Notice:
(1) DM course is held on Mondays and Wednesdays, 4:30 to 5:45 pm, in Wonchun Hall (11), room 509.
(2) For practical reason, the most essential information covered during our lectures is summarised in these
lecture notes. Thus, these lecture notes are true reflection of everything that was presented, discussed, or
practically exercised during our lectures. In order to run or to download any notes made available here, simply
click on the underlined part
(in green)
of the title of these notes!
(3) These lecture notes follow the course textbook [1] by Bernard Kolman, Robert C. Busby, Sharon Cutler Ross,
"Discrete Mathematical Structures",
Prentice-Hall, Inc.,
2000, ISBN 0-13-083143-3, pb.
In each subsequent lecture note, as well as in each subsequent week, another topic from this textbook is learned.
(4) For further instructions see the end of this web page.
Course Outline for Sem. 2/2007:
Course Outline (in "Word" .doc format).
Course participants during Sem. 2/2007:
Fig. #1: Here is a photograph of participants of the DM course in
semester 2, 2007. (Click on this photograph to enlarge it.)
Captured on this photo in order of the visibility of their faces,
from left to right, are as follows: RKM, WYR, JWK.
Fig. #2: Here is a photograph of DM course participants
taken together with their Professor by the front of EE Wonchun Hall
near the beginning of semester 2, 2007. (Click on this photograph
if you wish to to enlarge it.)
Captured on this photo in order of the visibility of their faces,
from left to right, are as follows: Prof., WYR, JWK, RKM.
Part 1: Lecture Notes (in "*.doc" format for the "WORD XP"):
Week 1 & lecture session 1 (Orientation. [1] Chap. 1 - Fundamentals: Sequences, Boolean Matrix Operations, Mathematical Structures.)
Week 2 & lecture session 2 ([1] Chap. 2 - Logic: Propositions and Logical Operations.)
Week 3 & lecture session 3 (Logic: Conditional Statements, Methods of Proof, Mathematical Inductions.)
An example of proof.
Week 4 & lecture session 4 ([1] Chap. 3 - Counting: Pigeonhole Principle, Recurrence Relations.)
Week 5 - Thanksgiving holiday (NO lectures.)
Week 6 & lecture session 5 ([1] Chap. 4 - Relations: Product Sets and Partitions, Relations and Digraphs.)
Week 7 & lecture session 6 (Paths in Relations and Digraphs; Properties of Relations.)
Week 8 (midterm break - no lectures): here it comes Wednesday, 17 October 2007, 4:30 to 5:45 pm - the time for your midterm exam (for details see parts 3 and 4 below)!
Week 9 & lecture session 7 (Equivalence Relations, Operations on Relations.)
Week 10 & lecture session 8 (Transitive Closure and Warshall's Algorithm; [1] Chap. 5 - Functions: Functions, Functions for Computer Science.)
Week 11 & lecture session 9 ([1] Chap. 6 - Partially Ordered Sets, Lattices.)
Week 12 & lecture session 10 (Finite Boolean Algebras with an example of applications.)
Week 13 & lecture session 11 ([1] Chap. 7 - Trees, Labelled Trees, Undirected Trees.)
Week 14 & lecture session 12 (Minimum Spanning Trees, ([1] Chap. 8) Graphs.)
Week 15 & lecture session 13 (Euler Paths/Circuits, Hamiltonian Paths/Circuits. ([1] Chap.10) Languages.)
Week 16 (final examinations break - no lectures): our final exam is on Monday, 10 December 2007, in the same venue and time as our normal classes! For sample problems see "Part 5" below.
Part 2: Lecture Presentations (in "*.ppt" format for the "Power Point"):
Notice that because of technical difficulties in writing mathematical symbols
in "Power Point", in lectures NOT listed below the lecture notes prepared in
"WORD.doc" are used for presentations instead of "Power Ponint" slides.
Week 1 & lecture session 1 (Orientation. Sequences, Boolean Matrix Operations.)
Week 2 & lecture session 2 (Mathematical Structures: Propositions/Logical Operations.)
Part 3: Preparations for the midterm exam (in WORD.DOC format for the WORD XP):
Please notice, that after 7 weeks of study this semester, a midterm exam will be held
during our normal class hours. The exact date and time of this exam is to be negotiated
and announced during our lectures (and then displayed here - tentatively decided
for Wednesday, 17 October 2007). During this exam students will be
asked to solve various problems from the area of Discrete Mathematics.
An example of exam paper and a question type is provided below (of course,
during the exam problems to solve will be different - this example shows only how
the question is to look like, what level of difficulty it is going to be, and how
it is going to be marked). The question for this midterm exam will be simlar to
one of the "midterm exam problems" provided below. If you are able to solve
each of the "midterm exam problems" provided below within the lecture time,
you should have no difficulty with passing this exam. Therefore, for your preparation
to the midterm exam, I would advice you to learn how to solve each "midterm exam problems"
listed below.
Midterm exam problems (to be solved by students as their preparation to this exam.)
Part 4: Midterm exam (in WORD.DOC format for the WORD XP):
The midterm exam will be a paper composed of selected
questions provided in the document "midterm exam problems"
from previous item. Questions may be slightly altered or have
different data than these given amongst the exam problems.
However, if one can answer the exam problems, should be
able to also answer the exam questions. There will be 1:15 hour
of time given to reply the midterm exam questions. The midterm
exam will be held in our usual class and in usual class time.
Part 5: Preparations for the final exam (in WORD.DOC format for the WORD XP):
Final exam problems (to be solved by students as their preparation for the final exam.)
Part 6: Educational humor:
Hawaiian Good Luck Sign
Four people: Everybody - Nobody
Part 7: Additional instructions (e.g. how to use this web page):
(A) Each C program (if utilised in this course) is provided here
as a source code (*.cpp), which is preperad for execution by the MS Visual
Studio, version 6.0. Many of these programs were previously working on
Borland C as well.
(B) In order to download any source code (e.g. in *.cpp, in *.c, etc.) to your computer,
simply click on this code,
and then follow the procedure of downloading source code from a web page.
(C) My office room is: 440; office tel. ext.: 1742.
(D) My e-mail contact is:
pajakjan@gmail.com.
Date of starting this web page: 27 August 2007.
Date of the latest update of this page: 30 November 2007.
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