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

Handouts

 Handout 1: Latin squares and Cayley tables Handout 2: The dihedral groups

Exams

 Practice quizzes and exams (from an old syllabus) Midterm Exam Final Exam: Will be administered on Monday, August 17, from 8am to 10am

 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