Math 221 - Linear Algebra - Spring 2011
Location: Academic Building IV - Room 151
Time: Tues and Thurs 2:30-3:45

Course Information

Instructor: Dr. Bradford E. Peercy
Office: Math/Psych 436
Email: bpeercy@umbc.edu
Phone: 410-455-2436
Office Hours: Tues and Thurs 11:00-12:00 and by appointment
Prerequisites: Math 151 or Math 155 with a C or better, or approval of instructor
Course Textbook: David C. Lay's Linear Algebra and Its Applications, third edition, Addison-Wesley, 2003 (or updated printing 2006). Associated webpage: http://www.laylinalgebra.com. This webpage makes available Chapter 1 and some other information in PDF-files, in case you have not obtained the textbook at this point!
Course Description
Linear algebra is ubiquitous in disciplines scientific and social and is a thriving discipline on its own with branches in applied science and more theoretical analysis. In this course we will begin with systems of linear equations and their solutions and then start to abstract these techniques and create a general system of vector spaces from which more general manipulations are possible. We will ground the theory in many examples.

Objectives


Grading Policy
Your grade will be broken down as 45% for in-class exams (15% for each of 3 exams), 25% for the final exam, and 30% for homework. There will be approximately 14 weekly assignments 3 of which may be dropped. Since you may drop up to 3 homework assignments, I will not be allowing any late homework. You are still responsible for the material on the homework even if it is not turned in. You must clear a missed exam with me prior to the test day. In the case of an emergency, you must be able to provide verification (e.g. a doctor's note).

Letter grades follow the traditional scale (90's are A's, 80's are B's, etc.) However, I reserve the right to incorporate participation for a student's benefit. Blackboard will be used to post grades.


Academic Integrity Statement
By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage www.umbc.edu/integrity, or the Graduate School website www.umbc.edu/gradschool.
Course Help
Spend 2-3 hours per credit hour in class doing the following
Computational Component
We will use MATLAB (MATrix LABoratory) for some homework problems this semester You may find MATLAB in one of the campus computer labs. You may also choose to purchase a student version from MathWorks.
Tentative Course Schedule
Tuesday Thursday
Jan 27
Introduction and 1.1-Systems of Linear Equations
HW1: Sec.1.1 #13,15,19,21,23,25, and ask Matlab: Why? (i.e. find a computer with Matlab installed, launch Matlab, at the prompt enter why, and press return.) Record Matlab's answer. Does repeated querying yield insight?
Feb 1
1.2-Row Reduction and Echelon Forms
HW2: 7,10,17,20,21,23,24
Feb 3
Cont. 1.2
HW1 Due
Feb 8
1.3-Vector Equations
HW2: 3,10,12,21,23
Feb 10
1.4-The Matrix Equation Ax=b
HW3: 2,4,8,10,18,20,23
HW2 Due
Feb 15
1.5-Solution Sets of Linear Systems
HW3: 6,12,13,16,23,27
Feb 17
1.7-Linear Independence
HW4: 10,12,21,29,36
HW3 Due
Feb 22
1.8-Introduction to Linear Transformations
HW4: 4,8,10,12,16,18,21
Feb 24
1.9-The Matrix of a Linear Transformation
HW5:2,6,11,13,23,26,38M,40M
Matlab assignment on Blackboard in iteration_example.txt
HW4 Due
Mar 1
2.1-Matrix Operations
HW5:2,4,9,12,15,28,34,37M
Mar 3
Test #1
Mar 8
2.1-Matrix Operations
HW5:2,4,9,12,15,28,34,37M
Mar 10
2.2-The Inverse of a Matrix
HW6:6,9,14,18,32
HW5 Due
Mar 15
2.3-Characterizations of Invertible Matrices
HW6:7,8,11,14,18,20,28(hint:see 27),34,37
4.1-Vector Spaces and Subspaces
HW7:2.8: 2,6
4.1: 2,4,8,10,23,26
Mar 17
4.2-Null Spaces, Column Spaces, and Linear Transformations
HW7:2.8: 8,12; 4.2: 2,6,8,10,25
4.3-Linearly Independent Sets; Bases
4.4-Coordinate Systems
HW7: 2.8: 21
4.3:8,14,16,20,21,26
4.4:4,8,15

HW6 Due
Mar 22
Spring Break
Mar 24
Spring Break
Mar 29
4.5-The Dimension of a Vector Space
4.6-Rank
HW8:4.5: 6,14,19,29
4.6: 4,6,14,17
Mar 31
3.1-Introduction to Determinants
HW8:3.1:4,12,14,18,20,39
HW7 Due
Apr 5
3.2-Properties of Determinants
HW8:3.2:8,12,18,26,27,31,32

Apr 7
Test #2
Apr 12
5.1-Eigenvectors and Eigenvalues
HW9:6,8,16,21,24
HW8 Due
Apr 14
5.2-Characteristic Equation
HW9:2,8,12,18,21
Apr 19
5.3-Diagonalization
HW10:2,6,14,21,26,31,32,36 (find eigenvalues using Matlab's eig function, use null function to calculate eigenvectors)
HW9 Due
Apr 21
6.1-Inner Product, Length, and Orthogonality
HW10:6,8,12,18,19,30
Apr 26
6.2-Orthogonal Sets
HW11:10,14,23
6.3-Orthogonal Projections
HW11:2,14,21(not e)
HW10 Due
Apr 28
6.5-Least Squares
HW11:6,10,17

May 3

6.6-Application of Least Squares
HW12:4 and Matlab:Synapse Fitting
HW11 Due
May 5
7.1-Diagonalization of Symmetric Matrices
HW12:13,17,25, Construct a spectral decomposition for 17.
May 10
Semester Recap/Test Prep

HW12 Due
May 12
Test #3
May 17 May 19
FINAL 1:00-3:00