University of Rhode Island      Department of Mathematics

MTH 215  Linear Algebra

M-Th 10am-11:45am    Chafee 235

 Instructor Dr. Mark Comerford Office Lippitt 102 F Phone 874 5984 Email mcomerford@math.uri.edu Office Hours W 2-4pm Lippitt 102F or by appointment TAs Elliott Bertrand, Joe Erickson, Jean Guillaume, Toufik Khyat, James Marcotte David McArdle, Christoper Staniszewski, Thomas Valletta, Melissa Williams TA Office Hours Providence, Kingston Text David Lay Linear Algebra and its Applications, Fifth Edition, Addison Wesley; ISBN: 032198238X Prerequisites Mth 131, Mth 141 or equivalent

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, 15, 29, 31 (4th Ed. 1, 5, 7, 17, 29, 31)

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

3.1 1, 3, 11, 23, 25, 30 (4th Ed. 1, 3, 11, 23, 25, 29)

3.2 4, 9, 11, 13, 15, 19, 21, 25, 31 (4th Ed. 4, 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, 19, 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

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.