Instructor
Mark Comerford
Office: Tyler Hall 210
Phone: (401) 874-5984
Email: mcomerford@math.uri.edu
Office Hours: tbd.
Textbook: Linear Algebra and its Applications,
Third Edition David Lay,
Addison Wesley; ISBN: 0201709708
About the course: This is a first undergraduate course in linear algebra. In this course you will learn many of the foundations of linear algebra. Students are encouraged to use Maple to complement the topics, in fact this practice will be very useful for the future development of the projects. We will present some applications to motivate the subject.
SYLLABUS (provisional)
Chapter 1
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
Chapter 2
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.8 Subspaces of R^n
2.9 Dimension and Rank
Chapter 3
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
Chapter 4
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets: Bases
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
Chapter 5
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
Chapter 6
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
Lectures: The textbook has its own website which may be found at http://www.laylinalgebra.com On this site you can find versions of the lecture notes used in class as well as other resources. However, for your convenience, I have linked the lecture material to this webpage.
Extra (handwritten) material for Lecture 9
Extra two handwritten pages on angles.
Prerequisites: MTH 131, MTH 141 or equivalent.
Homework: Homework will be assigned weekly. A certain number of problems from each problem set will be selected at random by me and graded.
Exams: There will be two midterms, one on Friday October 5, 2007 and one on Wednesday November 14, 2007. Both will be at the regular class time of 10am in our regular classroom of Wales 223. The final will be on Friday December 14 from 8-11am, place to be determined. The material in the exams will be chosen with the homeworks in mind. If you are able to do all the homework problems, then you should have no trouble with the exams.
The first midterm covers up to and including section 2.3. A summary of what you need to know for this exam can be found here. Solutions for this exam are available here.
The second midterm covers sections 3.1, 3.2, 4.1,4.2, 4.3, 4.4, 4.5, 4.6, and 4.7. A summary of what you need to know for this exam can be found here. Solutions for this exam are available here.
The final covers all sections and will be in our usual classroom of Wales 223 on Friday December 14, 2007 from 8-11am. A summary of the entire course is available here.
Projects
The three projects are now online. The projects and the links for them are as follows:
The Adjacency Matrix of a Graph
Why Sheep need Matrices to Reproduce
Making Fractals using Iterated Function Systems
All three projects are due on Wednesday December 5, 2007. You may form yourselves into teams of two or three people to work on the projects. However, you should write up your projects individually. If there is time, I may ask teams to present their projects at the front of the class.
Homework Assignments
Week 1
Homework 1 Due September 17, 2007
Homework 2 Due September 24, 2007
Week 3
2.1 1,5,7,9,17
2.2 1,5,7,15,29,31
2.3 1,3,7,11,13,27
Week 4
3.1 1,3,11,23,25,29
3.2 3,9,11,13,15,19,21,25,31
4.1 1,3,7,9,13,21
Week 5
4.2 1,3,11,12,17,21
4.3 1,3,5,11,13,15,19,31
4.4 1,3,9,11,13
Week 6
4.5 1,3,7,11,17,21
4.6 1,3,5,7,11
Week 7
4.7 1,5,7,11
5.1 1,5,7,11,13,15,19,25,31
Week 8
5.2 1,3,9,13,17,21,25
5.3 1,3,5,7,8,11,19,27
Week 9
6.1 1,3,5,7,9,11,13,15,17,23,25,29
6.2 1,3,11,12,17,21
Week 10
6.3 1,3,9,11,13,15,17,23
6.4 1,3,9,11
Solutions for Homeworks 1 and 2 are now available online here.
Policies: You are expected to abide by the University's civility policy:
"The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class."
Cell phones, IPods, beepers and any electronic device must be turned off in class.
You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. Use of unauthorized aids such as cheat sheets or information stored in calculator memories, will be considered cheating. The Mathematics Department and the University strongly promote academic integrity.
Grading Policy:
Your grade will be determined by your scores on
Homework : 100pts Exam I : 100pts Exam II : 100pts Project : 50pts Final : 200pts (cumulative) Total : 550pts