Computer Science 70 - Discrete Mathematics and Probability Theory - Spring 2011
Time and Location
Announcements
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.