Math 221 - Linear Algebra (Schedule#:4441)
Location: Math/Psych 101
Time: Tues and Thurs 11:30-12:45

Course Information

Instructor: Dr. Bradford E. Peercy
Office: Math/Psych 436
Email: bpeercy@umbc.edu
Phone: 410-455-2436
Office Hours: Tues and Thurs 10:30-11:30 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. There will be opportunity for credit relating to computational projects. 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 may use MATLAB (MATrix LABoratory) for some extra projects this semester. Therefore, you would need to have access to it. You may use it in one of the campus computer labs. You may also choose to purchase a student version from MathWorks. Blackboard (via myUMBC) may be used to make sample code available.

Tentative Course Schedule
Tuesday Thursday
Aug 28
Introduction and 1.1-Systems of Linear Equations
HW1: 13,15,19,21,23,25
Sept 2
1.2-Row Reduction and Echelon Forms
HW2: 7,10,17,20,21,23,24
Sept 4
1.3-Vector Equations
HW2: 3,10,12,21,23
HW1 Due
Sept 9
1.4-The Matrix Equation Ax=b
HW3: 2,4,8,10,18,20,23
Sept 11
1.5-Solution Sets of Linear Systems
HW3: 6,12,13,16,23,27
HW2 Due
Sept 16
1.7-Linear Independence
HW4: 10,12,21,29,36
Sept 18
1.8-Introduction to Linear Transformations
HW4: 4,8,10,12,16,18,21
HW3 Due
Sept 23
1.9-The Matrix of a Linear Transformation
HW5:2,6,11,13,23,26
Sept 25
2.1-Matrix Operations
HW5:2,4,9,12,15,28,34
HW4 Due
Sept 30
2.2-The Inverse of a Matrix
HW6:6,9,14,18,32
Oct 2
2.3-Characterizations of Invertible Matrices
HW7:7,8,11,14,18,20,28(hint:see 27),34,37
HW5 Due
Oct 7
Test #1
Oct 9
2.8-Subspaces of Rn
HW:
HW6 Due
Oct 14
2.9-Dimension and Rank
4.1-Vector Spaces and Subspaces
HW7:2.8: 2,6
4.1: 2,4,8,10,23,26
Oct 16
4.2-Null Spaces, Column Spaces, and Linear Transformations
HW8:2.8: 8,12
4.2: 2,6,8,10,25
HW7 Due
Oct 21
4.3-Linearly Independent Sets; Bases
4.4-Coordinate Systems
HW8: 2.8: 21
4.3:8,14,16,20,21,26
4.4:4,8,15
Oct 23
4.5-The Dimension of a Vector Space
4.6-Rank
HW9:4.5: 6,14,19,29
4.6: 4,6,14,17
HW8 Due
Oct 28
3.1-Introduction to Determinants
HW10:3.1:4,12,14,18,20,39
Oct 30
Test #2
HW9 Due
Nov 4
3.2-Properties of Determinants
HW10:3.2:8,12,18,26,27,31,32
Nov 6
5.1-Eigenvectors and Eigenvalues
HW11:6,8,16,21,24
HW10 Due
Nov 11
5.2-Characteristic Equation
HW11:2,8,12,18,21
Nov 13
5.3-Diagonalization
HW12:2,6,14,21,26,31,32
HW11 Due
Nov 18
6.1-Inner Product, Length, and Orthogonality
HW12:6,8,12,18,19,30
Nov 20
6.2-Orthogonal Sets
HW13:10,14,23
HW12 Due
Nov 25
6.3-Orthogonal Projections
HW13:2,14,21
6.4-Gram Schmidt Process
HW13:10,17
6.5-Least Squares
HW13:6,10,17
6.6-Application of Least Squares
HW13:4
Nov 27
Thanksgiving
Dec 2
7.1 Diagonalization
HW14:1,2,3,4,5,6,13,25
HW13 Due
Dec 4
Test #3
Dec 9
Review
HW14 Due
Dec 11
FINAL 10:30-12:30