MATH 3GR3, Fall 2018
The goal of this course is to introduce the fundamental objects of abstract algebra: rings and groups. Rings and groups are important objects that appear in many branches of mathematics. Group theory has its roots in the study of roots of polynomials and plays a central role in the study of symmetry. Ring theory has some of its origins in the study of prime numbers, and plays a pivotal role in current areas of research like algebraic geometry. In this course we will illustrate the definitions of groups and ring with numerous examples (the set of all integers has both a ring structure and a group structure). By the end of the course, you will be introduced to some of the standard terminology to related to groups and rings (e.g., subgroups, subrings, group and ring homomorphisms, quotient groups and rings), and be introduced to important families of groups and rings (e.g., symmetric and alternating groups, integral domains, and fields). Another aim of this course will be to explore and understand various proof techniques. The prerequisite for this course is MATH 2R03. Students will be evaluated using a set of graded assignments, midterm tests, and a final exam.
INSTRUCTOR: A. VanTuyl
An introduction to groups and rings, with an emphasis on concrete examples. Topics include: groups, subgroups, normal subgroups, quotient groups, group homomorphisms, First Isomorphism Theorem for groups, symmetric and alternating groups, rings, subrings, ideals, quotient rings, ring homomorphisms, and the First Isomorphism for rings.
Three lectures, one tutorial (one hour); one term
Prerequisite(s): MATH 2R03
Antirequisite: MATH 3E03
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