Introduction
to the basic concepts of abstract algebra, with applications:
groups (cyclic, symmetric, Lagrange's theorem, quotients, homomorphism
theorems); rings (congruences, quotients, polynomials, integral domains,
PID's and UFD's); fields (field extensions,
constructions with ruler and compass, coding theory).
Algebra is the study of algebraic systems, that is, sets of
elements endowed with certain operations. A familiar example is
the set of integers with the operations of addition and
multiplication.
Algebra is used in almost every branch of mathematics; indeed, it
has simplified the study of mathematics by indicating connections
between seemingly unrelated topics. In addition the success of
the methods of algebra in unravelling the structure of
complicated systems has led to its use in many fields outside of
mathematics. One aim of this course is to help students learn to write
clear and concise proofs, read the mathematical literature, and
communicate mathematical ideas effectively, both orally and in
writing.
Any student who performed well in the prerequisite linear algebra
course is welcome to enrol, but
THIS COURSE IS INTENDED PRIMARILY FOR STUDENTS WHO HAVE TAKEN THE HONOURS VERSIONS OF FIRST AND SECOND YEAR COURSES.
The text will be Fraleigh, (6th
Ed.), AddisonWesley Longman.
The final grade will be based on assignments, class participation,
quizzes, class tests, and a final examination.
Prerequisite:AS/SC/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0.
Exclusion:AK/MATH 3420 6.0
Coordinator: J.W. Pelletier.
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