Math 315 - Fall 2007
Abstract Algebra I

Brief course description: This is the first-semester of a year-long course which will prepare graduate students for future work where algebra is needed. In the first semester we will cover topics from group theory, ring theory, and modules. This corresponds to Parts I, II, and some of Part III in the course text.

Prerequisites: Students should know material found in undergraduate books on group theory (Lagrange's theorem, Cauchy's theorem, Sylow theorems, center and conjugacy classes, normal subgroups and quotient groups, homomorphisms and the homomorphism theorems), ring theory (Euclidean domains, PIDs, prime and maximal ideals), and linear algebra (representing linear transformations and bilinear forms as matrices, eigenvalues and eigenvectors, Cayley-Hamilton theorem, Gram-Schmidt process for inner product spaces, diagonalizing real symmetric matrices).

Course grade:  This will be based on the following weighting:

• 40% homework, 30% midterm, 30% final.

Homework: Homework assignments will be posted on the bottom of this web. Due dates will be marked on each assignment. No late homeworks will be accepted.

• Computational homework problems should present a complete calculation, starting with the data of the problem. Do not just give the answer.

Exams:  There will be 1 midterm and a final.  

• There are no makeup exams. If you miss the midterm, the midterm grade is 0.
• If you need exam accomodations based on a documented disability, you need to speak with both the Center for Student Disabilities and the course instructor within the first two weeks of the semester.