Welcome
to the Course Page of
MATH 2320 3.00 M Discrete Mathematical Structures Winter 2011 

Department of Mathematics and Statistics 

April 29:  Please click here to see your final exam mark and unofficial letter grade 
for the course. Also, please note that your official grade will be sent to you  
by the Registrar's Office upon the approval by the Senate.  
HAVE A WONDERFUL SUMMER!  
April 06:  Please note the Final Examination will take place on Thursday, April 14 
from 19:00 to 22:00 in CLH H. On the exam you will be responsible for  
all material covered in this course according to Course Schedule.  
No calculator is permitted on the exam. However, you can bring an  
information sheet, which is a single sheet of paper, 21.6 cm by 28 cm, with  
writings on one side only, without flaps or layers. The information sheet  
cannot be shared.  
As it was announced in the class yesterday, during the examination period  
from April 06 to 21 the MathLab will be open from 10:30 to 15:30.  
Please also note that additional office hours for last minute questions will be  
held on Thursday, April 07 from 15:30 to 17:00.  
April 04:  Please note that Assignment #3 is due today. 
Practice exercises for Section 9.4:  
1, 3, 5, 14, 17, 22, 25, 46, 49, 53.  
Also, please note that this week the Wednesday's office hour will be held  
on Tuesday, April 05 from 16:00 to 17:00.  
March 25:  Please note that the graded Test #2 papers will be returned in the class on 
Monday, March 28. I am making avaialable solutions to the test questions.  
March 21:  Please note that Course evaluations are available online at the URL link 
http://courseevaluations.yorku.ca until Tuesday, April 5. It is the time for you  
to be the judge. Please go online and complete the course evaluation.  
Practice exercises for Sections 9.1, 9.2 and 9.3:  
9.1: #1, 2, 10, 13, 18, 24, 25, 29  
9.2: #15, 2023, 25, 26, 29, 35, 36, 42, 44, 47, 53, 59, 61  
9.3: #1, 5, 9, 13, 1517, 22, 25, 34, 35, 37, 39, 41, 43, 46, 54, 55, 58(a), 65.  
March 14:  As it was announced in the class today, we will write Test #2 during the regular 
class time on Friday, March 18. On the test you will be responsible for all the  
material covered in class from Sections 4.4, 5.15.5 and 7.17.2 of the textbook.  
March 11:  Please note that the next week there will be two Sessions of Open Forums for all 
Science and Engineering students. Please click here to obtain information on day,  
time and venue of the Forums.  
March 07:  Practice exercises for Chapter 7: 
7.1: #5, 7, 9(a), (b), (c), 11, 13, 19, 23, 24, 25, 27, 32, 35, 36, 40  
7.2: #1, 3, 7, 8, 13, 17, 19, 23  
7.4: #1, 2, 7, 13, 16, 19, 22, 23, 33, 34, 35.  
March 01:  Please click here to see your percentage grade for Test #1. 
February 17:  As it was announced in the class on Wednesday, Test #1 papers will be 
returned in the class on Friday, February 18.  
I am making available answers to Exercise #20 from Section 5.1:  
a) 142, b) 130, c) 12, d) 220, e) 208, f) 779, g) 738, h) 373.  
February 14:  Practice exercises for Chapter 5: 
5.1: #1, 2, 4, 11, 12, 13, 19, 20, 22, 26, 31, 33, 37, 39, 44, 49, 51, 53  
5.2: #6, 7, 8, 9, 12, 13, 22, 25, 32, 35, 37, 40  
5.3: #11, 13, 15, 17, 25, 33, 34, 35  
5.4: #4, 9, 17, 19, 22, 24, 29  
5.5: #3, 5, 8, 11, 15, 17, 25, 26, 29, 31, 40, 44, 45.  
February 12:  As it was announced in the class on Friday, starting the next week you can 
get a help for the course in the MathLab at S525 Ross on Wednesdays  
between 2:00 and 3:30 PM. Please approach Martin Merener only with  
your questions during this time. Also, starting the week of February 27  
an additional help will be available on Tuesdays between 10:30 AM and  
12:30 PM. Please approach Francesco Kibedi with your questions during  
this time. Please note that no other ATs will be responsible for MATH 2320.  
February 08:  Please note that the graded Test #1 papers will be returned in a class sometime 
the next week. I am making avaialable solutions to the test questions.  
February 04:  As it was announced in the class today, we will write Test #1 during the regular 
class time on Monday, February 07. On the test you will be responsible for all the  
material covered in class from Sections 3.1, 3.2, 3.3, 3.4 and 4.3 of the textbook.  
February 02:  Please note that due to the storm, effective 5:30 AM, Wednesday, February 02 
all day classes have been cancelled. Consequently, we will be writing Test #1  
on Monday, February 07. Hope, to see in the class on Friday, February 04.  
January 28:  Practice exercises for Sections 4.34.4: 
4.3: #1, 2, 17, 2224, 34, 35, 39, 40  
4.4: #4, 6, 7, 10, 11, 16, 17, 20, 21, 22, 23.  
