Welcome to the Course Page of

AS/SC/AK/MATH 2320 3.0 M

Discrete Mathematical Structures

Winter 2007


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.
May 03: 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 05: As it was announced earlier, the Final Examination will take place on
Friday, April 13 from 19:00 to 22:00 in TEL 1005.
The exam will be comprehensive, covering the entire semester's work
according to the  Course Schedulebut with an emphasis on more recent
material from the second half of the term.
April 02: Please note that Test #2 papers will be returned in the class today.
March 23: As it was announced in the class today, we will write Test #2 during the regular
class-time on Wednesday, March 28. On the test you will be responsible for all the
material covered in class from Sections 4.4, 5.1-5.5, 7.1-7.2 and 7.4 of the text-book.
March 11: Please note that the exam schedule has been published to the Registrar's web site.
The course web page has been updated to show exam date, time and venue.
However, it is your responsibility to check with official York web site in case
of last minute changes.
March 01: Please note that Test #1 papers will be returned in the class on Friday, March 02.
February 20: As it was announced in the class yesterday, we will write Test #1 during the regular
class-time on Friday, February 23. On the test you will be responsible for all the
material covered in class from Sections 3.1, 3.2, 3.3, 3.4, 3.7 and 4.3 of the text-book.
February 01: Please note that Quiz papers will be returned in the class on Friday, February 02.
January 19: As it was announced in the class today, we will be writing Quiz during the lecture
period on Friday, January 26. On the quiz you will be responsible for all the material
covered in class from Sections 3.1-3.3 of the text-book.
January 03: Welcome back!
Please read Appendices A-2 and A-3 on the back of the text-book.

To view and/or print PDF files you can download the free Acrobat Reader

Course Information

Course: Session: Winter 2007
  Section: M
  Lectures: MWF 1:30-2:20 P.M., VH B
Instructor: Name: Dr. Iulduz Raguimov
  Office: S512 Ross Building
  Phone: 416-736-5250 Ext.66092
  Mailbox: N520 Ross Building
  Office Hours: T 12:00-12:30, 1:30-2:00pm, R 12:00-1:30pm
and F 3:30-4:00pm
  E-mail: raguimov@mathstat.yorku.ca
TA: Name: Jinlian Wang
  Office: N629 Ross Building
  Office Hours: W 3:00-4:00pm
  E-mail: spell@mathstat.yorku.ca
Grading: Quiz: 10%
  Two Class-Tests:  25% each
  Final Examination: 40%

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 oh” 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. This course emphasizes analysis, problem solving and proofs. For a more detailed list of topics with references to the textbook, please see Course Schedule.

Text-book: Discrete Mathematics and Its Applications, Sixth Edition
by Kenneth H. Rosen
McGraw-Hill, 2006. ISBN 0-07-288088-2
Optional Aids: Student Solution Guide for 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 1090 3.0, or AS/SC/AK/MATH 1190 3.0, or AK/MATH 2441 3.0,
or any 2000-level MATH course without the second digit 5. Student who have not taken 
  AS/SC/AK/MATH 2090 3.0 or AS/SC/AK/MATH 1190 are advised to review set theory,
  functions, relations and induction proofs.
Course Credit Exclusion: AK/MATH 2442 3.0
Important Dates: January 03: Classes commence
January 18: Last date to enrol in the course without my permission
January 26: Last date to enrol in the course with my permission
March 09: Last date to withdraw from the course without receiving a final grade
April 02: Last day of classes
April 11-30: Examination period.

Course Schedule

(subject to any changes announced in class)




January 3-5 Introduction, 3.1 Classes begin Wednesday, January 03.
January 8-12 3.2-3.3  
January 15-19 3.3-3.4  
January 22-26 3.6-3.7, Quiz Quiz will take place on Friday, January 26.
Jan 29 - Feb 2 4.3-4.4  
February 5-9 5.1-5.2  
February 12-16 No classes Reading Week.
February 19-23 5.3-5.5, Test #1 Test #1 will take place on Friday, February 23.
Feb 26 - March 2 7.1-7.2  
March 5-9 7.2, 7.4  
March 12-16 9.1-9.3  
March 19-23 9.4-9.5  
March 26-30 10.1-10.2, Test #2 Test #2 will take place on Wednesday, March 28.
April 2 Review The classes end on Monday, April 02.
April 11-30 Final Examination Will take place on Friday, April 13, 19:00-22:00 in TEL 1005.

Note: The course will not cover all the sections of each chapter from the text-book.


