MATH-UA 343, Spring 2019: Algebra I
- Instructor: Robert Young (firstname.lastname@example.org)
- Office: WWH 601
- Office hours: Mondays, 1-3, WWH 601
- Lectures: (check Albert for location) TTh 11:00-12:15
- Recitations: (check Albert for location) F 9:30-10:45 (starting
- TA: Rodion Deev
- Office hours: Tuesdays, 5-6, WWH 608
- Textbook: Judson, Abstract Algebra: Theory and Applications
The textbook is available freely online and cheaply in print at
many retailers. Any print edition has similar content, but editions
before 2014 may have different numbering of theorems, figures, etc.
Please consider buying a print edition rather than downloading it
and printing it out; the cost of printing the PDF yourself is
generally more than buying a paperback copy, and the paperback is
easier to carry and use.
- Quiz 1: Friday, February 15th, in recitation
- Quiz 2: Friday, March 8th, in recitation
- Midterm: Friday, March 29th, in recitation
- Quiz 3: Friday, April 19th, in recitation
- Quiz 4: Friday, May 3th, in recitation
- Final: Thursday, May 16th, 10-11:50 AM
Assignments will usually be given on Tuesdays and handed in at
class the next Tuesday. 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 __________").
Late assignments will not be accepted except in the case of an
emergency. If you expect to be absent on a day when an assignment is
due, you can give your assignment to a classmate to turn in for you.
At the end of the semester, your two lowest assignment grades will be
dropped from your average. This is meant to accommodate non-emergency
absences, so try not to use this unless you have to.
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. So, as you read the textbook or review
your notes, read actively. Make up your own examples. Check calculations and check each step
of a proof. Fill in any gaps. Solve exercises. Try explaining
the proof to someone else. Try proving a theorem yourself before
looking at the proof. Ask yourself questions like:
- What would happen if I changed one of the hypotheses of this theorem?
- What new tricks and techniques does this proof use?
- What's a simple example of this definition?
- What's a complicated example of this definition?
- Problem Set 1 (due Tuesday, February 5)
- Problem Set 2 (due Tuesday, February 12)
- Problem Set 3 (due Tuesday, February 19)
- Problem Set 4 (due Tuesday, February 26)
- Problem Set 5 (due Tuesday, March 5)
- Problem Set 6 (due Tuesday, March 12)
- Problem Set 7 (due Tuesday, March 26)
- Midterm Study Guide
- Problem Set 8 (due Tuesday, April 2)
- Problem Set 9 (due Tuesday, April 9)
- Problem Set 10 (due Tuesday, April 16)
- Problem Set 11 (due Tuesday, April 23)
- Problem Set 12 (due Tuesday, April 30)
- Problem Set 13 (due Tuesday, May 6)
- Final Study Guide
||Sets and functions, what is a group?
||Ch. 1, 2, 3.1-3.2
||Subgroups and cyclic groups
||Ch. 3.3, 4.1-4.2
||Permutations and symmetries
||Odd and even permutations, the alternating group
||Number theory, Euler and Fermat's Theorems, isomorphisms
||Ch. 6, 9.1
||Cayley's theorem, products, homomorphisms
||Ch. 9.2, 11.1
||Kernels and images, factor groups
||Isomorphism theorems, finite abelian groups
||Ch. 11.2, Navarro
||Polynomials and polynomial rings
||Vector spaces and fields
||Vector spaces and fields