Math 113 (Abstract Algebra) with Dmitry Vaintrob

Some announcements.

Welcome to Abstract algebra (Spring 2019)! Please take a look at the syllabus.

Some resources for the exam.

Here are section-by-section notes on Fraleigh by Kelli Talaska. We covered up through section 27.

Here is her practice exam. Here are solutions. Look at problems 1 (skip g), 2 (you might want to look at the solution), 3 (skip c), 4 (skip h, i, j, k), 5, 8, 9; try 7.

Here is a practice exam by Alexander Paulin. NOTES:

Skip 7.
For 4.: two elements a, b in a ring are ``associated'' if b divide a and a divides b.
For Paulin, R^* is the set of all invertible elements (R^x for us), and the "subset" sign ⊂ means a possibly non-proper subset (⊆ for us)

solutions.

Here are solutions to the big quiz (number 4).

Here are solutions to the midterm.

Here are solutions to quiz 1.

Here are solutions to homework 1.

For the first several lectures we will be reading Alexander Paulin's notes. After that, we will follow the 7th edition of Fraleigh's "A first course in Abstract Algebra".

Readings

Date	Chapters	Notes
1/31	Ch. 1, 2 of Paulin
2/5	Sections 0-3 of Fraleigh
2/7	Sections 4-5 of Fraleigh
2/12	Quiz: re-read notes and section 0 of Fraleigh; set terminology.
2/14	Sections 6 and 8 of Fraleigh	Skipping section 7 (not used in rest of class)
2/21	Section 8 of Fraleigh
2/26	Sections 9 and 10 of Fraleigh
3/5	Re-read section 10, prepare for quiz on cosets
3/12	Sections 11, 13 of Fraleigh	Skipping section 12
3/19	Sections 14, 15 of Fraleigh
4/9	Sections 18, 19 of Fraleigh
4/23	Sections 20, 22, 23 of Fraleigh	Skipping 21
4/30	Sections 26, 27 of Fraleigh	Skipping 24, 25
5/2	Reviewing 26-27. Try reading section 28	Section 28 is not on the test, but it's a good explanation of "next steps" of the algebra of polynomials and commutative rings (related to algebraic geometry)

Syllabus

Homework sets.

Homework 1, due 1/29 at the beginning of classLaTeX code

Homework 2, due 2/5 at the beginning of class LaTeX code

Homework 3, due 2/12 at the beginning of class LaTeX code Selected solutions Solutions LaTeX code

Homework 4, due 2/19 at the beginning of class LaTeX code Selected solutions

Homework 5, due 2/26 at the beginning of class LaTeX code

Homework 6, due 3/5 at the beginning of class LaTeX code

Homework 7, due 3/12 at the beginning of class LaTeX code

Homework 8, due 3/19 at the beginning of class LaTeX code

Homework 9, due 4/2 at the beginning of class No late submissions LaTeX code

Homework 10, due 4/9 at the beginning of class LaTeX code

Homework 11, LaTeX code

Homework 12, LaTeX code

Homework 13, due 5/2/19 (note: Thursday!) at the beginning of class LaTeX code

LaTeX homework templates: tex and pdf .

Math 113 (Abstract Algebra) with Dmitry Vaintrob

Some announcements.

Readings

Syllabus

Homework sets.

An introduction to set terminology (please take a look!)