Honors Algebra II - Spring 2014
Monday, Wednesday, Friday 10:30 am - 11:20 am, TBA
Course website:
nd.edu/~smapes1/HonorsLinearAlgebra2.html
Instructor:
Sonja Mapes
Email:
smapes1 (at) nd.edu
Office: 228 (Hayes-Healey)
Tel: (574) 631-7586
Office hours:
TBA
Or by appointment.
Textbook:
Linear Algebra Done Right (Third edition) by Sheldon Axler
Grading:
Homework 15%; Midterms 30% (15% each); Quizes 10%; Term Paper 15%; Final 30%
Midterms:
There will be two midterm exams. The first is
Friday Feb. 24 and the second is
Friday April 7. The
exams will cover the material up to the Friday before the exam.
Announcements as to exactly what sections will be on the exam will be
made closer to the exam date.
Quizes:
There will be in class quizzes roughly every three weeks on Mondays each taking about
20 minutes. The objective of the quizzes is for you to get direct
feedback from me on your written work.
Depending on the topics you should expect that each quiz will
consist of one computational problem and one proof.
Term Paper:
This semester I will ask that each of you write a 5 to 10 page paper
which will allow you to explore applications of linear algebra to
other fields of mathematics or to some real life situations. There
will be more resources on this for you as the semester goes on but
roughly speaking I would like your topic to be chosen by spring
break, and a first draft by April 10.
Final:
The projected final exam date is
TBA .
Homework:
There will be weekly written assignments which can be found below along with the due date.
- Late homework will not be accepted.
- The two lowest homework grades will be dropped.
- Please staple or paper clip your work.
- Don't forget to write your name on it!
Honesty:
This class follows the binding Code of Honor at Notre Dame. The graded work you do in this class must be your own. In the case where you collaborate on homework with other students make sure to fairly attribute their contribution to your project. For more information on the honor code see
www.honorcode.nd.edu .
Syllabus
This is a tentative syllabus and it is likely to change as the course progresses.
| Date |
Reading - sections in textbook |
Homework |
| Jan. 18,20 |
Mini Course on Determinants
|
Homework 1
due 1/25 in class |
| Jan. 23,25,27 |
Generalized Eigenvectors, Decomposition of an Operator
sec. 8.A, 8.B |
Homework 2
due 2/1 in class |
| Jan. 30, Feb 1,3 |
Characteristic Polynomials, Jordan Form Quiz 1.
sec. 8.C-8.D |
Homework 3
due 2/8 in class |
| Feb. 6,8,10 |
Inner products and orthanormal bases
sec. 6.A-6.B |
Homework 4
due 2/15 in class |
| Feb. 13,15,17 |
Orthogonal complements and self-adjoint operators
sec. 6.C-7.A |
Homework 5
due 2/22 in class |
| Feb. 20,22,24 |
Spectral Theorem Midterm 1.
sec. 7.B |
Homework 6
due 3/1 in class |
| Feb. 27, Mar 1,3 |
Positive operators and isometries, singular value decomposition
sec. 7.C - 7.D |
Homework 7
due 3/8 in class |
| Mar. 6,8,10 |
Complexification, operators on real inner product spaces Quiz 2.
sec. 9.A-9.B |
Homework 8
due 3/22 in class |
| Mar. 13,15,17 |
Spring break. |
|
| Mar. 20,22,24 |
Trace and Determinant
sec. 10.A-10.B |
Homework 9
due 3/29 in class |
| Mar. 27,29,31 |
Multilinear functionals and tensor products
sec. |
Homework 10
due 4/5 in class |
| Apr. 3,5,7 |
Symmetric algebra and exterior algebra .Midterm 2.
sec. |
Homework 11
due 4/12 in class |
| April 10,12 |
Exterior algebra, connectin to trace and determinant Easter (no
class on 14th).
sec. |
Homework 11
due 4/19 in class |
| April 19,21 |
TBA Easter (no
class on 17th).
sec. |
Homework 12
due 4/26 in class |
| April 24,26,28 |
TBA Quiz 3.
sec. |
Homework 13
due 4/3 in class |
| May 1,3 |
TBA |
|