MATH-UA 343, Fall 2017: Algebra I

Basic information

Grading scheme

Final exam30%

Exam dates

About assignments

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


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.

Problem sets

Course outline

9/6 What is algebra? Groups
9/11,9/13 Examples of groups, subgroups
9/18,9/20 Cyclic groups, Homomorphisms
9/25,9/27 Functions, homomorphisms, cosets
10/2,10/4 Normal subgroups, isomorphisms. Quiz
10/11 Equivalence relations
10/16,10/18 Cosets, congruence, Lagrange's Theorem
10/23,10/25 Modular arithmetic, quotient groups
10/30,11/1 Isomorphism Theorem, fields
11/6,11/8 Vector spaces and linear algebra over a field
11/13,11/15 Dimension, bases, error-correcting codes
11/20 Matrices, linear transformations, conjugacy
11/27, 11/29 Eigenstructure, the orthogonal group
12/4, 12/6 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