The Department of Computer Science & Engineering |
CSE 191:
DISCRETE STRUCTURES Spring 2009 |
http://www.cse.buffalo.edu/~rapaport/191/S09/syl.html
Last Update: 27 April 2009
Note: or material is highlighted |
This course covers various topics in "discrete" (as opposed to "continuous") mathematics.
The differential and integral calculus that you study in MTH 141-142 covers "continuous" mathematical topics in the sense that it analyzes data whose values can be real numbers. The real-number line has no gaps in it.
On the other hand, this course covers "discrete" mathematical topics in the sense that it analyzes data whose values are "separated", like the integers. The integer number line has gaps.
(Compare an analog clockone with handswith a digital clock: With the former, every point on the circle that is the "face" of the clock represents a time that one of the clock's hands can point tothere are no gaps. With the latter, not every time between any two times is represented (e.g., there's no time between 11:50 and 11:51). Analog clocks are "continuous"; digital clocks are "discrete".)
This course provides some of the mathematical foundations and skills that you will need in your further study of computer science and engineering. The central concept of computer science is that of an algorithm. Algorithms are discrete-mathematical objects. To understand an algorithm, you need to appreciate that it is a formal mathematical entity, not a program in a particular language; it is based on the discrete-mathematical notion of recursion. To design an algorithm, you need to know logic, set theory, relations, functions, graph theory, and other discrete structures. To verify that an algorithm works correctly, you need mathematical rigor and good proof techniquesin particular, mathematical induction. These are the areas covered by this course.
We will begin with a study of logic (propositional and first-order predicate logics), a subject which is at the foundation of mathematics and computer science. Logic can be considered as what AI researchers call a language for knowledge representation and reasoning. As a language, it enables us to talk precisely about anything in mathematics, just as a programming language enables us to talk precisely about computational procedures.
But we need objects to talk about. We will see that we can represent any mathematical or computational object in terms of a single data type: sets (along with their members and the set-membership relation [∈] between them); so, we will study set theory.
Then we'll use the language of logic and the set data-type to investigate relations among objects, including recursive relations (which are at the heart of computer science), as well as investigating functions (which are a special kind of relation)and computable functions are what computer science is all about.
Finally, we'll use logic, set theory, and relations to discuss graphs and trees, yet another very general and useful data type.
CSE 113 or 115 or permission of the instructor.
No programming will be
required, but you will be expected to understand various high-level
programming-language algorithmic
techniques,
structures, and terminology from an introductory computer-science or
programming course.
Teaching Assistants:
Recitations will begin meeting the week of January 19.
which is supposed to be packaged together with:
Grossman, Jerrold (2007),
Student Solutions Guide to Accompany Discrete Mathematics and
Its Applications, 6th Edition
(New York: McGraw-Hill);
combined ISBN = 0073503177.
Note:
I have adjusted some of the dates and assignments below to reflect what
we actually did in class, rather than on what I had planned or hoped to do:-)
1st meeting of
Last drop/add day
Propositional Equivs (cont'd);
Announce Mid-Term Exam!
Last R Day
"You can lead a horse to water, but you can't make him drink."
American Proverb
"You can lead a horse to water, but you must convince him it is water
before there is any chance he will drink." Albert Goldfain
"Education is not filling a bucket, but lighting a fire"
William Butler Yeats
"Reading is to the mind what exercise is to the body."
Sir Richard Steele
Therefore...
"The more you read, the more intelligent you are. It's really that
simple."
Ethan Hawke
But...
"To read critically is to read skeptically. The reader [should] ask...not only,
'Do I understand what this means?' but 'Do I buy it?' "
Kenneth S. Goodman
If you try to hand yours in after they have been collected
(e.g., at the end of lecture, in my mailbox, in the
TA's mailbox, etc.), it will not be accepted. To
repeat:
This is so that the HW can be discussed in the class period when
it is due.
at the top right-hand side of each page.
Announcements may also be posted to the course website or the class
email list.
You will automatically be placed on the UBLearns email list for the course.
I will use this list as my main means of
communicating with you out of class.
And you can use it to communicate with the rest of us.
You may send questions and comments
that are of general interest to the entire class using the UBLearns
email list.
