Math 2370
*** MATRICES & LINEAR OPERATORS *** Fall 2008
Instructor: David
Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures:
MWF 10:0010:50am, Thackeray 704
Recitations: Th 1010:50am, Thackeray
704, Instructor Jonathan Holland
jonathan.e.holland@gmail.com
Office
Hours: MW 2:00am3:30pm, Thackeray
511, or by appointment.
Course
Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math2370.html
Course
Description
Undergraduate
linear algebra courses deal primarily with matrices and their properties, solution
of systems of linear equations, eigenvalue analysis. This course covers the
basic theory of linear vector spaces and linear transformations using axiomatic
approach that builds upon primitive concepts toward more complex ones.
Prerequisites
Undergraduate
linear algebra or matrix theory.
Textbook
(Available
at The Book Center on Fifth Ave.)
Other recommended books
Beautifully
written book that provides brief and tothepoint explanation of the main
concepts and their motivations. Should be read alongside of Lax.
Book
written from the point of view of abstract algebra. Rich in examples and
exercises, covers more than necessary.
Undergraduate
level, focuses on matrices, good for first reading or as a refresher.
Grading
Scheme
Quizzes: 15%
Homework: 20%
Midterm
Exam: 30%
Final
Exam: 35%
Schedule
Tentative
syllabus is given below, with a list of assigned reading for the week.
Every Friday
a list of practice problems for the next week will be given. The students are
expected to work out the practice problems and consult the instructor if
difficulties arise. Few times during the term, with advance notice, the
problems will be collected and graded as a homework. The approximate schedule
and a list of practice problems will be posted below.
Every
Friday the lecture will start with a 20 min quiz based on the material covered
since the last quiz. Quizzes will be graded and will count towards the final
grade.
The
recitations on Thursdays will be spend on the discussion of practice problems
assigned for the week, so please come prepared.
Syllabus
Week 
Reading 
Topics 
Practice
problems 
Notes 
Aug
25  Aug 29 
[L]
1 
Linear
space, linear dependence, basis, dimension, subspace, quotient space 

Sep
1 Labor Day Sep
2  Sep 5 
[L]
2 
Linear
functionals, annihilator codimension 

Sep
8  Sep 12 
[L]
3 
Linear
mappings, domain, nullspace, range, fundamental
theorem 

Sep
15  Sep 19 
[L]
3 
Algebra
of linear mappings, transposition, similarity, projections, Matrices,
rank 
Set IV is a HOMEWORK
due Sep 19 

Sep
22  Sep 26 
[L]
4 
Simplices,
trace, permutation group 

Sep
29  Oct 1 
[L]
5 
Determinant,
multiplicative property 

Oct
6  Oct 10 
[L]
5 
Laplace’s
expansion, Cramer’s rule, trace 

Oct
14 
Review 


Oct
17 
Midterm Exam Covers
[L] 15 

Oct
20  Oct 24 
[L]
6 
Iteration
of linear maps, eigenvalues, eigenvectors, characteristic polynomial,
Spectral mapping theorem 
Set VII is a HOMEWORK due Oct 24 

Oct
27  Oct 29 
[L]
6 
CayleyHamilton
theorem, Generalized eigenvectors, minimal polynomial, similarity of matrices 

Nov
3  Nov 7 
[L]
7 
Scalar
product, distance, orthonormal basis, completeness,
local compactness 
Set IX is a HOMEWORK due Nov 12 

Nov
10  Nov 14 
[L]
7 
Orthogonal
complement, orthogonal projection, adjoint, norm, Isometry, orthogonal groups 

Nov
24 Thanksgiving

[L]
8 
Quadratic
forms, spectral resolution, 


Dec
1  Dec 5 
[L]
8 
commuting
maps, Normal maps, Rayleigh quotient, 


Dec
8 
[L]
8 
minmax
principle 

Dec
10 

Review 


Dec
12 

Final Exam 10:00  12:00am Thackeray Rm
704 