January 19:  As it was announced in the last class today, you may get bonus marks 
if you submit written solution by 13:30 P.M. on Monday, January 24th to  
the following question related to the worstcase time complexity of the  
TwoLevel Search Algorithm: Determine the value of m for which the Two  
Level Search Algorithm have the "best" worstcase time complexity.  
January 17:  Practice exercises for Sections 3.33.4: 
3.3: #5, 7, 8, 9, 11(a), (b), 17, 19, 27, 28(a), (b)  
3.4: #5, 6, 9, 11, 12, 14, 17, 18, 19, 20, 21, 22, 23(a), 31, 33.  
January 12:  I am making available Migration Tables from the 5th Edition to the 6th Edition 
of the textbook.  
January 10:  I am making available Errata Corrections to the 1st printing of the 6th Edition 
of the textbook with additional web resourse references.  
January 05:  Welcome back! 
Please read Appendices A2 and A3 on the back of the textbook.  
To view and/or print PDF files you can download the free Acrobat Reader  
Practice exercises for Appendix A3:  
# 1, 2, 3  
Practice exercises for Sections 3.13.2:  
3.1: # 9, 13, 15, 17, 18, 19, 23, 24, 25, 29, 31, 32, 35, 39, 53  
3.2: # 1, 2, 9, 12, 17, 18, 21, 24, 25, 28, 32, 51, 53, 60, 63. 
Course:  Session:  Winter 2011 
Section:  M  
Lectures:  MWF 1:302:20 P.M., CLH M  
Instructor:  Name:  Iulduz Raguimov 
Office:  S512 Ross Building  
Phone:  4167365250 or 4167362100, Ext.66092  
Mailbox:  N520 Ross Building  
Office Hours:  W 4:005:00 P.M., F 12:001:00 P.M., also by appointment  
Email:  raguimov@mathstat.yorku.ca  
TA:  Name:  TBA 
Email:  TBA  
Grading:  Two ClassTests:  25% each 
Final Examination:  50% 
Course Description: The course covers the algebraic and combinatorial structures that are needed in Computer Science and other disciplines. Consultation with the Departments of Computer Science and of Mathematics, and with the ITEC Program, has led to the following list of topics for emphasis: “Big O” notation, complexity of formulae and algorithms, modular arithmetic, recursive definitions, general inductions, counting principles, recurrence relations and methods for solving them, trees and simple graph theory. The emphasis will include examples arising from algorithms and the ability to carry out analysis, problem solving, proofs and calculations which will be required in upper level courses. The course does not require previous knowledge of computer science. A student of mathematics should enjoy this introduction to a variety of mathematical topics, many of which are not covered elsewhere. We will emphasize analysis, problem solving, and proofs. For a more detailed list of topics with references to the textbook, please see Course Schedule.
Textbook:  Discrete Mathematics and Its Applications, Sixth Edition 
by Kenneth H. Rosen  
McGrawHill, 2007. ISBN 0072880082  
Optional Aids:  Student Solutions Guide to accompany Discrete Mathematics and Its Applications, 
Sixth Edition by Kenneth H. Rosen  
McGrawHill, 2006. ISBN 0073107794  
Course Prerequisite:  AS/SC/AK/MATH 1190 3.00, or AS/SC/AK/MATH 1090 3.00, or any 2000level MATH 
course without the second digit 5. Student who have not taken AS/SC/AK/MATH 1190 3.00  
or AS/SC/AK/MATH 2090 3.00 are advised to review set theory, functions, relations  
and induction proofs in Chapters 1, 2 and 4, before the course begins.  
Important Dates:  January 04: Classes commence. 
January 17: Last date to enrol in the course without my permission.  
January 31: Last date to enrol in the course with my permission.  
March 04: Last date to withdraw from the course without receiving a final grade.  
April 05: Last day of classes.  
April 0723: Examination period. 
(subject to any changes announced in class)
Week 
Sections 
Comments 
January 57  Introduction, 3.1  Classes begin Wednesday, January 05. 
January 1014  3.13.2  
January 1721  3.33.4  
January 2428  4.34.4  . 
Jan 31  Feb 4  4.4, 5.1  
February 711  5.2, Test #1  Test #1 will take place on Friday, February 07. 
February 1418  5.35.4  
February 2125  No classes  Reading/CoCurricularWeek. 
Feb 28  March 4  5.5, 7.1  
March 711  7.17.2  
March 1418  7.4, Test #2  Test #2 will take place on Friday, March 18. 
March 2125  9.19.2  
March 28  Apr 1  9.29.3  
April 45  9.4, Review  The classes end on Monday, April 04. 
April 723  Final Examination  TBA. 
Note: The course will not cover all the sections of each chapter from the textbook.
