CISC-102: Discrete Mathematics for Computing I

(Winter 2019)

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: Wednesday 1:30-3:30
Or contact me after class or by e-mail to make an appointment. I will continue my office hours up to Wednesday April 10.

Course Teaching Assistants

TA office hours will begin on Monday January 14. All office hours will be held in Goodwin Hall room 241. TA office hours will end on April 3.
The following table lists all the teaching assistants and their office hours. Office hours will all be held in Goodwin Hall room 241.

Name Day Time
Jacqueline Heaton Monday 11:30 - 13:30
Meggie Hodgson Monday 14:30 - 16:30
Rebecca Hisey Tuesday 10:30 - 12:30
Yao Kundi Tuesday 13:30 - 15:30
Leo Toueg Wednesday 10:30 - 12:30

Class Hours and Locations

Classes will be held in Kingston Hall room 201. You can get detailed instructions to find the class here.
Monday 9:30-10:30
Wednesday 8:30-9:30
Thursday 10:30-11:30


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

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

I use both of these books, but you should view the Schaum's notes as the only required book. 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.
The quizzes will be scheduled as follows:
Quiz 1: Thursday, February 7.
Quiz 2: Thursday, March 7.
Quiz 3: Thursday, March 28.
Please make every effort to be present for the midterm quizzes. However, writing any of the quizzes is up to you, all quizzes are optional. At the end of the term I will tally four grades for everyone in the class as follows.
1. 3 quizzes 20% each and 40% Final.
2. Best 2 quiz grades 20% each and 60% Final.
3. Best single quiz grade 20% and 80% Final
4. 100% Final.
You will then get the maximum of the grades 1, 2, 3, or 4, with the exception that if you get 49% or less on the final exam, then that will be your grade.

Calculator Policy

Calculators, scrap paper, or anything other than pencils, pens, and/or erasers, 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 (Fall 2018), 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.
Monday, January 7
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.
Homework 1

Wednesday, January 9
Thursday, January 10

Week 2
Laws of Set Theory, Indexed Sets, Principle of Inclusion and Exclusion
Notes for week 2.
Monday, January 14
Solutions Homework 1
Homework 2
Wednesday, January 16
I have updated the notes for week 2 and reposted them today.
Thursday, January 17

We completed the notes for week 2, and move on to the notes for week 3.
Week 3
Mathematical Induction
Notes for week 3.
Monday, January 21
Homework 3
Solutions Homework 2
Wednesday, January 23
Thursday, January 24
Week 4
Notes for week 4.
Monday, January 28
Solutions Homework 3
Homework 4
Wednesday, January 30
Thursday, January 31
Week 5
Notes for week 5.
Monday, February 4
Solutions Homework 4
Homework 5
Wednesday, February 6
Thursday, February 7
Quiz 1 is based on homework 1, 2, 3, and 4. The quiz will be held in two separate rooms, our classroom Kingston Hall room 201, and also in the Humphrey Hall auditorium. Check your Queen's email for a message informing you which room to go to. The quiz runs from 10:30-11:20. 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, scrap paper, or anything other than pen, pencil, and/or erasers are permitted for this quiz, or any of the others.
Week 6
Integers, Primes
Notes for week 6.
Monday, February 11
Solutions Homework 5.
Solutions to Quiz #1
Homework 6
Wednesday, February 13
Thursday, February 14
Monday, February 18
Wednesday, February 20
Thursday, February 21
Week 7
Congruence Relations, Counting.
Notes for week 7.
Monday, February 25
Solutions Homework 6
Homework 7
Wednesday, February 27
Thursday, February 28
Week 8
Principles of Counting, The Binomial theorem
Notes for week 8.
Monday, March 4
Solutions Homework 7
Homework 8
Wednesday, March 6

Thursday, March 7
Quiz 2 is based on homework 5, 6, and 7. The quiz will be held in two separate rooms, our classroom Kingston Hall room 201, and also in the Humphrey Hall auditorium. The quiz runs from 10:30-11:20. 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, scrap paper, or anything other than pen, pencil, and/or erasers are permitted for this quiz, or any of the others.

Week 9
Binomial Coefficients. Fibonacci numbers.
Notes for week 9.
Monday, March 11
Homework 9
Solutions Homework 8
Solutions to Quiz #2
Wednesday, March 13

Thursday, March 14
Week 10
Propositional Logic
Notes for week 10.
Monday, March 18
Homework 10.
Solutions Homework 9
Wednesday, March 20
Thursday, March 21
Week 11
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, March 25
Solutions Homework 10
I have attached a copy of a sample final exam for practice. I will go over the solutions next Monday. 2014 Final Exam
Wednesday, March 27

Thursday, March 28
Quiz 3 is based on homework 8, 9, and 10. The quiz will be held in two separate rooms, our classroom Kingston Hall room 201, and also in the Humphrey Hall auditorium. The quiz runs from 10:30-11:20. 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, scrap paper, or anything other than pen, pencil, and/or erasers are permitted for this quiz, or any of the others.
Week 12
Wrap up and Review
Monday, April 1
2014 Final Exam Solutions
Solutions to Quiz #3
Wednesday, April 3

Thursday, April 4

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