Math 335: Abstract Algebra I, Fall 2023
Instructor: Noah
Aydin
Office/Phone: RBH 319 / 5674
Office Hours: MWF: 10:10-12pm; F: 10:10-11am and by appointment. Here
is my weekly schedule.
Textbook: A
first course in Abstract Algebra, (e-book) J. B. Fraleigh, 8th ed,
Pearson, ISBN: 9780135859759.
Room & Time: RBH 215, MWF 9:10-10 am
Course Description: Abstract Algebra is one of the principle branches of modern mathematics. It is the study of general properties of algebraic structures. The abstraction refers to the perspective taken in the subject, which is very different from that of high school algebra courses. Rather than looking for the solutions to a particular problem, we will be interested in such questions as: When does a solution exist? If a solution does exist, is it unique? What general properties does a solution possess? What general properties are common between different algebraic structures? Our exploration will go beyond such algebraic structures as the integers and the real numbers, and our approach will be axiomatic. Indeed, working from a fairly small set of axioms one can describe the properties of a wide range of algebraic structures concisely and elegantly. Focusing on group theory, our study will be motivated by the desire to describe algebraic structures in a rigorous, concise, and elegant way. Rigorously proving theorems and writing formal proofs in the context of axiomatic algebraic systems is a major goal of this course as well as communicating proofs and solutions to problems orally. Group theory also allows us to quantify various types of symmetries so prevalent in the world around us. In fact, abstract algebra turns out to have a surprisingly wide range of applications some of which will be briefly discussed. We will cover most of the topics in sections 1-17 in the textbook. These chapters include the following topics: Binary operations, groups, subgroups, cyclic groups, permutation groups, group isomorphisms, cosets and the theorem of Lagrange, finitely generated Abelian groups, homomorphisms, factor groups, groups actions, isomorphism theorems, Sylow theory. The course will focus on theory, proof writing and problem solving. Active learning methods will be used throughout the semester. Prerequisite: Math 222 or equivalent.
Teaching Philosophy and Expectations
General Course Information and Syllabus
Course Calendar, Hmw and Reading Assignments