about algorithms Notes [ps] [pdf].
[Rosen 3.5]
7September 16 Stable marriages External notes
8September 18 Cake cutting Notes (in outline form): [txt].
9September 23 Algebraic algorithms Notes [ps] [pdf].
[Rosen 2.1]
10September 25 Number theory (continuing from same notes as last time). [Rosen 2.4,2.5]
11September 30 Midterm review Notes (in outline form): [txt].
October 2 Midterm 1  
12October 7 Primality testing Notes [ps] [pdf].
[Rosen 2.6]
13October 9 RSA Notes [ps] [pdf]. Also [ps] [pdf] (revised 10/9). [Rosen 2.6]
14October 14 Fingerprints, ECC, Secret Sharing Notes [ps] [pdf].
15October 16 Basics of counting Notes [txt].
[Rosen 4.1-4.4]
16October 21 Basic probability Notes [ps] [pdf].
[Rosen 5.1, 5.2]
17October 23 Conditional probability Notes [ps] [pdf].
[Rosen 5.1, 5.2]
18October 28 Midterm review  
October 30 Midterm 2  
19November 4 How to lie with statisics  
20November 6 Hashing Notes [ps] [pdf].
November 11 No class!  
21November 13 Random variables, expected values Notes [ps] [pdf].
[Rosen 5.3]
22November 18 Variance Notes [ps] [pdf].
[Rosen 5.3]
23November 20 Polling Notes [ps] [pdf].
24November 25 "Bits on forehead"  
November 27 No class! Have a great Thanksgivings Day holiday!
25December 2 Countability, diagonalization, computability  
26December 4 Halting problem, Godel's theorem, P vs. NP A relevant essay [ps] [pdf]

Extra optional reading:


Unfortunately, there is no book that adequately covers all the material in this course at the right level. We will provide lecture notes for most of the lectures. The book Discrete Mathematics and its Applications, 5th Edition (Kenneth H. Rosen, McGraw-Hill, Inc., New York, 2003) is recommended.

Note that you should not view the availability of lecture notes as a substitute for attending class: our discussion in class may deviate somewhat from the written material, and you should take your own notes as well.


You must have taken CS 61A, Math 1A and Math 1B (or equivalents). If you struggled with any of these courses, you should probably take Math 55 instead of CS 70 as CS 70 is likely to be more conceptual in nature. If you are in any doubt about your preparation for the class, please come and talk to any one of us as soon as possible.

Grading Summary

Grading will be on an absolute scale. (However, the instructor reserves the right to add extra points to your grade at the end of the class, in extreme cases.)

The grading standard is available and has been fixed at the beginning of the course.

The homeworks will be graded by the course reader; depending on the time available, we reserve the right to grade some of the problems in more detail than others, and to award correspondingly more credit for them. Thus, if you turn in incomplete homeworks you are gambling on your grade.


Collaboration on homeworks is welcome and warmly encouraged. You may work in groups of at most three people; however, you must always write up the solutions on your own. Similarly, you may use references to help solve homework problems, but you must write up the solution on your own and cite your sources. You may not share written work or programs with anyone else. You may not receive help on homework assignments from students who have taken the course in previous years, and you may not review homework solutions from previous years.

You will be asked to acknowledge all help you received from others. This will not be used to penalize you, nor will it affect your grade in any way. Rather, is intended only for your own protection.

In writing up your homework you are allowed to consult any book, paper, or published material. If you do so, you are required to cite your source(s). Simply copying a proof is not sufficient; you are expected to write it up in your own words, and you must be able to explain it if you are asked to do so. Your proofs may refer to course material and to homeworks from earlier in the semester. Except for this, all results you use must be proved explicitly.

Copying solutions or code, in whole or in part, from other students or any other source without acknowledgment constitutes cheating. Any student found to be cheating in this class will automatically receive an F grade and will also be referred to the Office of Student Conduct.

We believe that most students can distinguish between helping other students and cheating. Explaining the meaning of a question, discussing a way of approaching a solution, or collaboratively exploring how to solve a problem within your group is an interaction that we encourage. On the other hand, you should never read another student's solution or partial solution, nor have it in your possession, either electronically or on paper. You should write your homework solution strictly by yourself. You must explicitly acknowledge everyone who you have worked with or who has given you any significant ideas about the homework. Not only is this good scholarly conduct, it also protects you from accusations of theft of your colleagues' ideas.

Presenting another person's work as your own constitutes cheating, whether that person is a friend, an unknown student in this class or a previous semester's class, a solution set from a previous semester of this course, or an anonymous person on the Web who happens to have solved the problem you've been asked to solve. Everything you turn in must be your own doing, and it is your responsibility to make it clear to the graders that it really is your own work. The following activities are specifically forbidden in all graded course work:

Academic dishonesty has no place in a university; it wastes our time and yours, and it is unfair to the majority of students.

In our experience, nobody begins the semester with the intention of cheating. Students who cheat do so because they fall behind gradually and then panic. Some students get into this situation because they are afraid of an unpleasant conversation with a professor if they admit to not understanding something. We would much rather deal with your misunderstanding early than deal with its consequences later. Even if you are convinced that you are the only person in the class that doesn't understand the material, and that it is entirely your fault for having fallen behind, please overcome your feeling of guilt and ask for help as soon as you need it. Remember that the other students in the class are working under similar constraints--they are taking multiple classes and are often holding down outside employment. Don't hesitate to ask us for help--helping you learn the material is what we're paid to do, after all!

Contact information

If you have a question, your best option is to post a message to the ucb.class.cs70 newsgroup. The staff (instructor and TAs) 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 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 cs70@cory.eecs.berkeley.edu. Email to cs70@cory is forwarded to the instructor and all TAs. We prefer that you use the cs70@cory address, rather than emailing directly 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 any of us by email. There are about 50 of you to every one of us, so please reserve email for the questions you can't get answered in office hours, in discussion sections, or through the newsgroup.

The instructor and TAs will post announcements, clarifications, hints, etc. to this website and to the class newsgroup. Hence you should read the newsgroup regularly whether you post questions to it or not. If you've never done this before, there is online information about how to access UCB newsgroups (see also here for more).

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 to send us email without revealing your identity, like this one.

Accounts and grading software

Some of you may already have named accounts for the lab machines from Instructional Facilities. Lab machines may be found in 2nd floor Soda. If you do not already have an instructional account, go to a Unix machine in 273 Soda and login as 'newacct' (password: 'newacct'). You should receive a 'named' account. You can also read the online instructions.

After you have obtained your account, you will need to register with our grading software. See these instructions.


In addition to office hours for the class instructors, HKN (the Eta Kappa Nu honor society) offers free drop-in tutoring every weekday 10am-4pm in 345 Soda. Contact them for more information.

Mail inquiries to cs70@cory.eecs.berkeley.edu.