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 introduce students to the basic concepts and methods of abstract algebra through the study of groups, rings, and fields. Motivation will come from number theory and geometry.
A second 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.
The textbook has not yet been chosen.
THIS COURSE IS INTENDED PRIMARILY FOR STUDENTS WHO HAVE TAKEN THE HONOURS VERSIONS OF FIRST AND SECOND YEAR COURSES.
The prerequisite is MATH2021.03/2022.03 (formerly MATH2000.06), MATH2221.03/MATH2222.03 (formerly MATH2220.06) or ACMS2010.06, or permission of the instructor.
The final grade will be based on assignments, class participation, class tests and quizzes, and a final examination.
The grade breakdown has not yet been determined.