CISC-102: Discrete Mathematics for Computing I

(Fall 2017)

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

Additional TA Office hours,

Normal TA office hours stopped at the end of term. However, there will be several more TA office hours during the month of December as follows:

Swawibe Ul Alam
Friday, December 8, 13:30-15:30

Mathew Holden
Friday, December 8, and Friday December 15, 11:30-13:30

Course Instructor

David Rappaport
E-MAIL: daver AT cs dot queensu dot ca
OFFICE HOURS: Tuesday 13:30-15:30
Or contact me after class or by e-mail to make an appointment.
Please note: I will be available for office hours on Tuesday Dec. 5, but not on Tuesday Dec. 12.

Course Teaching Assistants

All TA hours including my own office hours will be held on Monday and Tuesday. The hours will commence on Monday September 18.
Rebecca Hisey
OFFICE HOURS: Monday 12:00-13:00

Swawibe Ul Alam
OFFICE HOURS: Monday 13:00-15:00

Meggie Hodgson
OFFICE HOURS: Monday 15:00-16:00

Maxwell Keleher
OFFICE HOURS: Monday 16:00-17:00

Katherine Baillie
OFFICE HOURS: Tuesday 11:30-12:30

Chuck Fu
OFFICE HOURS: Tuesday 12:30-13:30

Mathew Holden
OFFICE HOURS: Tuesday 14:00-16:00

Benjamin Lee
OFFICE HOURS: Tuesday 16:00-17:00

Alex Jin
OFFICE HOURS: Tuesday 18:00-19:00

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.
Monday 10:30-11:30
Wednesday 9:30-10:30
Friday 8:30-9:30


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 in class midterm quizzes, each worth 15%, 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 4: Wednesday, October 4.
Quiz 2: Week 6: Wednesday, October 18. Week 7: Wednesday, October 25.
Quiz 3: Week 9: Wednesday, November 8.
Quiz 4: Week 12: Wednesday, 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 miss a quiz. If you miss one or more quizzes then the marking scheme will be revised for you as follows:
1 missed - 3 quizzes 15% each and 55% final.
2 missed - 2 quizzes 15%, and 70% final.
3 missed - 1 quiz 15% and 85% final.
4 missed - 100% 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 year (Fall 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 18.
Monday, September 11
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.
Wednesday, September 13

Friday, September 15

Week 2
Laws of Set Theory, Indexed Sets, Principle of Inclusion and Exclusion
Notes for week 2.
Monday, September 18
This morning Carly D'Amico, Promotions and Administrative Coordinator of Queen's Student Academic Success Services gave a presentation to the class. This is a link to an image of the fact sheet that was shown on the data projector.
Solutions Homework 1
Homework 2
Wednesday, September 20
Set cardinality, the power set, partitions of a set, indexed sets.
Friday, September 22

Indexed Sets reviewed. The Principle of Inclusion and Exclusion.
Week 3
Mathematical Induction
Notes for week 3.
Monday, September 25
Homework 3
Solutions Homework 2
Note taker(s) needed. Please see the announcement from Queen's Student Accessibility Services
Wednesday, September 27
Mathematical induction.
Friday, September 29
More mathematical induction. Notes for week 3 have been updated.
Week 4
Notes for week 4.
Monday, October 2
Solutions Homework 3
Wednesday, October 4
Quiz #1 based on Homework 1, 2 and 3. The quiz will be held in class. Please arrive a bit early so that we can start the quiz at 9:30 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.
Friday, October 6
Homework 4
Week 5
Notes for week 5.
Monday, October 9
Wednesday, October 11
I will post solutions to Quiz #1 and to Homework 4 after I go over them in class today.
Solutions Homework 4
Solutions to Quiz #1
Friday, October 13
Homework 5
Week 6
Integers, Primes, G.C.D., L.C.M.
Notes for week 6.
Monday, October 16
Wednesday, October 18
Friday, October 20
I will go over solutions to homework 5 today.
Solutions Homework 5.
Homework 6.
Week 7
Prime numbers, Congruence Relations
Notes for week 7.
Monday, October 23
Wednesday, October 25
Quiz #2 based on homework 4 and 5.
Friday, October 27
I will go over solutions to homework 6 today.
I completed the notes for week 7. I will do solutions to homework 6 and homework 7 next Monday.
Homework 7.
Week 8
Counting, Binomial coefficients
Notes for week 8.
Monday, October 30
Solutions to homework 6 and 7.
Solutions Homework 6
Solutions Homework 7
Wednesday, November 1
Solutions Quiz 2
Homework 8
Friday, November 3
Week 9
Counting, pigeon hole principle, the binomial theorem
Notes for week 9.
Monday, November 6
Solutions Homework 8
Wednesday, November 8

Quiz #3 based on Homework 6, 7 and 8. Please arrive a bit early so that we can start the quiz at 9:30 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.
Friday, November 10
The binomial theorem, and the pigeon hole principle.
Homework 9
Solutions to Quiz #3

Week 10
Pascal's Triangle, Propositional Logic
Notes for week 10.
Monday, November 13
Wednesday, November 15
Solutions Homework 9

Friday, November 17
Homework 10
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 20
Homework 11. Note this homework is only reading, with no problems to solve.
Wednesday, November 22
Solutions Homework 10
Friday, November 24
Week 12
Wrap up and Review
Monday, November 27
2014 Final Exam
Wednesday, November 29
Quiz #4
Quiz #4 based on Homework 9 and 10. Please arrive a bit early so that we can start the quiz at 9:30 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.

Friday, December 1
Final review
Solutions to Quiz #4
2014 Final Exam Solutions

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Students are responsible for familiarizing themselves with the regulations concerning academic integrity and for ensuring that their assignments conform to the principles of academic integrity. Information on academic integrity is available in the Arts and Science Calendar (see Academic Regulation 1 ), on the Arts and Science website (see Academic Integrity ), and from the instructor of this course. Departures from academic integrity include plagiarism, use of unauthorized materials, facilitation, forgery and falsification, and are antithetical to the development of an academic community at Queen's. Given the seriousness of these matters, actions which contravene the regulation on academic integrity carry sanctions that can range from a warning or the loss of grades on an assignment to the failure of a course to a requirement to withdraw from the university.

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