You can also send email just to me, at:
Be sure to send your mail from your buffalo.edu account and
to fill in the subject line, beginning with
"CSE 191",
so that my mailer doesn't think that it's spam.
If you send email just to me that I deem to be of general interest, I will
feel
free to remail it to the email list along with my reply
unless you explicitly tell me that you want to remain anonymous,
in which case I may choose to remail it to the email list preserving
your anonymity.
The emails will be
archived at
http://www.cse.buffalo.edu/~rapaport/191/S09/EMAIL/.
For information on my philosophy of grading, see my web document on "How I Grade"
For more information on Incomplete policies, see the Undergraduate
Catalog
"Explanation of Grades" (scroll down to "Incomplete
Grades"). Note that my policy on when a grade of Incomplete must be
completed differs from the University policy!
Although it is acceptable to discuss general
approaches with your fellow students, the work you turn in must be your
own.
It is the policy of this department that any violation of
academic integrity will
result in an F for the course, that all departmental
financial support including teaching
assistantships, research assistantships, or scholarships
be
terminated, that notification of this
action be placed in the student's confidential
departmental record, and that the student be
permanently ineligible for future departmental financial
support.
If you need help doing the assignments, see your TA or Prof. Rapaport.
Please be sure to read the
UB webpage
and the
CSE webpages
which spells out all the
details of this, and related, policies.
For some hints on how to avoid
plagiarism when writing essays for courses, see my website
"Plagiarism".
Professor:
Dr. William J. Rapaport,
214 Bell Hall,
645-3180 x 112,
rapaport@cse.buffalo.edu
Office Hours:
Mondays, 3:00-3:50 p.m.;
Tuesdays, 10:00-10:50 a.m.;
Fridays, 2:00-2:50 p.m.;
and by appointment.
Office Hours:
Thursdays & Fridays, 1:00-1:50 p.m.;
and by appointment.
Office Hours:
Tuesdays, 11:00-11:50 a.m.;
Wednesdays, 1:00-1:50 p.m.;
and by appointment.
CLASS
INSTR.
REG. #
DAYS
HOURS
LOCN
Lecture
Rapaport
326525
MWF
11:00-11:50 a.m.
NSC 220
Recitation R1
Evanko
387915
T
8:00-8:50 a.m.
Capen 260
Recitation R2
Evanko
309977
W
12:00 noon - 12:50 p.m.
Capen 10
Recitation R3
Chen
200557
Th
3:00-3:50 p.m.
Norton 213
DAY
MONTH
DATE
TOPICS
SUB-TOPICS
§ in Rosen
HW
M
Jan
12
DISCRETE MATH
Intro. to course;
What is discrete math?pp. xx-xxii
HW #1 assigned
W
14
LOGIC
What is discrete math? (cont'd);
Propositional Logic1.1
F
16
Propositional Logic (cont'd)
1.1-1.2
M
19
No class:
Martin Luther King Day
T
20
1st meeting of
Recitation R1
W
21
Propositional Logic (cont'd);
Propositional Equivalences
Recitation R2
1.1-1.2
HW #1 due
HW #2 assigned
Th
22
1st meeting of
Recitation R3
F
23
Propositional Equivalences (cont'd)
1.2
M
26
HOW TO STUDY MATH;
Predicates & Quantifiers
1.2-1.3
W
28
Preds & Qfrs (cont'd)
1.3
HW #2 due
HW #3 assigned
F
30
Preds & Qfrs (cont'd)
1.3
M
Feb
2
Nested Qfrs;
Peano's Axioms for Arithmetic
1.4;
p.A-5
W
4
Peano's axioms (cont'd);
Rules of Inf
p.A-5;
1.5
HW #3 due;
HW #4 assigned
F
6
Rules of Inference (cont'd);
Proofs
1.5-1.6
M
9
Rules of Inf & Pfs (cont'd)
1.5-1.6
W
11
Rules of Inf & Pfs (cont'd)
1.5-1.6
F
13
Pfs (cont'd)
1.6-1.7
HW #4 due TODAY!;
HW #5 assigned
M
16
Pfs (cont'd)
1.7
W
18
Pfs (cont'd)
1.7
F
20
Pfs (cont'd)
1.7
HW #5 due;
Virtual HW #6 assigned
M
23
Pfs (cont'd)
1.7
W
25
SET THEORY
Sets
2.1
F
27
Sets (cont'd);
Set Opns
2.1-2.2
HW #6 answers will be posted
M
Mar
2!
