MATH 2320: Discrete mathematical structures

Winter 2015


Important Information:

  • I will hold special office hours on Monday April 20 from 1:30 to 3:30 pm in my office Ross N515.
  • The final exam will be held on Wednesday April 22 from 2:00 pm to 5:00 pm in room ACW 005 (see below for the syllabus of the final). A non-programmable calculator is allowed.

  • General Information:

  • Instructor: Dr. Youness Lamzouri.
                           Office: N515 Ross Building.
                           Email: lamzouri@mathstat.yorku.ca.
                           Website: www.math.yorku.ca/~lamzouri.
  • Lectures: Monday, Wednesday and Friday, 1:30-2:20 pm, in R S203 (Ross South).
  • Office hours: Monday, Wednesday and Friday 12:30-1:10 pm.
  • Textbook: "Discrete Mathematics and its Applications". By Kenneth H. Rosen; 7th edition, McGraw-Hill.

  • List of practice problems:

  • Week 1 (Jan 5-9): Section 3.1 : 6, 10, 16, 28, 34, 36, 52, 56. Section 3.2 : 6, 10, 16, 18.

  • Week 2 (Jan 12-16): Section 3.2 : 22, 26, 28, 30, 32, 36, 40, 44, 46, 50.

  • Week 3 (Jan 19-23): Section 3.3 : 2, 4, 8, 13, 18. Section 4.1 : 2, 6, 8, 10, 18.

  • Week 4 (Jan 26-30): Section 4.1 : 12, 14, 24, 26,28, 34, 38, 40. Section 4.3 : 2, 4, 5, 9.

  • Week 5 (Feb 2-6): Section 4.3 : 7, 12, 18, 19, 20.

  • Week 6 (Feb 9-13): Section 4.3 : 21, 22, 23. Section 4.4 : 33, 34, 37, 38 a), 39 a), 40.

  • Week 7 (Feb 23-27): Section 4.6 : 1 a) and b), 2 a) and b), 4, 5, 7, 8, 24, 25.

  • Week 8 (March 17-20): Section 5.3 : 2, 4, 6 a), b), c), 7, 8, 12, 13. (Pages of the text covered this week are: 345, 346, and 347).

  • Week 9 (March 23-27): Section 5.4 : 2, 6, 8, 12, 18, 32. Section 6.1 : 2, 4, 6, 8, 12, 26, 28, 36, 48, 64, 66. (Pages of the text covered this week are: 386-395 and 361-367).

  • Week 10 (March 30- April 3): Section 6.2 : 2, 4, 6, 14, 18, 26, 32, 34, 36, 44, 46.

  • Week 11 (April 6- April 10): Section 6.3 : 4, 6, 8, 14, 16, 18, 20, 22, 28, 30, 32. Section 8.1 : 2, 8.

  • Week 12 (April 13- April 17): Section 8.2 : 2; 3 a), b), c), f), g); 4 a), b), c), e), g); 11.


  • Course Description :

    This course is an introduction to a variety of mathematical topics, including growth of functions (Big O, Omega, Theta notation), complexity of formulae and algorithms, modular arithmetic, recursive definitions, general inductions, counting principles, and recurrence relations and methods for solving them. The emphasis will include examples arising from algorithms and the ability to carry out analysis, problem solving and proofs. We will cover the followings sections of the textbook:

    Chapter 3: 3.1-3.3.
    Chapter 4: 4.1, 4.3 (only primes), 4.4 (only Fermat's Little Theorem and pseudoprimes), Wilson's Theorem, Euler's Theorem and the Euler phi-function, 4.6.
    Chapter 5: 5.3, 5.4.
    Chapter 6: 6.1-6.3.
    Chapter 8: 8.1, 8.2.


    Course Evaluation:

  • 30% Quizzes and assignments : There will be two in-class quizzes and two take home assignments.

    Quiz 1 will be held on Wednesday January 21 from 1:30 to 1:55 pm. It Covers Sections 3.1 and 3.2. The problems of the quiz will be selected among the practice problems of weeks 1 and 2.

    Quiz 2 will be held on Wednesday February 4 from 1:30 to 1:55 pm. It Covers Sections 4.1 and 4.3 (only primes). The problems of the quiz will be selected among the practice problems of weeks 3 and 4.

    Assignment 1 will consist of the following problems from the textbook:
    From Section 5.3 : exercises 8 and 12, from Section 5.4 : exercise 32, and from Section 6.1: exercises 26, 48 and 64. The assignment is due on Monday April 6.

    Here is the solution of assignment 1.

    Assignment 2 will consist of the following problems from the textbook:
    From Section 6.2: exercises 14, 36 from Section 6.3 : exercises 18, 30. The assignment is due on Friday April 17.

    Here is the solution of assignment 2.

  • 25% Midterm test: The midterm exam will be in-class. The date of the midterm test is: Friday, February 27, 2015, from 1:30 pm to 2:20 pm. The material of the test includes Sections 3.1, 3.2, 3.3, 4.1, 4.3 (only primes), 4.4 (only Fermat's Little Theorem and pseudoprimes), Wilson's Theorem, Euler's Theorem and the Euler phi-function, 4.6 (only shift ciphers).
    Here is the solution of the midterm.


  • 45% Final Exam: The final exam will be comprehensive. Here is the syllabus of the final exam.

    Notes: There will be no makeup test or quizzes. If you miss the midterm test or one of the quizzes and have a valid excuse (with an acceptable documentation), the exam weight will be transferred to the final exam.