Linear Algebra - Fall 2015

Instructor: Christopher Sadowski

Email: csadowski at ursinus dot edu

Office: Pfahler Hall 101H

Office Hours: MTWF 10:30-11:30

Text: Linear Algebra and its Applications, Fourth Edition, by David C. Lay

Please make sure the textbook you purchase has access to MyMathLab!

Course Objectives: Students will learn the basic ideas and proof techniques in linear algebra. Students will be required to know:

  • Systems of linear equations, row reduction, and matrix and vector equations
  • Matrices, matrix operations, matrix inversion.
  • Vector spaces, subspaces, and linear transformations
  • The notion of dimension, rank, and nullity.
  • Eigenvalues, eigenvectors, and diagonalization of matrices
  • Inner products, orthogonal sets, and the Gram-Schmidt process

Learning Goals: This course will meet the following departmental learning goals:

  • Organize and synthesize evidence to identify patterns and formulate conjectures
  • Demonstrate mastery of the standard proof techniques
  • Solve problems with mathematical components, and use standard software packages when appropriate
  • Communicate to technical and non-technical audiences, and work independently and in groups

Location: Pfahler Hall 107

Meeting times: Section A: MTWF: 8:00-8:50

Section B: MTWF: 9:00-9:50

Grading:

-10% Homework

-10% Quizzes

-15% Midterm 1

-15% Midterm 2

-15% Midterm 3

-35% Final Exam

Homework: Computational problems will be assigned using MyMathLab.

Proof based and conceptual questions will also be assigned, and are to be handed in in class.

Please watch your email for homework updates!

Quizzes: We will have weekly quizzes on Wednesday, after our problem solving session. The quizzes will cover material from the previous week.

Exams:

Exam 1: 10/2/15

Exam 2: 11/6/15

Exam 3: 12/4/15

Final Exam: 8am section: 12/15/15 9am-12pm

9am section: 12/16/15: 1pm-4pm

Academic Honesty: Students may work together and discuss assignments with one another, but all work handed in must be solely the student's. Any incident of cheating on a quiz or exam will results in a grade of 0 for the assignment, with no make-up allowed. A second incident of cheating will result in a failing grade for the course. All incidents of cheating will be reported to the Dean's Office. Please refer to the Student Handbook on Academic Honesty and the Statement on Plagiarism.

Attendance: Students are expected to attend all classes. If you are unable to attend class for a legitimate reason, please email me before class.

Inclement Weather Policy: Students will be emailed in the event that class is cancelled due to inclement weather.Ac

Accommodations Policy: Students requiring accommodations should provide me with the appropriate paperwork from the Accommodations Office at the beginning of the semester.

SPTQ: Towards the end of the semester, students will be reminded to fill out SPTQ forms. These forms are invaluable to both the instructor and the department, since they provide valuable feedback to the instructor on how to improve the course, and provide evaluation information to the department chair. Honest constructive feedback (both positive and negative!) is appreciated.

Inclusive climate in the classroom: In this class we will work to promote an environment where everyone feels safe and welcome, even during uncomfortable conversations. Every voice in the classroom has something of value to contribute to class discussion. Because the class will represent a diversity of individual beliefs, backgrounds, and experiences, every member of this class must show respect for every other member of this class. You are encouraged to not only take advantage of opportunities to express your own ideas, but also, learn from the information and ideas shared by other students.

Syllabus (subject to change as the course progresses):

Week 1: 8/31, 9/2

1.1 Systems of Linear Equations

1.2 Row Reduction and Echelon Forms

1.3 Vector Equations

Week 2: 9/7, 9/9

1.3 Vector Equations (continued)

1.4 The Matrix Equation Ax=b

1.5 Solution Sets of Linear Systems

Week 3: 9/14, 9/16

1.5 Solution Sets of Linear Systems (continued)

1.6 Applications of Linear Systems

1.7 Linear Independence

Week 4: 9/21, 9/23

1.7 Linear Independence (continued)

1.8 Introduction to Linear Transformations

Week 5: 9/28, 9/30

1.9 The Matrix of a Linear Transformation

2.1 Matrix Operations

Exam 1: 10/2/15 (on all material up to and including 1.8)

Week 6: 10/5, 10/7

2.2 The Inverse of a Matrix

2.3 Characterizations of Invertible Matrices

4.1 Vector Spaces and Subspaces

Fall Break: 10/9- 10/13

Week 7: 10/14

Quiz

Week 8: 10/19, 10/21

4.1 Vector Spaces and Subspaces

4.2 Null Spaces, Column Spaces, and Linear Transformations

4.3 Linearly Independent Sets and Bases

Week 9: 10/26, 10/28

4.3 Linearly Independent Sets and Bases

4.4 Coordinate Systems

4.5 Dimension of a Vector Space

Week 10: 11/2, 11/4

4.6 Rank

Week 11: 11/9, 11/11

3.1 Introduction to Determinants

3.2 Properties of Determinants

Week 12: 11/16, 11/18

3.3 Cramer's Rule

5.1 Eigenvalues and Eigenvectors

Week 13: 11/23, 11/25

5.2 The Characteristic Equation

5.3 Diagonalization

Week 14: 11/30, 12/2

5.5 Complex Eigenvalues

6.1 Inner Product, Length, and Orthogonality

Week 15: 12/7, 12/9

6.2 Orthogonal Sets

6.3 Orthogonal Projections

6.4 Gram-Schmidt Process