Teaching

Fall 2019

In the Fall semester 2019, I will be teaching MATH-UA.0343-003 Algebra.

Lectures:

MW 9:30-10:45pm in CIWW 202. Recitation F 9:30-10:45 in CIWW 102.

Contact information:

Office 604
bilu @ cims.nyu.edu (remove blank spaces around @)

Office hours:

M 10:45-11:45am and Th 10:30-11:30, or by appointment.

Contents of the course:

This is a course in Abstract Algebra. It will be centered on the notion of group, with examples coming from number theory, linear algebra and geometry. After some reminders on set theory, we will start with a chapter on arithmetic and congruences in order to introduce a very important example of group, Z/nZ. We will go on to give the definition of a group and derive some of its main properties. Then we will give a whole other new set of examples, called permutation groups. After that,
we will introduce more advanced topics, among which cosets, normal subgroups, quotient groups.
The syllabus for this course can be found here.

Notes

Current version Remarks or questions welcome! Pay attention to the fact that these notes are an abridged version of what has been seen in class, and, in particular, do not contain some of the proofs. If you've missed a lecture, make sure to borrow someone's notes.

Recommended books

I do not require a textbook for this course, but a good reference is Judson's Abstract Algebra, available online here.

Homeworks:

Homeworks are always due in the beginning of Wednesday's class, unless otherwise announced. If you cannot attend class, you can e-mail me your homework before the beginning of class, or leave it in my mailbox (number 38 on the right side of the mailboxes behind the guard's desk in the lobby of WWH). Late homeworks are usually not accepted, except if you have a valid excuse, which you should e-mail me about in advance. The two lowest homework grades will be dropped.

Homework 1 (due September 18th) Solution
Homework 2 (due September 25th) Solution
Homework 3 (due October 2nd) Solution
Homework 4 (due October 9th) Solution
Homework 5 (due October 16th) Solution
Homework 6 (due October 30th) Solution
Homework 7 (due November 6th) Solution
Homework 8 (due November 13th) Solution
Homework 9 (due November 20th) Solution
Homework 10 (due December 4th) Solution
Homework 11 (will not be graded) Solution

Quizzes:

There will be short quizzes during recitation on the following dates: October 4th (on material up to September 25th lecture), November 15th, December 6th.

Exams:

There will be one Midterm exam, on Wednesday October 23 during normal lecture hours. The Final exam will be on December 18th, 8-9:50am.

Midterm Solutions
Final

Grading:


Older teaching: