
Professor Alexandru I. Suciu 

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
 Week 1:
Lecture 1,
Lecture 2,
Lecture 3,
Lecture 4
 Week 2:
Lecture 5,
Lecture 6,
Lecture 7,
Lecture 8
 Week 3:
Lecture 9,
Lecture 10,
Lecture 11,
Lecture 12
 Week 4:
Lecture 13,
Lecture 14,
Lecture 15,
Lecture 16
 Week 5:
Lecture 17,
Lecture 18,
Lecture 19,
Lecture 20
 Week 6:
Lecture 21,
Lecture 22,
Lecture 23,
Lecture 24

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


Handouts
Exams
