Math 221 - Linear Algebra - Fall 2015
Location: Mathematics/Psychology 101
Time: MW 10:00-11:15am

Course Information

Instructor: Dr. Bradford E. Peercy
Office: Math/Psych 436
Email: bpeercy@umbc.edu
Phone: 410-455-2436
Office Hours: MW 11:15-12:00 and by appointment
Prerequisites: Math 151 or Math 155 with a C or better, or approval of instructor
Course Textbook: Linear Algebra and Its Applications by David C. Lay and Steven R. Lay and Judi J. McDonald, 5th edition, Addison-Wesley, 2016. Associated webpage: http://www.laylinalgebra.com. This webpage makes available Chapter 1 (in 3rd edition) and some other information in PDF-files, in case you have not obtained the textbook at this point! Additional student resources are available with the 5th edition at www.pearsonhighered.com/lay.

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 three in-class exams (15% each), 25% for the final exam, and 30% for homework. There will be approximately 12 weekly assignments 2 of which may be dropped. Since you may drop up to 2 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.) Participation will be to 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

Day and Date	Topic	Homework
Thurs Aug 27	Introduction and 1.1-Systems of Linear Equations
Tues Sept 1	1.2-Row Reduction and Echelon Forms
Thurs Sept 3	1.3-Vector Equations	Due HW1: Sec.1.1 #3,7,13,16,17,23,24,25,27,31
Tues Sept 8	1.4-The Matrix Equation Ax=b
Thurs Sep 10	1.5-Solution Sets of Linear Systems	Due HW2: 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? Sec 1.2 #2,6,13,15,19,21,22,27,29,31
Tues Sept 15	1.7-Linear Independence
Thurs Sept 17	1.8-Introduction to Linear Transformations	Due HW3:
Tues Sept 22	1.9-The Matrix of a Linear Transformation
Thurs Sept 24	2.1-Matrix Operations	Due HW4:
Tues Sept 29	Exam #1
Thurs Oct 1	2.2-The Inverse of a Matrix
Tues Oct 6	2.3-Characterizations of Invertible Matrices 4.1-Vector Spaces and Subspaces
Thurs Oct 8	4.2-Null Spaces, Column Spaces, and Linear Transformations	Due HW5:
Tues Oct 13	4.3-Linearly Independent Sets; Bases 4.4-Coordinate Systems
Thurs Oct 15	4.5-The Dimension of a Vector Space 4.6-Rank	Due HW6:
Tues Oct 20	3.1-Introduction to Determinants
Thurs Oct 22	3.2-Properties of Determinants	Due HW7:
Tues Oct 27	Exam #2
Thurs Oct 29	5.1-Eigenvectors and Eigenvalues	Due HW8:
Tues Nov 3	5.2-Characteristic Equation
Thurs Nov 5	5.3-Diagonalization	Due HW9:
Tues Nov 17	6.3-Orthogonal Projections
Thurs Nov 19	6.5-Least Squares	Due HW11:
Tues Nov 24	6.6-Application of Least Squares
Thurs Nov 26	Thanksgiving Break
Tues Dec 1		Due HW12:
Thurs Dec 3	Exam #3
Tues Dec 8	RECAP
Thurs Dec 10	Reading day
Tues Dec 15	FINAL EXAM 10:30-12:30 MP 101