Review for Mid-Term Exam
W
4
MID-TERM EXAM
(will cover §§1.1-1.7)
clock
F
6
Review of Mid-Term Exam
+ mid-semester course evaluation
M-F
9-13
Spring Break
M
16
Set operations
2.2
HW #7 assigned (!)
W
18
FUNCTIONS
Set Opns (cont'd);
Functions
2.2-
2.3
F
20
Functions (cont'd)
2.3
HW #7 due;
HW #8 assigned
M
23
Functions (cont'd)
2.3
W
25
RECURSION
Functions (cont'd);
Sequences;
Mathematical Induction;
2.3-
2.4;
4.1
F
27
Math Ind'n (cont'd)
4.1
HW #8 due;
HW #9 assigned
M
30
Math. Ind'n (cont'd)
4.1
W
Apr
1
Recursive Definitions
4.3
F
3
Rec. Defs (cont'd)
4.3
HW #9 due;
HW #10 assigned
M
6
Structural Induction;
Recurrence Relations
4.3;
7.1
W
8
Recurrence rel'ns (cont'd)
7.1-7.2
F
10
Recurrence relns (cont'd)
7.2
HW #10 due;
HW #11 assigned
M
13
RELATIONS
Relations;
n-ry Relns;
8.1;
8.2
W
15
GRAPH THEORY
Equivalence Relns;
Representing Relns
8.5;
8.3
F
17
Rep'g Relns (cont'd);
Graphs:
basic defs;
Euler paths & circuits
8.3;
9.1
§9.5 to p.640
HW #11 due;
HW #12 assignedM
20
Graphs (cont'd):
Traveling Salesman Problem;
Planar Graphs & Euler's formula;
4 Color Thm
§9.6, esp. pp.653-655;
§9.7 to p.663;
§9.8
W
22
Trees:
basic defs;
rooted trees;
|E|=|V|–1
10.1
F
24
Tree traversal algorithms
10.3
HW #12 due;
Virtual HW #13 assigned
M
27
Last Class:
Summary &
Review
T-W
28-29
Reading Days
Th
30
FINAL EXAM:
11:45 a.m. - 2:45 p.m.
Knox 109
"Teachers open the door, but you must enter by yourself."
Chinese Proverb
Consequently, in lectures, I will only be able to
skim the surface of the issues.
But I will assign a lot of reading,
which I will expect you all to do.
In
lecture, we shall only cover interesting or difficult material, plus
occasionally material that is not in the text.
You are
responsible for all material in the text and in the
lectures.
Therefore, you should try all exercises whose answers are given in the
text.
And there are 3 supplementary texts with extra exercises.
You
might want to consider forming study groups to practice solving
problems, checking each other's answers.
(However, DO NOT
CHEAT! see below.)
Taking both exams is a logically necessary condition for passing
the course.
No programming will be required.
HWs will be collected at the start of lecture on the
due date.
NO LATE HOMEWORKS WILL BE ACCEPTED
You should assume that you
will fail to turn in one HW (oversleep, get stuck in traffic,
etc.)that's the one that will be dropped.
Do your work on timethis is one course you simply cannot
cram for at the last minute, so don't even try! I cannot stress this
strongly enough.
Remember that the homeworks may be fairly
time-consuming, so please consider your other commitments, and
plan your time accordingly.
Therefore, be
sure to get a classmate's phone number or email address (for instance, 1
or 2
people sitting next to you in class, whomever they are!)
so that you will not miss
announcements in the unlikely event that you miss a class.
If you do not normally read email at the email address that
UB
has as your official address, please either do so for this course, or
else have your mail forwarded.
Recitation Assignments
(including attendance, HWs, quizzes)40% Mid-Term Exam 20% Final Exam 40% Total 100% Incompletes:
It is University policy that a grade of Incomplete
is to be given only when a small amount of work or a single exam is
missed due to circumstances beyond the student's control, and that
student is otherwise doing passing work. I will follow this policy
strictly! Thus, you should assume that I will not give
incompletes :-)
Any incompletes that I might give,
in a lapse of judgment :-),
will have to be made up by the end of the
Fall 2009