CISC-102: Discrete Mathematics for Computing I

(Fall 2016)

Last Modified:

Education is not the filling of a pail, but the lighting of a fire. Plutarch.

Quick Links

Class Hours and Locations
Outline and Schedule

Course Instructor

David Rappaport
E-MAIL: daver AT cs dot queensu dot ca
OFFICE HOURS: Monday 13:00-15:00
Or contact me after class or by e-mail appointment.

Course Teaching Assistants

Jacob Clarke-Mcrae
E-MAIL: 13jjmc AT queensu dot ca
OFFICE HOURS: Monday 13:30-15:30

Hassan Hanino
E-MAIL: 13hah2 AT queensu dot ca
OFFICE HOURS: Monday 12:30-14:30

Faria Khandaker
E-MAIL: khandake AT cs dot queensu dot ca
OFFICE HOURS: Friday 10:00-12:00

Jacob Peoples
E-MAIL: peoples AT cs dot queensu dot ca
OFFICE HOURS: Friday 13:00-15:00

Joey Sun
E-MAIL: 14cyjs AT queensu dot ca
OFFICE HOURS: Thursday 12:00-14:00

Rachel Venis
E-MAIL: 14rnv AT queensu dot ca
OFFICE HOURS: Monday 10:30-12:30

Class Hours and Locations

Monday 8:30-9:30 Ellis Hall Auditorium
Tuesday 10:30-11:30 Ellis Hall Auditorium
Thursday 9:30-10:30 Ellis Hall Auditorium


Marc Lipson, Seymour Lipschutz, Schaum's Outline of Discrete Mathematics, McGraw-Hill Education (2009).

L. Lovász, J. Pelikán, K. Vesztergombi, Discrete Mathematics Elementary and Beyond, Springer (2003).

I will use both of these books. They are both available in paperback, and the total cost of the two books is well under $100.

Intended Student Learning Outcomes

To complete this course students will demonstrate their ability to:
1. Understand standard Mathematics notation used in the field of Computing.
2. Recognize the difference between a proof and a counter example.
3. Able to formulate elementary proofs using mathematical induction.
4. Recognize comparative magnitudes of functions such as log(n), n2, 2n.
5. Ability to read and understand some elementary logical proofs.


Grades will be made up of, midterm quizzes and a final.
Four Three in class midterm quizzes, each worth 20%, total: 60%
Final exam: 40%
NOTE: A minimum of 50% must be obtained on the final exam to pass the course. <
The quizzes will be scheduled as follows:
Quiz 1: Week 3: Tuesday, September 27.
Quiz 2: Week 6: Tuesday, October 18. Cancelled due to instructor error.
Quiz 3: Week 9: Tuesday, November 8.
Quiz 4: Week 12: Tuesday, November 29.
Please make every effort to be present for the midterm quizzes. It may be that you will be forced to miss a quiz for health, or other legitimate reasons. With my permission, you may a quiz. miss up to two of the quizzes. If you miss a quiz then the marking scheme will be revised for you as follows:
1 missed - 2 quizzes 25%, and 50% final.

Calculator Policy

Calculators will not be needed nor will they be permitted at any of the quizzes or the final exam.

Grading Method

All components of this course will receive numerical percentage marks. The final grade you receive for the course will be derived by converting your numerical course average to a letter grade according to the Queen's grade conversion scale.
Numeric Range Letter Grade GPA
90-100 A+ 4.3
85-89 A 4.0
80-84 A- 3.7
77-79 B+ 3.3
73-76 B 3.0
70-72 B- 2.7
67-69 C+ 2.3
63-66 C 2.0
60-62 C- 1.7
57-59 D+ 1.3
53-56 D 1.0
50-52 D- 0.7
0-49 F 0

Location and Timing of Final Examinations

As noted in Academic Regulation 8.2.1, "the final examination in any class offered in a term or session (including Summer Term) must be written on the campus on which it was taken, at the end of the appropriate term or session at the time scheduled by the Examinations Office." The exam period is listed in the key dates prior to the start of the academic year in the Faculty of Arts and Science Academic Calendar and on the Office of the University Registrar's webpage. A detailed exam schedule for the Fall Term is posted before the Thanksgiving holiday; for the Winter Term it is posted the Friday before Reading Week, and for the Summer Term the window of dates is noted on the Arts and Science Online syllabus prior to the start of the course. Students should delay finalizing any travel plans until after the examination schedule has been posted. Exams will not be moved or deferred to accommodate employment, travel /holiday plans or flight reservations.


Homework will be assigned weekly. This work will not be collected for grading, rather, solutions to homework will be done in class. There will be four midterm quizzes that will be directly based on the homework assignments. Please see the grading scheme above.

Course Description

Calendar Description of CISC-102

Introduction to mathematical discourse and proof methods. Sets, functions, sequences, and relations. Properties of the integers. Induction. Equivalence relations. Linear and partial orderings.

This course is a direct prerequisite to CISC-203/3.0 (Discrete Mathematics for Computing II) CISC-204/3.0 (Logic in Computing) and a co- or pre-requisite to CISC-121/3.0.

This course is required in all Computing programs except COMA.

