MATH 5111 - Algebra 1

Fall 2013


Course Information (updated Aug. 27, 2013)

Time and place: Mon., Wed. 5:50 pm - 7:20 pm, 544 Nightingale Hall
Text: Notes by Jerzy Weyman, to be distributed as pdf file at start of classes.
Instructor: Ryan Kinser
Office and phone: 550 Nightingale Hall, (617) 373-5028.
(From the Nightingale entrance go to the 5th floor, then from the stairway/elevator head straight until you get to Jerzy Weyman's office, then my office is the one to your right.)
Email: r.kinser (at) neu (dot) edu
Office hours: Mon. 3:45-4:45, Tues. 10-11, Wed. 11-12 (These are times when you can drop in and speak with me about anything, without appointment.)


Course Description

  1. Vector spaces.
  2. Systems of linear equations. Gauss-Jordan elimination.
  3. Linear independence, basis, dimension, subspaces.
  4. Matrices and linear operators. Rank of a matrix. Determinants.
  5. Linear functions and dual spaces.
  6. Multilinear algebra: tensor products, exterior and symmetric powers of vector spaces.
  7. Jordan canonical form of an endomorphism.
  8. Quadratic forms and their invariants.
  9. Euclidean spaces, orthogonal matrices.
  10. Hermitian spaces.
Covering these topics we will also introduce basic notions of group theory and we will discuss the language of categories and functors. This will include the notion of a group, subgroup, normal subgroup, homomorphism of groups and the discussion of permutation groups.

The grading will be based on homework.

Attendance will be taken and you are expected to be present for every class. It is your responsibility to be aware of any changes in the syllabus announced in class. Students are responsible for all information given when they are absent.


Background resources:

Homework:
Each reading assignment should be started on the indicated date (or earlier!) and completed before the next class meeting.

It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.

All students in the course are responsible for being aware of and following the University's Academic Integrity Policy.