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.
An open-source algebra textbook with a more elementary presentation (but note that the order of topics is different from Artin's book)
Assignments | 25% |
Midterm | 25% |
Quizzes | 20% |
Final exam | 30% |
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.
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 |