CISC-102: Discrete Mathematics for Computing I

(Fall 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: Tuesday 12:30-2:30
Or contact me after class or by e-mail to make an appointment.

Course Teaching Assistants

Teaching assistants will all hold their office hours in Goodwin Hall room 230.
Teaching assistant office hours will commence on September 9 and run until the last week of classes, November 25 - 29.
I will hold my normal office hours on Tuesday Dec. 3 from 12:30-2:30
The Computing Students Association (COMPSA) will be holding a special tutorial session for students of CISC 102 on Monday Dec. 2 from 1:30-3:30 in Dunning Hall room 27.
Name Day Time
Zhiwei Fu Monday 9:30 - 11:30
Leo Toueg Monday 11:30 - 1:30
Joey Sun Monday 1:30 - 3:30
Catherine Wu Tuesday 9:30 - 11:30
Wissam Ghoudi Tuesday 11:30 - 12:30
Ronny Rochwerg Tuesday 3:30 - 5:30
Joseph Lumney Tuesday 4:30 - 6:30
Sam McPhail Tuesday 5:30 - 7:30
Aleks Jugovic Tuesday 6:30 - 8:30
Yudong Zhou Wednesday 2:30 - 4:30
Shiyao Long Wednesday 4:30 - 6:30
Wissam Ghoudi Thursday 11:30 - 12:30
Emily Hunter Thursday 12:30 - 2:30
Vedant Srinivasan Kartik Srinivasan Thursday 2:30 - 4:30
A B M Bodrul Alam Thursday 4:30 - 6:30

Class Hours and Locations

Classes will be held in the Biosciences Auditorium (also know as BIO 1101). You can get detailed instructions to find the class here.
Tuesday 8:30-9:30
Wednesday 10:30-11:30
Friday 9:30-10:30


(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 about $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.
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: Wednesday, October 2.
Quiz 2: Wednesday, October 30.
Quiz 3: Wednesday, November 27.
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 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 year (Winter 2019), 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 0
Introduction, Notation, Set Theory, Counting Problems
Notes for week 1.
Please read the lecture notes for week 1, the readings posted for homework, and work on homework 1 so that you finish it by Friday September 13.
Homework 1
Tuesday, September 3
Wednesday, September 4
Friday, September 6
We get a head start on lecture notes for week 1.
Week 1
Introduction, Notation, Set Theory, Counting Problems
Notes for week 1.
Please read the lecture notes for week 1, the readings posted for homework, and work on homework 1 so that you finish it by Tuesday September 17.
Tuesday, September 10
Sets and subsets.
Wednesday, September 11
Set operations, permutations, and combinations.
Friday, September 13
We will get a head start on the notes for week 2.
Week 2
Laws of Set Theory, Indexed Sets, Principle of Inclusion and Exclusion
Please read the lecture notes for week 2, the readings posted for homework, and work on homework 2 so that you finish it by Friday September 20.

Notes for week 2.
The notes for week 2 have been updated on September 17.
Homework 2
Tuesday, September 17
Solutions to Homework 1
Wednesday, September 18
Friday, September 20
We will get a head start on the notes for week 3.
Week 3
Mathematical Induction
Homework 3
Notes for week 3.
Tuesday, September 24
Solutions to Homework 2
Wednesday, September 25
Proofs by mathematical induction
Friday, September 27
More proofs by mathematical induction.
Week 4
Notes for week 4.
Homework 4
Tuesday, October 1
Solutions Homework 3
Wednesday, October 2
Quiz #1 based on Homework 1, 2 and 3.
Friday, October 4
Week 5
Notes for week 5.
Homework 5
Tuesday, October 8
Quiz 1 solutions
Wednesday, October 9
Solutions Homework 4.
Friday, October 11
Week 6
Chapter 11. Properties of the Integers
Notes for week 6.
Homework 6.
Tuesday, October 15
Wednesday, October 16
Solutions Homework 5
Friday, October 18
Week 7
Chapter 11. Properties of the Integers
Notes for week 7 same as for week 6.
Homework 6.
Tuesday, October 22
Wednesday, October 23
Friday, October 25
Week 8
Congruence Relations
Notes for week 8
Homework 7
Tuesday, October 29
Solutions Homework 6
Wednesday, October 30
Quiz #2 based on homework 4, 5, and 6.

Friday, November 1

Week 9
Chapter 5. Counting, Permutations, Combinations, Binomial Coefficients.
Notes for week 9.
Homework 8
Tuesday, November 5
Solutions to Quiz #2
Wednesday, November 6
Solutions Homework 7

Friday, November 8
Week 10
Binomial Theorem, Pascal's Triangle, Propositional Logic
Notes for week 10.
Homework 9.
Tuesday, November 12
Solutions Homework 8
Wednesday, November 13
Friday, November 15
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 )
Tuesday, November 19
Solutions Homework 9
Wednesday, November 20

Friday, November 22

Week 12
Wrap up and Review
Tuesday, November 26
2014 Final Exam for practice and review. Solutions will be presented on Friday November 29.
Wednesday, November 27
Quiz #3 based on homework 7,8, and 9.

Friday, November 29
Solutions to Quiz #3
2014 Final Exam Solutions

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