Math 1180: Linear Algebra Fall 2014
Instructor: David
Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures:
MWF 9:009:50am, Thackeray 704
Office
Hours: MWF 10:0011:30am, Thackeray
511, or by appointment.
Grader: Roxana Tanase,
rot26@pitt.edu, office hours Monday 57pm, Friday 911am, at MAC
Web
Page: http://www.math.pitt.edu/~swigon/math1180.html
Course
Description
This is a
core undergraduate course in linear algebra and matrix analysis for mathematics
majors. The emphasis will be placed on
the understanding of concepts and their application in further development of
the theory. Specifically, the course covers topics such as solutions of linear
equations, matrix algebra, linear transformations, orthogonality, general
linear vector spaces, basis, dimension, eigenvalues/eigenvectors.
The grade will be based on evaluation of both problem solving and theorem
proving skills.
Prerequisites
Multivariable Calculus (Math 0240 or equivalent), and familiarity with
solving of systems of linear equations. Introduction to Theoretical Mathematics (Math 0413
or equivalent).
Textbook
D. Poole , Linear Algebra; a Modern Introduction, 2nd edition, Brooks & Cole, 2006.
ISBN 0534405967
Grading
Scheme
Homework
Assignments: 20%
Two midterm exams: 40%
(20% each)
Cumulative Final Exam: 40%
Schedule
The precise
schedule and a list of homework problems will be given out in advance and
posted on the web. Homework is
assigned every Friday and is due at the beginning of a class one week after it
was assigned. You MAY NOT use a computer or other electronic tools in solving
the homework unless I specifically say otherwise.
Policy
Attendance is expected. No late homework will be
accepted and there will be no make up exams.
Disability Resource Services
If
you have a disability for which you are or may be requesting an accommodation,
you are encouraged to contact both your instructor and
Disability Resources and Services, 140 William Pitt Union, 4126487890 or
4123837355 (TTY) as early as possible in the term. DRS will verify your
disability and determine reasonable accommodations for this course.
Academic Integrity
Cheating/plagiarism will not be tolerated. Students
suspected of violating the University of Pittsburgh Policy on Academic
Integrity will incur a minimum sanction of a zero score for the quiz, exam or
paper in question. Additional sanctions may be imposed, depending on the
severity of the infraction. On homework,
you may work with other students or use library resources, but each student
must write up his or her solutions independently. Copying solutions from other
students will be considered cheating, and handled accordingly.
Schedule
Please note that the
schedule is approximate and the pace and/or order of the topics may change
during the semester.
LECTURE 
CHAPTERS 
TOPICS 
HOMEWORK
ASSIGNED Due
Friday the week after (numbers in parentheses refer to the 3^{rd}
edition of the textbook) 
Aug
25  Aug 29 
1.11.2 1.3 2.1 
Geometry
and algebra of vectors, length and angle, dot product Lines,
planes, cross product Systems
of linear equations, Row echelon form 
Chap
1.2 #17, 30, 37(43), 44(50), 50(56), 56(62) Chap
1.3 #4, 8 Chap
2.1 #8, 17 Due Sep 5 
Sep 1 
Labor Day (no school) 


Sep
3  Sep 5 
2.2 2.3 
Gaussian
elimination Spanning
sets & linear independence 
Chap
2.2 #13, 18, 21, 30, 38, 49, 50 Chap
2.3 #8, 12 Due Sep 12 
Sep
8  Sep 12 
2.3 2.4 
Spanning
sets & linear independence Application: Resource allocation, Network Analysis 
Chap
2.3 #21, 24, 27, 30, 43 Chap
2.4 #2, 5, 17 Due Sep 19 
Sep
15  Sep 19 
3.12 3.3 
Matrices,
matrix operations, Matrix algebra Matrix
inverse 
Chap
3.1 #14, 23, 24, 28, 30, 38 Chap
3.2 #20, 27 Chap
3.3 #2, 9, 12 Due Sep 26 
Sep
22  Sep 26 
3.5 
Subspaces,
bases, dimension, rank 
Chap
3.3 # 43, 47, 52, 55 Chap
3.5 # 2, 6, 12, 18, 29, 40, 44, 57(59) Due
Wednesday Oct 1 
Sep
29 – Oct 1 
3.7 
Applications: Markov chains and graphs Review 

Oct 3 
Exam I 

Oct
6  Oct 10 
4.1 4.2 
Introduction
to eigenvalues and eigenvectors Determinants

Chap
3.7 # 58, 12 Chap
4.1 # 3, 6, 9, 14, 23, 26, 35, 36 Chap
4.2 # 6, 12, 33, 38, 46, 49, 55 Due Oct 17 
Oct 13 
Fall Break (no school) 


Oct
14 – Oct 17 
4.3 4.4 
Eigenvalues
and eigenvectors of n x n matrices Similarity
and diagonalization 
Chap
4.3 # 2, 5, 9, 17, 18,19, 20, 24 Chap
4.4 # 2, 4, 10, 11 Due Oct 24 
Oct
20 – Oct 24 
4.4 4.6 
Similarity
and diagonalization Applications: Recurrence relations, Systems of linear
differential equations 
Chap
4.4 #12, 17, 28, 34, 43, 44 Chap
4.6 #45(47), 47(49), 53ab(55ab), 58(60) (numbers in parentheses refer to the 3^{rd}
edition of the textbook) Due Oct 31 
Oct
27 – Oct 31 
5.1 5.2 
Orthogonality Orthogonal
complements and projection 
Chap
5.1 #3, 5, 10, 13, 19, 23, 30, 35 Chap
5.2 #4, 13, 16, 21, 27 Due Nov 7 
Nov
3 – Nov 7 
5.3 5.4 
GramSchmidt
process Orthogonal
diagonalization of symmetric matrices 
Chap
5.3 #4, 7, 10, 12, 13 Chap
5.4 #2, 7, 24, 25 Due
Wednesday Nov 12 
Nov
10  Nov 12 
Application: Quadratic forms Review 


Nov 14 
Exam II 


Nov
17 – Nov 21 
6.1 6.2 
Vector
spaces and subspaces Linear
independence, basis, dimension 

Nov
24 
6.2 
Basis,
dimension 

Dec
1  Dec 5 
6.4 6.5 
Linear
transformations Kernel
and range of a linear transformation, Invertibility of a linear transformation Review for final exam 
Chap
6.1 #3, 5, 33, 36 Chap
6.2 #4, 14, 23, 27, 37 Chap
6.4 #3, 10, 16, 22 Chap
6.5 #3, 12, 17, 20 Due
Friday Dec 5 
Tuesday Dec 9 

FINAL EXAM 4:00  5:50 pm THACK 704 