University of Rhode Island      Department of Mathematics

MTH 215  Linear Algebra

M, W 6-9:45pm Room 440 CCE




Instructor  Dr. Mark Comerford
Office  Lippitt 102 F
Phone  874 5984
Email  mcomerford@math.uri.edu
Office Hours
 M, W 5-6pm, CCE Cafeteria
or by appointment
TAs Addie Armstrong,
Elliott Bertrand,
Erin Denette,
Chad Estabrooks,
Toufik Khyat,
James Marcotte
David McArdle, Diana Smith,
Christoper Staniszewski, Thomas Valletta
TA Office Hours
  Providence, Kingston

Text David Lay
Linear Algebra and its Applications,
Fourth Edition,
Addison Wesley; ISBN: 0321385179
Prerequisites  Mth 131, Mth 141 or equivalent


About this 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


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

1.6 Linear Independence

1.7 Introduction to Linear Transformations

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.

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Extra (handwritten) material for Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 13.5 (Cramer's Rule)

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22

Lecture 23

Lecture 24

Extra two handwritten pages on angles.

Lecture 25

Lecture 26

Lecture 27

Lecture 28


Homework

Homework will be assigned weekly. However the weekly quiz may be based on homework assignments.  If you do your weekly homework assignments you will have no problem with the exams.


Homework Problems

Week 1

Homework 1

Homework 2

Week 2

2.1 1, 5, 7, 9, 17

2.2 1, 5, 7, 17, 29, 31 (3rd Ed. 1, 5, 7, 15, 29, 31)

2.3 1, 3, 7, 11,13, 27

3.1 1, 3, 11, 23, 25, 29

3.2 3, 9, 11, 13, 15, 19, 21, 25, 31

3.3 1, 5, 6

Week 3

4.1 1, 3, 7, 9, 13, 21

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

4.5 1, 3, 7, 11, 17, 21

4.6 1, 3, 5, 7, 11

4.7 1, 5, 7, 11

Week 4

5.1 1, 5, 7, 11, 13, 15, 19, 25, 31

5.2 1, 3, 9, 13, 17, 21, 25

5.3 1, 3, 5, 7, 8, 11, 19, 27

6.1 1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 29

6.2 1, 3, 11, 12, 17, 21

6.3 1, 3, 9, 11, 13, 15, 17, 23

6.4 1, 3, 9, 11


Evaluation


Exam I   100pts
Exam II   100pts
Exam III   100pts
Final   200pts
Total 500pts









Grading Scale

Your total score out of 500 will be divided by 5 and the resulting score out of 100 will determine your grade: A 93 - 100, A- 90 - 93, B+ 87 - 90, B 83 - 87, B- 80 - 83, C+ 77 - 80, C 73 - 77, C- 70 - 73, D+ 67 - 70, D 60 - 67, F < 60.


A summary of the course material is available 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.


Accommodations

Any student with a documented disability is welcome to contact me early in the semester so that we may work out reasonable accommodations to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 330 Memorial Union, 874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.