MATH 3175 Group Theory

  • Last modification date Updated On April 26, 2024

Spring 2024

Course Information

CourseMATH 3175 · Group Theory · CRN 41595 · Section 3
InstructorAlex Suciu
Course Web Sitehttps://suciu.sites.northeastern.edu/courses/math-3175-group-theory/
Time and Place544 Nightingale Hall – Tuesday and Friday, 1:35 pm–3:15 pm
Office435 LA – Lake Hall
Emaila.suciu@northeastern.edu
Office HoursTuesday 3:25pm–4:25pm and Friday 12:25pm–1:25pm, or by appointment
Prerequisites:MATH 2331, Linear Algebra and MATH 2321, Calculus 3
TextbookAbstract Algebra, 4th Edition (2019) by John A. Beachy & William D. Blair, Waveland Press, ISBN: 9781478638698
Course DescriptionThis course is an introduction to the theory of groups. Groups are algebraic structures that describe
symmetries of objects that appear in mathematics, physics, chemistry, and other sciences. Topics include:

* The definition of a group using axioms and deriving properties of groups from it.
* Important classes of groups such as abelian groups, cyclic groups, dihedral groups and permutation groups.
* The structure theorem for finite abelian groups.
* Product groups, subgroups, normal subgroups and quotient groups.
* Cosets of subgroups and the Lagrange Theorem.
* Group homomorphisms and isomorphism theorems for groups.
* Actions of a group on a set and the Sylow theorems.

The theory will be illustrated by examples from geometry, linear algebra, and combinatorics, and applications will be discussed. The course will cover Chapters 1, 2, 3 and Chapter 7 up to §7.5 of the textbook, with §7.6 and §7.7 as optional topics.
Course GoalsStudents will understand the basic ideas and some applications of groups, and will be able to explain groups, factor groups, and their relation to symmetry. Students will recognize mathematical objects that are groups, and be able to classify them as abelian, cyclic, direct products, etc. Students will understand homomorphisms and quotients of groups, as well as group actions on a set, orbits and stabilizers, conjugacy, and be able to determine when a group has a normal subgroup. Students will be able to reason mathematically, to write simple proofs, and be able to judge whether an attempted proof in group theory is correct/complete.
Coursework and GradesThe coursework consists of quizzes and homework assignments (40% of grade), a midterm exam (20%), and a final exam (40%).

Assignments

Exams

Class Materials

Handouts
Summer 2022
Summer 2020
Fall 2010