Abstract Algebra, by Beachy and Blair Professor Alexandru I. Suciu Abstract Algebra, by Beachy and Blair
MATH 3175 · Group Theory
Summer 2, 2020

* Course Information

Course MATH 3175 · Group Theory: CRN 60442, Section 1
Instructor Alex Suciu
Course Web Site web.northeastern.edu/suciu/MATH3175/ugroup.su20.html
Time and Place Mon, Tue, Wed, Th 9:50am–11:30am, on Zoom (through Canvas)
Email a.suciu@northeastern.edu
Office Hours Tuesday 12 Noon–3 pm on Zoom (through Canvas)
Teaching Assistant Tomas Skacel
Undergraduate Math Mentor Karthik Boyareddygari
Prerequisites: MATH 2331, Linear Algebra and MATH 2321, Calculus 3
Textbook Abstract Algebra, 4th Edition (2019) by John A. Beachy & William D. Blair, Waveland Press, ISBN: 1478638699
Course Description The course introduces some of the basic ideas of Group Theory, including symmetry groups, abelian, cyclic, and permutation groups, as well as subgroups, normal subgroups, group homomorphisms, quotient groups, direct products, group actions 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. We will cover parts of preparatory Chapters 1 & 2 and then Chapters 3 & 7 from the textbook, emphasizing group actions on a set as a unifying theme.
Course Goals Students 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.
Grade Based on homework (50%), midterm exam (20%), and final exam (30%).

* Class Materials

Lectures

Homework assignments

    Rules, explanations, and assignments by Tomas Skacel, solutions by Karthik Boyareddygari

Handouts

Exams


Department of Mathematics Office: 441 Lake Hall Messages: (617) 373-2450
Northeastern University Phone: (617) 373-3833 Fax: (617) 373-5658
Boston, MA, 02115 Email: a.suciu@northeastern.edu Directions

Home Started: April 28, 2020
Last modified: August 6, 2020
web.northeastern.edu/suciu/MATH3175/ugroup.su20.html