MATH-UA 343, Fall 2017: Algebra I
- Instructor: Robert Young (firstname.lastname@example.org)
- Office: WWH 601
- Office hours: Mondays, 1--3, WWH 601
- Lectures: (check Albert for location) MW 9:30--10:45
- Recitations: (check Albert for location) F 9:30--10:45 (starting September 14)
- TA office hours: Mondays 5--7, WWH 524
- Textbook: Michael Artin, Algebra, second edition.
- Supplementary sources
It can be helpful to read different takes on the same material. In class, we will primarily follow Artin, but there are many other sources available. Some of these are freely available online; others are available in the library.
- Quiz 1: October 6
- Midterm: October 27
- Quiz 2: TBA (early-mid November)
- Quiz 3: TBA
- Final: TBA
Assignments will usually be given on Wednesdays and handed in at
class the next Wednesday. Collaboration is
encouraged, but each student must write up and hand in their own
solutions. If you work closely with someone else, please identify
them on your assignment (e.g., "I worked with __________").
To earn credit, assignments must be turned in at the start of
recitation. Assignments will not be accepted by email or in a mailbox; if you must miss class
due to some emergency, please give your assignment to a classmate to turn in
for you. At the end of the semester, your lowest grade on an
assignment will be dropped from your average.
Solving problems is important! Doing exercises and understanding
the assignments is the best way to master the material.
How to do well in this class
- Come to class and recitation!
- Solve problems!
- Ask me questions: Feel free to ask me questions in class,
after class, at office hours, or by email. Feel free to ask
questions in recitation.
- Ask your classmates questions: Mathematics is about
collaboration. Explaining something to someone else is one of the
best ways to learn.
- Read actively and study diligently! The true goal of
this course is to learn how to prove theorems and facts about
groups, rings, and fields. So, as you read the textbook or review
your notes, read actively. Check calculations and check each step
of a proof. Fill in any gaps. Solve exercises. Try explaining
the proof to someone else. Try proving theorems yourself before
looking at the proof. Ask yourself questions like:
- What new tricks and techniques does this proof use?
- What if I tried another way to prove this?
- What's a simple example of this definition?
- What's a complicated example of this definition?
Note: The sections here are a rough guide. We will cover different material in class than the material
covered in the book. If you miss a class, please try to get notes
from a classmate.
- Wednesday, September 6th: Artin, Chapter 1, Sec 2.1-2.2
- Monday, September 11th: Artin, Sec 2.3
- Wednesday, September 13th: Artin, Sec 2.4
- Problem Set 1 (due September 15)
- Problem Set 2 (due September 22) [revised 2017-09-18]
- Problem Set 3 (due Wednesday, September 27)
- Problem Set 4 (due Wednesday, October 4)
- Review problems
- Problem Set 5 (due Wednesday, October 11)
- Problem Set 6 (due Wednesday, October 18)
- Problem Set 7 (due Wednesday, October 25)
- Review questions
- Problem Set 8 (due Wednesday, November 1)
- Problem Set 9 (due Wednesday, November 8)
- Problem Set 10 (due Wednesday, November 15)
- Quiz 2 review
- Problem Set 11 (due Wednesday, November 29)
- Problem Set 12 (due Wednesday, December 6)
- Isometries (do not turn these in)
- Review questions
||What is algebra? Groups
||Examples of groups, subgroups
||Cyclic groups, Homomorphisms
||Functions, homomorphisms, cosets
||Normal subgroups, isomorphisms. Quiz
||Cosets, congruence, Lagrange's Theorem
||Modular arithmetic, quotient groups
||Isomorphism Theorem, fields
||Vector spaces and linear algebra over a field
||Dimension, bases, error-correcting codes
||Matrices, linear transformations, conjugacy
||Eigenstructure, the orthogonal group
||Isometries of R^n and R^2, finite groups of isometries of the plane
|12/11, 12/12, 12/13
||Finite groups of isometries of the plane, discrete groups of isometries of the plane, the crystallographic restriction