Course Syllabus

Mathematics plays an important role in many aspects of computer science. This course sets the stage for the type of mathematics that computer scientists rely on to produce effective software solutions. This course can be viewed as a language course, that is, you will be learning the language of mathematics. I will follow two books that cover similar material in distinctly different ways. Schaum's Notes (SN) are an excellent resource for a well organized source of course material. Discrete Mathematics Elementary and Beyond (DMEB) provides colour and motivation for the same material.
The course will consist of the following elements:

Notation and definitions and notational conventions: Using the language learning analogy this is equivalent to learning vocabulary and grammar and colloquialisms. SN will be the main source for this material.

Tricks and techniques: Sticking with the language learning analogy, this is equivalent to learning writing styles, problem solving methods. SN does a good job of presenting this. However, DMEB is better at providing lots of insight from experts. SN is a great guide for students, whereas DMEB comes straight from the experts in a more informal but also more insightful way.

Practice, practice, practice: This is the key to success. Doing exercises is the only way to absorb the material properly. You can't learn to play a sport, play an instrument, or how to be a good writer solely by reading a book. This material is no different.

Outline and Schedule

Topics. Chapter numbers are from SN. Topics from DMEB will be selected as the course progresses.

Sets (Chapter 1)
Relations (Chapter 2)
Functions (Chapter 3)
Logic (Chapter 4)
Counting Techniques (Chapter 5 and 6)
Integers and Induction (Chapter 11)
Patterns of Proof (PDF Handout) (Chapter 4)
The topics covered this term will be similar to last term (Winter 2016), but may differ slightly at times. You can see a fairly detailed record on last term's web page:
The following table will be updated as the term progresses.
Week 1
Introduction, Notation, Set Theory, Counting Problems
Notes for week 1.
Homework 1 Solutions to Homework 1 will be done in class on Monday September 19.
Monday, September 12
Good morning. Please read the lecture notes for week 1, the readings posted for homework, and work on homework 1 so that you finish it by next Monday.
Tuesday, September 13

Thursday, September 15

Week 2
Laws of Set Theory, Indexed Sets, Principle of Inclusion and Exclusion
Notes for week 2.
Monday, September 19
Homework 2
Solutions Homework 1
Tuesday, September 20
Thursday, September 22

Week 3
Mathematical Induction
Notes for week 3.
Monday, September 26
Homework 3
Solutions Homework 2
Tuesday, September 27
Quiz #1 based on Homework 1 and 2. Please arrive a bit early so that we can start the quiz at 10:30 sharp. Late comers run the risk of not being admitted into the room. No calculators are permitted for this quiz, or any of the others.
Thursday, September 29
Week 4
Product sets, Relations, Functions
Notes for week 4.
Monday, October 3
Homework 4
Solutions Homework 3
Tuesday, October 4
Thursday, October 6
Solutions to Quiz #1
Week 5
Properties of the Integers (Read sections 11.1, 11.2, 11.3, 11.4, 11.5 of Schaum's Outline of Discrete Mathematics.)
Notes for week 5.
Monday, October 10
Thanksgiving, no class.
Homework 5
Solutions to homework 4 will be presented on Tuesday Oct. 11.
Tuesday, October 11
Solutions Homework 4
Thursday, October 13
Week 6
Integers, Primes, G.C.D., L.C.M.
Notes for week 6.
Monday, October 17
Solutions Homework 5.
Homework 6
Tuesday, October 18
Quiz #2 based on Homework 3, 4 and 5. CANCELLED.
Here is quiz#2 for you to practice with.
Quiz 2
I will post solutions next Monday.
Thursday, October 20
Week 7
Congruence Relations, Counting
Notes for week 7.
Monday, October 24
Homework 7
Solutions Homework 6
Solutions Quiz 2
Tuesday, October 25
Thursday, October 27
Week 8
Counting, Binomial coefficients
Notes for week 8.
Monday, October 31
Homework 8
Solutions Homework 7
Tuesday, November 1
Thursday, November 3
Week 9
Proofs using counting arguments.
Notes for week 9.
Monday, November 7
Solutions Homework 8
Homework 9
Tuesday, November 8

Quiz #3 based on Homework 6, 7 and 8. Please arrive a bit early so that we can start the quiz at 10:30 sharp. Late comers run the risk of not being admitted into the room. No calculators are permitted for this quiz, or any of the others.
Thursday, November 10

Week 10
Pascal's Triangle, Propositional Logic
Notes for week 10.
Monday, November 14
Solutions Homework 9
Homework 10
Tuesday, November 15
Solutions Quiz 3.

Thursday, November 17
Week 11
Propositional Logic, Methods of Mathematical Proof
Notes for week 11.
(Please see Patterns of Proof Tom Leighton, and Marten Dijk. 6.042J Mathematics for Computer Science, Fall 2010. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 18 Nov, 2015). License: Creative Commons BY-NC-SA )
Monday, November 21
Homework 11. Note this homework is only reading, with no problems to solve.
Solutions Homework 10
Tuesday, November 22 Thursday, November 24
Week 12
Wrap up and Review
Monday, November 28
2014 Final Exam
Tuesday, November 29
Quiz #4 based on Homework 9 and 10. and 11. Please arrive a bit early so that we can start the quiz at 10:30 sharp. Late comers run the risk of not being admitted into the room. No calculators are permitted for this quiz, or any of the others.

Thursday, December 1
Final review
Solutions to Quiz #4

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