Syllabus

A PDF version of this syllabus is available here.

Lectures

Recitations

Instructor

Note: I am teaching two different courses this semester. To keep office hours more organized, please try to come to my office hours between 3-4 PM with questions about this course. However, if you need to come before 3 PM, it is fine as well.

TA

Learning outcomes

The goal of this course is to introduce basic notions and methods of abstract algebra. Course topics include:

• Definition and elementary properties of groups.
• Cyclic groups, dihedral groups, symmetric groups.
• Homomorphisms and isomorphisms of groups.
• Subgroups
• Direct products of groups.
• Cosets, Lagrange theorem.
• Normal subgroups and quotient groups.
• Isomorphism theorems.
• Classification of finitely generated abelian groups.
• Rings.
• Ideals of rings and quotient rings.
• Ring homomorphisms.
• Integral domains.
• Polynomial rings.
• Fields.

Prerequisites

The main expectation is that students taking this course are familiar with reading and writing mathematical proofs to the extent that is covered in MTH 311. We will also use some notions related to sets and functions (also typically covered in MTH 311), as well as some elementary number theory (divisibility of integers, the greatest common divisor etc.). From time to time we will also use linear algebra (matrices, determinants, vector spaces etc.). These topics are cover in MTH 309.

Textbook

Joseph A. Gallian, Contemporary Abstract Algebra.

This book is currently in the 11th edition, but any older edition is just as fine - they all cover the same material and changes between various editions are mostly cosmetic.

I will also provide my own notes that will be posted here.

Grading

Homework

Homework problems will be assigned every week. You can collaborate on homework problems with other students in this course, but you must write solutions entirely on your own. Copying solutions from other students or from any other sources is a violation of the UB academic integrity policy and may result in academic sanctions (reduction of the course grade, course failure etc.). Any use of generative AI (Chat GPT etc.) for homework problems is prohibited.

Exams

Incomplete Grades

See the UB Catalog for the UB Incomplete Policy.

Academic Integrity

See the UB Catalog for the UB Academic Integrity Policy.

Accessibility Resources

If you need accommodations due to a physical or learning disability please contact the UB Accessibility Resources Office to get help with making appropriate arrangements.