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

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. 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

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

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