MTHE 217 - Algebraic Structures with Applications
Office: Jeffery Hall, Room 402
Tuesday 3:30 (Jeffery 127), Wednesday 9:30 (Jeffery 126), Thursday 4:30 (Jeffery 127).
Monday 11:30 -- Jeffery Hall, Room 127.
(Tutorials will be run by the TA. They are devoted
for quizes, solving illustrative problems and for students to ask questions
about the course material.)
- The course will have 10 homeworks in total.
The homeworks will not be collected. However, a problem from the homeworks
(or a variation thereof) will appear in the corresponding quiz.
Solutions to the homeworks will be posted after their corresponding quiz was held.
- The course will have 4 quizzes, each 20 minutes long and worth 5%.
Each quiz will be held at the beginning of a tutorial lecture.
The schedule of quizzes is available here.
Thursday 1:30 - 2:30, or by appointment.
Students are also welcome to drop by the
Math Help and Study Center (Jeffery Hall, Room 201) to ask for help
from dedicated tutors (appointments are not required).
Textbook and Notes
Online Lecture Notes (by. F. Alajaji and A. Hoefel):
J. F. Humphreys and M. Y. Prest, Numbers, Groups and Codes,
Second Edition, Cambridge University Press, 2004.
Midterm Exam: 30%
Final Exam: 50%
The Midterm Exam is
scheduled for Week 8: Tuesday, October 31, 2017.
All assignments and exams in this course will receive numerical marks. The final
grade students receive for the course will be derived by converting their numerical
course average to a letter grade according to the
Queens Official Grade Conversion Scale.
Policy for Missing Exams:
There will be no
makeup exams. If a student misses the midterm
due to severe illness or a personal tragedy, then
the final exam will count towards 80% of the
Students with Special Needs:
Students with diverse learning styles and needs are welcome at Queen's. In
particular, if you have a disability or health consideration that may require
accommodations, please feel free to approach me and/or
Queen's Student Accessibility Services.
Academic integrity is constituted by the five core fundamental values of honesty,
trust, fairness, respect and responsibility.
These values are central to the building, nurturing and sustaining of an academic
community in which all members of the community will thrive. Adherence to the values
expressed through academic integrity forms a foundation for the "freedom of inquiry
and exchange of ideas" essential to the intellectual life of the University.
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 on these websites:
Arts and Science
Engineering and Applied Science.
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.
The purpose of the course is to provide an introduction to elementary abstract
algebraic systems, and to illustrate the concepts with engineering applications.
Topics covered are:
- Propositional logic, valid arguments, methods of proof;
applications to switching and logic circuits.
- Quantifyers, set theory.
- Equivalence relations and mappings.
- The integers: mathematical induction,
primes and factorization,
the division algorithm, greatest common divisors,
congruence classes and modular arithmetic.
- Group theory: groups, subgroups,
cyclic groups, cosets and Lagrange's theorem, normal subgroups,
homomorphisms and isomorphisms.
- Applications to error-control codes:
binary block codes for noisy communication channels,
Hamming distance, nearest neighbor decoding,
code error detection/correction capabilities, group (linear) codes,
coset decoding, generator and parity check matrices, syndrome decoding.
- Introduction to other algebraic structures:
rings, fields, vector spaces, boolean algebras (time permitting).