Mathematical Reasoning

Brock University

Introduction to mathematical INDGraction, logic and proofs including mathematical induction.

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Basil Nanayakkara

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MATH 1P66 Lecture 25: Boolean Arithmetic

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Mathematics and Statistics
Basil Nanayakkara

MATH 1P66 Syllabus for Basil Nanayakkara — Fall 2018

Brock University - Department of Mathematics & Statistics
Math 1P66: Mathematical Reasoning - Fall 2018
Lectures:section 1: Tuesdays and Thursdays 3:30 - 4:45 pm
section 2: Wednesdays 11:30 am - 12:45 pm and Fridays 12:30 - 1:45 pm
(All the lectures will be in TH325.)
Instructor: Basil Nanayakkara
Email: bnanayakk[email protected]
Office: MCJ 401
Office hours: Mondays 11:15 am - 12:15 pm
Tuesdays 12:45 - 3:15 pm
Wednesdays 10:15 - 11:15 am
Fridays 2:15 - 3:15 pm
Learning Centre: Math Learning Centre hours can be found on the course website.
MLC is located in MCJ434.
Teaching Assistants: Arezoo Rezaei ([email protected], Leila Meskine ([email protected],
Jared Wu ([email protected] and Yucen Jin ([email protected])
TEXT:Discrete Mathematics and its applications by Kenneth Rosen, eighth edition, McGraw Hill.
PREREQUISITE: MATH 1P20 or one grade 12 mathematics credit.
ASSIGNMENTS: There will be four assignments, each worth 2.5% of your final grade. Assignments
must be dropped off in the dropbox designated for the course by 12:00 noon on the due date. The
dropbox is located in front of MCJ 434, by the water fountain. Late assignments and electronic
submissions will not be accepted. A cover page must be attached to your assignment. The cover
page should state your name (first and last in full), student id number and the course code. Please
staple the completed assignment at the upper left corner. Please write only on one side of the
paper, and do not write in two (or more) columns.
TESTS: There will be a midterm test on Saturday, October 20th (1:00 - 3:00 pm). This midterm test
is worth 40% of your final grade.
The final exam will be held in December. The exact date and time will be determined by the registrar’s
office by mid-November. This exam is worth 50% of your final grade.
Calculators, textbooks and the like are not allowed on the midterm test and the final
exam. You must be able to produce your student ID card during the tests.
It is the student’s responsibility to write the examinations at the scheduled times. If the midterm test
is missed due to a legitimate reason, a make-up test is not given. Instead, the weight of the test will
be transferred to the final exam.
Four assignments (each worth 2.5%) 10%
Midterm test 40%
Final exam 50%
Total 100%
Note 1: Overriding these weights, a candidate must obtain at least 40% on the final examination in
order to pass the course.
Note 2: If you have an average of 50% or more going into the final exam, and if it is to your
advantage, then the final exam will count 100%.
Assignment 1 Due Friday, Sept. 21st, 12:00 noon
Assignment 2 Due Friday, October 5th, 12:00 noon
Midterm test Saturday, October 20th (1:00 - 3:00 pm)
Assignment 3 Due Friday, November 2nd, 12:00 noon
Assignment 4 Due Friday, November 16th, 12:00 noon
Final exam (in December)
Propositional Logic: Propositions, logical operators, conditional statements, compound proposi-
Logical equivalences: introduction, equivalence laws
Predicate Logic: introduction, quantification.
Proofs: Direct proofs, proof by contraposition, proof by contradiction, proof by cases, constructive
proofs, nonconstructive proofs
Sets: introduction, notations, equality of sets, Venn diagrams, cardinality, power sets, cartesian
product, set operations, set identities.
Set Equalities and Functions: Proving set equalities, introduction to functions, one-to-one func-
tions, onto functions, inverse of a function, composition of functions
Mathematical Induction: Principle of mathematical induction, examples, induction in non-numerical
settings, strong induction.
Selected Topics: countable sets, uncountable sets, Boolean algebra
PLAGIARISM: PLEASE READ CAREFULLY. You are encouraged to discuss general ideas
and compare answers with other students. However, you must do your own computation and express
ideas in your own words. Note that any form of cheating (use of unauthorized materials in examinations,
impersonation, copying, etc.) is punishable by a grade of zero for all students involved, and that repeat
offenders may be expelled from the university. Please refer to the university calendar for details.

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