Math 5111: Algebra 1

Math 5111 (Algebra 1), Fall 2019

This course page is now archived. Exams and solutions are no longer available here. If you are a Northeastern instructor and would like copies, please email me.

Course Information
Instructor	Class Times	Office Hours
Evan Dummit edummit at northeastern dot edu	W 5:55pm-9:00pm, Richards Hall 237	MR 10:45am-12:15pm MR 3:00pm-4:00pm 571 Lake Hall
Due to external circumstances, I have taken over the instructional duties for this course for the remainder of the fall term from Ben Knudsen, who will remain involved in an advisory capacity.

Homework Assignments
Homework assignments 1-10 are available on B. Knudsen's webpage . Homework #10, due Wed November 20th. (You may find helpful this note on adjoints and orthogonal complements .) Homework #11, due Wed November 27th. There is no class on that day so please email it or submit it to me in person on Monday Nov 25th. (Updated 11/22: corrected typos in problem 6) Homework #12, due Wed December 4th, the last day of class. (Updated 12/1: added assumption that F is algebraically closed to problem 5) The take-home final exam, covering linear algebra only, is due via email to Ben Knudsen by December 11th.

Homework Assignments

Homework assignments 1-10 are available on B. Knudsen's webpage .

Homework #10, due Wed November 20th. (You may find helpful this note on adjoints and orthogonal complements .)

Homework #11, due Wed November 27th. There is no class on that day so please email it or submit it to me in person on Monday Nov 25th. (Updated 11/22: corrected typos in problem 6)

Homework #12, due Wed December 4th, the last day of class. (Updated 12/1: added assumption that F is algebraically closed to problem 5)

The take-home final exam, covering linear algebra only, is due via email to Ben Knudsen by December 11th.

Handouts / Lecture Notes
Handout	Topics
All material from B. Knudsen's portion of the course (from the start of the course to the lecture on 10/30) is available on his webpage .
Lecture 11/6: Inner Products, Orthogonality, Adjoints	Notes on Inner Products / (alternate presentation) (section 1.6) Notes on Adjoints (section 2.5) Extra note on adjoints and orthogonal complements
Lecture 11/13: Determinants, Eigenvalues, Diagonalization	Notes on Determinants (section 3.3, note that this is not exactly the way the material was presented in class) Notes on Eigenvalues and Diagonalization (sections 4.1-4.2)
Lecture 11/20: Generalized Eigenvectors, Jordan Canonical Form, Spectral Theorem	Notes on Generalized Eigenvectors and the Jordan Canonical Form (section 4.3) Notes on Hermitian operators and the spectral theorem
Lecture 12/4: Bilinear Forms, Quadratic Forms	Notes on Quadratic Forms