Throughout the term, practice exercises will be posted to the Announcements section. In order to develop your understanding of the course material you must do all assigned problems. These will not be collected for grading and hence will not directly affect your grade. However, it is extremely important that you complete all assigned exercises. Do not memorize them. Rather, learn how to solve problems like them. Learning Mathematics is not a spectacular sport, it is a participatory event. There is nothing like a bit of computation to strengthen understanding in mathematics! Use the Solutions Manual only after you have tried the problem. Successful students must keep up with homework and seek help for points they do not understand as soon as possible. Do not fall behind! It is recommended to read the relevant sections of the textbook before every class. Next to the classes, working out the answers to the problems is the most important preparation for the tests and exam that will contain for the most part but not exclusively, questions very similar to those from the textbook. It is quite practical to work on your own or together in small groups. Each student should do at least two hours of independent study for every lecture hour. The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend working on problems.
Please turn off all cell phones and
pagers before entering the lecture hall. For tests and
exam cell phones, calculators, digital dictionaries,
palms, pagers or other electronic devices are NOT
allowed. All such devices as well as all books, papers, knapsacks, and
briefcases must be left at the front of the lecture hall. Anyone caught with
electronic devices will be charged with Academic Dishonesty (see the
next page). The only items you may have at your seat are
pens, pencils, student ID and purses.
You are responsible for all material covered in lectures.
Note: Photo identification and signingin are required at all
tests and exam.
The official grades at York University are LETTER grades.
Qualitative descriptions of these grades can be found in the York Calendar at
this
link. Your test marks will be on a numerical scale because these have to be
weighted and averaged in various ways, but THERE IS NO AUTOMATIC
PREDETERMINED CORRELATION BETWEEN NUMERICAL GRADES AND LETTER GRADES in this
course. In particular, the "numerical" grades you receive are NOT to be
interpreted as percentages; they are merely 'raw scores'. When the tests are
returned in class, the distribution of 'raw scores'
will be announced along with an approximate conversion to
letter grades. The median letter grade for the course will likely fall between C
and C+.
The composition of the final grade is as follows:
Two Tests (50 minutes each
written tests held in lecture periods): 25% each
(Tentative dates for the tests: Monday, February 09 and Friday, March 18).
Final Examination:
50% of the overall grade, will take place
during the examination period between April 07 and 23, 2011.
Note: Students
have five days from the date of the return of test papers to appeal their marks.
Some test papers (randomly selected)
are photocopied before they are handed back, so we can detect subsequent
alterations. Once you have written both tests and your final exam
grade is higher than your average test grade, your final exam will be counted as
60% and each test as 20% of your overall grade for the course.
Makeup Policy:
No permission will be given to a
student to write tests in advance of their scheduled
dates. No makeups will be done for the tests. A
missed test will be counted as zero, except under extreme
circumstances in which case the corresponding percentage
of the overall grade will be
"forwarded" to the final exam.
If you miss a termtest for medical reasons
you must turn in within
one week following the test date the Attending
Physician's Statement form provided
here after getting it filled in by your doctor.
No other type of medical note will be accepted.
However, missing tests is extremely dangerous and
not recommended. As experience has shown, students who miss class
tests because of some 'mysterious
illnesses' will usually average 30% on the final exam.
A student who misses the final examination
will be allowed to write a makeup
exam only if both of the following conditions are met:
1)
the student notifies me (raguimov@mathstat.yorku.ca)
or the Department of Mathematics and Statistics (Undergraduate Office, N502/503
Ross Building,
2)
the student submits
within one week following the exam date the
Attending Physician's Statement form provided
here after getting it filled in by his/her doctor .
Students who miss the final examination
and do not meet both conditions will receive a grade of F. It is
student's responsibility to fill out and submit the Deferred Standing Agreement
Form.
Note: Do not make vacation/job plan until the final exam date is
known: having a plane ticket for Hawaii or Las Vegas on April
16 is NOT a legitimate excuse for absence from a
final exam on April 20.
Religious Observance:
York University is committed to respecting the religious beliefs and practices of all members of the community and making accommodations for observances of special significance to adherents. If any of the dates specified in the course schedule for inclass tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) by the end of the third week of classes. Please note that if the final exam date poses a conflict, students must complete the Examination Accommodation Form, which can be obtained from the Registrar’s Office
Academic Honesty
Students are responsible for familiarizing themselves with University Policies and Regulations. Conduct that violates the ethical or legal standards of the university community or of one’s programme or specialization may result in serious consequences. Refer to the Senate Policy on Academic Honesty. Photo identification and signingin are required at all tests and exam. Also, some test papers (randomly selected) will be photocopied before they are returned so that subsequent alterations can be detected.
Individual questions can be discussed by email, or in person after class, or during office hours. Please send all email notes as plain text within the body of the message. Do not send attachments nor HTMLformatted mail. Also, if the name of your account is an alias, I will not know who the mail is from unless you sign it; it also risks being accidentally discarded as junk mail. The course web page will be updated regularly to include important announcements made in class, such as the material to be covered on the tests. Email notes requesting such information contained on the web page will be answered the last.
1
McGrawHill Online Learning Centre
2
Study Groups
3 York
Undergraduate Math Program
4 The Great
Internet Mersenne Prime Search
www.mersenne.org
Questions and comments regarding this Web page please send to raguimov@mathstat.yorku.ca
© 20042011, All Rights Reserved, York University & Iouldouz S. Raguimov
Last updated April 29, 2011