Welcome to the Course Page of

MATH 2320 3.00 M

Discrete Mathematical Structures

Winter 2011


Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto, Ontario  M3J 1P3

Course Organization:

Course Information
Course Schedule
Exams  Information
Links & Other Resources


This area will contain announcements and solutions to tests. Announcements made in class will be posted here in reverse chronological order and will not be repeated in class. Please take a minute to read the announcements carefully, as they often get updated. You may need to Reload/Refresh this page.
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.
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 on-line at the URL link
http://courseevaluations.yorku.ca until Tuesday, April 5. It is the time for you
to be the judge. Please go on-line 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:  #1-5, 20-23, 25, 26, 29, 35, 36, 42, 44, 47, 53, 59, 61
9.3:  #1, 5, 9, 13, 15-17, 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, 5.1-5.5 and 7.1-7.2 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 Math-Lab 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 4.3-4.4:
4.3:  #1, 2, 17, 22-24, 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 worst-case time complexity of the
Two-Level Search Algorithm: Determine the value of m for which the Two-
Level  Search Algorithm have the "best" worst-case time complexity.
January 17: Practice exercises for Sections 3.3-3.4:
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 A-2 and A-3 on the back of the textbook.
To view and/or print PDF files you can download the free Acrobat Reader
Practice exercises for Appendix A-3:
# 1, 2, 3
Practice exercises for Sections 3.1-3.2:
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 Information

Course: Session: Winter 2011
  Section: M
  Lectures: MWF 1:30-2:20 P.M., CLH M
Instructor: Name: Iulduz Raguimov
  Office: S512 Ross Building
  Phone: 416-736-5250 or 416-736-2100, Ext.66092
  Mailbox: N520 Ross Building
  Office Hours: W 4:00-5:00 P.M., F 12:00-1:00 P.M., also by appointment
  E-mail: raguimov@mathstat.yorku.ca
TA: Name: TBA
  E-mail: TBA
Grading: Two Class-Tests:  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
McGraw-Hill, 2007. ISBN 0-07-288008-2
Optional Aids: Student Solutions Guide to accompany Discrete Mathematics and Its Applications,
  Sixth Edition by Kenneth H. Rosen
  McGraw-Hill, 2006. ISBN 0-07-310779-4
Course Prerequisite: AS/SC/AK/MATH 1190 3.00, or AS/SC/AK/MATH 1090 3.00, or any 2000-level 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 07-23: Examination period.

Course Schedule

(subject to any changes announced in class)




January 5-7 Introduction, 3.1 Classes begin Wednesday, January 05.
January 10-14 3.1-3.2  
January 17-21 3.3-3.4  
January 24-28 4.3-4.4 .
Jan 31 - Feb 4 4.4, 5.1  
February 7-11 5.2, Test #1 Test #1 will take place on Friday, February 07.
February 14-18 5.3-5.4  
February 21-25 No classes Reading/Co-CurricularWeek.
Feb 28 - March 4 5.5, 7.1  
March 7-11 7.1-7.2  
March 14-18 7.4, Test #2 Test #2 will take place on Friday, March 18.
March 21-25 9.1-9.2  
March 28 - Apr 1 9.2-9.3  
April 4-5 9.4, Review The classes end on Monday, April 04.
April 7-23 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.

Exams Information

Lecture/Exam Rules:

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 signing-in are required at all
tests and exam.

Final Grade:

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):   25each (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.
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.

Make-up Policy:

No permission will be given to a student to write tests in advance of their scheduled dates. No make-ups 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 term-test  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 make-up 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,  416-736-2100  416-736-2100,  Ext. 55902 or 33969) in advance that the exam will be missed,
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 in-class 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 signing-in 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 e-mail, or in person after class, or during office hours. Please send all e-mail notes as plain text within the body of the message. Do not send attachments nor HTML-formatted 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 up-dated regularly to include important announcements made in class, such as the material to be covered on the tests. E-mail notes requesting such information contained on the web page will be answered the last.

Links and Other Resources

1-   McGraw-Hill 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

© 2004-2011, All Rights Reserved, York University & Iouldouz S. Raguimov

Last updated April 29, 2011