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

Competence in basic manipulations of matrices and vectors (e.g., ability to solve low-dimensional systems by hand, understand and implement a general row reduction algorithm to solve a linear system, calculate eigenvalues and eigenvectors, construct orthogonal bases and projections, diagonalize matrices)
Grasp of basic theory including existence of solutions, linear independence of vectors, determinants and matrix invertibility, nullspaces, column spaces and the rank theorem, characteristic equations and eigenvalues, eigenvectors and bases, geometry of orthogonal projections.

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

Reading the textbook
Working the examples
Trying the problems
Talking to a classmate
Visiting my office
Scheduling free tutoring (LRC)

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 HW5:2,6,11,13,23,26,38^M,40^M Matlab assignment on Blackboard in iteration_example.txt HW4 Due
Mar 1 2.1-Matrix Operations HW5:2,4,9,12,15,28,34,37^M	Mar 3 Test #1
Mar 8 2.1-Matrix Operations HW5:2,4,9,12,15,28,34,37^M	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