Math 31: Topics in Algebra

Summer 2013

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Course Information



Exams & Quizzes



This page tentative day-by-day schedule for the course, along with some announcements and course documents. It will be updated throughout the term to reflect our actual progress through the material. The reading assignment listed for each day is meant to be read after that day's class. It will generally be comprised of the sections in the book that we intend to cover in the next lecture, and it should be read before coming to the next class. There is no need to understand every detail of the assigned reading, but seeing it beforehand will help. All reading assignments are from Saracino unless otherwise noted.

Since I sometimes deviate from the textbook, or cover topics that are not fully addressed in the book, I will be posting a PDF version of my lecture notes here. I will generally update them on a weekly basis.

Course Documents

Notes and handouts: Homework assignments:


Lectures Brief Description Reading Assignment
6/21 Overview: What is Abstract Algebra? Set Theory handout and/or Section 0, Example 8 of Section 2 (Ignore the word "group" for now.)
6/22 Motivating examples of groups: the Integers mod $n$ Sections 1 and 2 (first two pages)
6/24 The Euclidean Algorithm and inverses mod $n$; Binary operations Section 2
6/25 (x-hour) Proof Workshop
6/26 First definitions for groups Sections 7 and 8 (first two pages), Section 3
6/28 Abelian groups and group tables Sections 7 and 8 (first two pages), Section 3
7/1 The symmetric and dihedral groups Section 3
7/2 (x-hour) Proof Workshop
7/3 The dihedral group; Basic properties of groups Section 4
7/5 Powers of an element and order Section 5
7/8 Cyclic groups Section 5
7/9 (x-hour) Research Workshop (with Shirley Zhao) and LaTeX tips
7/10 Subgroups Section 5
7/12 Subgroups (continued) Section 9 and 10
7/15 Subgroups of Cyclic Groups; Preview of Lagrange's Theorem Sections 9 and 10
7/16 (x-hour)
7/17 Equivalence relations Section 10
7/19 Cosets and Lagrange's theorem Section 10
7/22 Consequences of Lagrange's theorem Section 12
7/23 (x-hour) MIDTERM EXAM
7/24 Homomorphisms and Isomorphisms Section 8
7/26 The symmetric group revisited Section 8 and the last page of Section 12
7/29 Cayley's theorem Sections 11 and 13
7/30 (x-hour) Even and odd permutations Sections 11 and 13
7/31 Kernels of homomorphisms Sections 11, 12, and 13
8/2 Quotient groups and normal subgroups groups Sections 6 and 14
8/5 Normal subgroups and the Fundamental Homomorphism Theorem Section 14
8/6 (x-hour) Research Workshop (with Shirley Zhao)
8/7 Direct Products and the Fundamental theorem of finite abelian groups Section 16
8/9 The classification of finite abelian groups Section 16
8/12 Rings
8/13 (x-hour) Homomorphisms, Ideals, and Quotient Rings
8/14 Presentations
8/16 Presentations
8/19 Ideals and Quotient Rings
8/20 (x-hour)
8/21 Roots of polynomials and a brief overview of Galois theory