Homework Problems 

Appendix A-3:   Exercises: 1, 2, 3
Chapter 3: Section 3.1 Exercises: 9, 13, 15, 17, 18, 19, 23, 24, 25, 29, 31, 32, 35, 39, 53
  Section 3.2 Exercises: 1, 2, 9, 12, 17, 18, 21, 24, 25, 28, 32, 51, 53, 60, 63
  Section 3.3 Exercises: 5, 7, 8, 9, 11(a), (b), 17, 19, 27, 28(a), (b)
  Section 3.4 Exercises: 5, 6, 9, 14, 17, 18, 19, 20, 21, 22, 23a
  Section 3.7 Exercises: 2(e), (f), (g), 3, 5, 10-13, 18, 19, 23-29, 36-39, 46, 47
Chapter 4: Section 4.3 Exercises: 1, 2, 17, 22-24, 34, 35, 39, 40
  Section 4.4 Exercises: 4, 6, 7, 10, 11, 16, 17, 20, 21, 22, 23
Chapter 5: Section 5.1 Exercises: 1, 2, 4, 11, 12, 13, 19, 20, 22, 26, 31, 33, 37, 39, 44, 49, 51, 53
  Section 5.2 Exercises: 6, 7, 8, 9, 12, 13, 22, 25, 32, 35, 37, 40
  Section 5.3 Exercises: 11, 13, 15, 17, 25, 33, 34, 35
  Section 5.4 Exercises: 4, 9, 17, 19, 22, 24, 29
  Section 5.5 Exercises: 3, 5, 8, 11, 15, 17, 25, 26, 29, 31, 40, 44, 45
Chapter 7: Section 7.1 Exercises: 5, 7, 9(a), (b), (c), 11, 13, 19, 23, 24, 25, 27, 32, 35, 36, 40
  Section 7.2 Exercises: 1, 3, 7, 8, 13, 17, 23
  Section 7.4 Exercises: 1, 2, 7, 13, 16, 19, 22, 23, 33, 34, 35
Chapter 9: Section 9.1 Exercises: 1, 2, 10, 13, 18, 24, 25, 29
  Section 9.2 Exercises: 1-5, 20-23, 25, 26, 29, 35, 36, 42, 44, 47, 53, 59, 61
  Section 9.3 Exercises: 1, 5, 9, 13, 15-17, 22, 25, 34, 35, 37, 39, 41, 43, 46, 54, 55, 58(a), 65
  Section 9.4 Exercises: 1, 3, 5, 14, 17, 22, 25, 46, 49, 53
  Section 9.5 Exercises: 1, 3, 5, 7, 9, 13, 15, 18, 21, 26, 27, 37, 44
Chapter 10: Section 10.1 Exercises: 2, 5, 7, 9, 11, 15, 16, 17, 19, 21, 27, 28, 30, 34, 37, 45
  Section 10.2 Exercises: 1, 3, 5, 7-9, 11, 13, 15-18.

The homework problems are posted but solutions will not be collected for grading. While these will not directly affect your grade, it is extremely important that you complete as many problems as possible. Do not memorize them. Rather, learn how to solve problems like them. Use the Solutions Manual only after you have tried the problem. There is nothing like a bit of computation to strengthen understanding in mathematics! 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 relevant sections of the text-book 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 text-book. It is quite practical to work on your own or together in small groups. Each student should do at least three 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 quizzes, tests and exam cell phones, 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, a non-graphing, non-programmable calculator, purses and coats.
You are responsible for all material covered in lectures.
Note: Photo identification and signing-in are required at all
the quiz, tests and exam.

Final Grade:

The composition of the final grade is as follows:
Quiz (25 minute written quiz held in the lecture period): 10% of the overall grade (Tentative date for the quiz: Friday, January 26); Two Class-Tests (50 minute each written tests held in the lecture period): 25% of the overall grade each (Tentative dates for the tests: Friday, February 23 and Wednesday, March 28).
Final Examination
(3-hour exam scheduled by the Registar's Office): 40% of the overall grade, will take place on Friday, April 13 of 2007 from 19:00 to 22:00 in TEL 1005.
All test and quiz marks you receive should be interpreted as raw scores - not as "percentages". The statistics of scores for the both tests and quiz will be announced.  Students have seven days from the date of the return of a paper to appeal their marks. Cut-off for converting midterm scores into letter grades will be announced prior to the drop date.

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 class-tests. Missed tests 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 class-test  for medical reasons you must turn in  within one week following the test a copy of the medical report 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, Ext. 55902 or 33969; Fax: 416-736-5757) in advance that the exam will be missed;
2) the student submits a copy of the medical report form provided  here after getting it filled in by his/her doctor within one week following the exam.
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 15 is NOT a legitimate excuse for absence from a final exam on April 19.

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 second 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

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


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-  York Undergraduate Math Program

2- The Great Internet Mersenne Prime Search  www.mersenne.org

Questions and comments regarding this Web page please send to raguimov@mathstat.yorku.ca

© 2007, All Rights Reserved, York University & Iouldouz S. Raguimov

Last modified May 03, 2007