Math 417 Introduction to abstract algebra, Spring 2020.

Textbook: A first course in abstract algebra, seventh edition, by John B. Fraleigh.
Class time: MWF 2:00pm-2:50pm
Class location: 141 Altgeld Hall

Professor: Igor Mineyev, 243 Illini Hall. Email is not very efficient for discussions. Please talk to me before/during/after classes and come to office hours.
Office hours: See below.


Because of COVID19, this course and many other courses will transition to an online format, at least for the two weeks after the spring break. I am learning what can and will be done. Prepare for a wild ride. We will need to implement a least-disruptive plan possible. As we proceed, more information will be posted here, please check this page in the coming days and weeks.
About the course. Below is a tentative list of topics to be covered.

The Integers Division algorithm. Greatest common divisor. Fundamental theorem of arithmetic. Congruence arithmetic. Permutations Cycle decomposition. Order of a permutation. Even and odd permutations. Group Theory Definition and examples. Subgroups, cosets and Lagrange's theorem. Normal subgroups and quotient groups. Homomorphisms. The Isomorphism Theorems. Group Actions. Cayley's theorem. Burnside's theorem. Conjugacy classes and centralizers. Applications of group actions, eg. to Sylow's theorem. Ring Theory I Definition and examples. Polynomial rings. Subrings, ideals and quotient rings. Homomorphisms of rings. The Isomorphism Theorems for rings. Integral domains and fields. Division algorithm for polynomial rings over a field. Roots of polynomials and the Remainder Theorem. The Fundamental Theorem of Algebra (without proof). Maximal ideals in polynomial rings over fields, with application to the construction of fields.

Homework will be listed here. If a newer version does not show up, restart your browser.

Exams and grades. Do not miss the exams. There will be two midterm exams at the regular class time:

The highest-score midterm exam will count as 25%, the homework 25%, the project 20%, and the final exam 30%. One lowest midterm exam and two lowest homework assignments will be dropped at the end of the semester to allow for emergency situations. Do not miss classes, exams or homework. If you miss seven or more classes during the semester (counting regular classes, midterms, and the final exam), a failing grade will be assigned at the end of the course regardless of performance during the semester. To see your current score for the class, click on the "Score Reports" link on the left in www.math.illinois.edu/Classes/, then enter your password. The dropped assignments and exams will be marked with "**" at the end of semester.

The project. Closer to the second half of the semester, the students will be randomly split into groups to work on a project, to write a report, and to present it to the class closer to the end of the semester. Select the topic of your project early and start working on it now. Take initiative, discuss it with me and others in advance. The main requirements for the project: