Introduction to Linear Algebra
Course Notes and Assignments

overview

Course Description (from SDSU General Catalog)

Math 254. Introduction to Linear Algebra. 3 units.
Prerequisite: Mathematics 151. Gaussian elimination, determinants, vector spaces, linear transformations, orthogonality, eigenvalues, and eigenvectors.

TPHS/SDSU Collaboration

Notes

Please refer to the Course Outline for details about topics covered.

Book: Elementary Linear Algebra, Howard Anton (8th edition)

SDUHSD students may meet the prerequisite by passing the Advanced Placement Calculus BC exam with a grade of 3 or higher. At TPHS, students should take Math 252/Calculus D before or concurrently with Math 254/Linear Algebra. Also, please refer to the TPHS Math Department Course Information.

The course costs $102 per unit. That is $306 per student per semester.

expectations

Bring Each Day

Pencil and Paper
Calculator(s) - Graphing and/or Scientific
Notebook
Book: Elementary Linear Algebra, Howard Anton (8th edition)

Test Policies and Expectations

All students should be in class on the day of a test.
If you are absent:
- I expect a note, e-mail, or phone call from a parent/guardian on the test day or soon after.
- The absence must also be excused through the attendance office.
- You will take a make-up exam as soon as possible and not more than one week after returning.
- Make-up exams are different than the original test, are difficult, and will not have any bonus questions.
During a Test:
- No one will be excused to use the restroom. (Go before class.)
- Ask for scratch paper if you need some.
- All class materials will be clearly put away.
Students should not discuss a test with anyone after taking it. (You don’t know who is listening.)
Do not ask your friends about the test. This pressures them to tell you something they shouldn’t.
Tests may vary by class period. However, sharing any information about the test is still not allowed.
There are no re-takes for tests and no tests are dropped from grades.

Introductory Letter

Dear Students and Parents/Guardians,

This class is a unique opportunity for the students in the San Dieguito Union High School District. We are very fortunate to have the cooperation of the Math Department at San Diego State University to award college credit to students who are successful in this course. I will communicate with you regarding the details of course fees and enrollment procedures as they become available.

Please note that, as a participant in a 3 unit college course, students are expected to spend significant, meaningful time outside of class working on assignments, reviewing material, and preparing for exams. One “rule of thumb” is that students should be committed to work toward mastery at least 2 hours per unit per week outside of class, that is 6 hours per week for a 3 unit course.

Also, as part of a standards-based curriculum at TPHS and throughout SDUHSD, you/your student will be engaged in a variety of instructional strategies and assessments. Through presentations, interviews, pictures, project journals, reflective writing, peer critique, and videotape I hope to record the progress of your/your student's learning. My goal is to enhance all students' learning through reflective practice, a framework for learning that my colleagues and I have found motivating and effective.

One of the strategies that I employ to cultivate my own learning as an educator is to share what I do in my class with others--teachers, administrators, parents, students, and professionals in and outside of the Torrey Pines High School community. In a few weeks I will send home a letter describing more details of the project I have in mind and will be asking for your permission to share your student's work with others.

I am looking forward to this new school year with much enthusiasm. Each student will have the opportunity to explore new mathematical ideas and share what they have learned with others. If you have any questions or concerns please contact me through the school at (858) 755-0125 ext. 2120 (voice mail only) or abby.brown@sduhsd.net (e-mail preferred).

Thank You,
Abigail Brown

grades

80% Tests (Two Exams 20% each + Final Exam 40%)
20% Notebook, Quizzes, Projects, Extra Activities, Participation, Attendance
__________________

100% Final Grade

Note: The only “extra credit” in this course is through a few bonus questions on tests.

Please note that grades are usually updated and posted online after tests. Progress reports for students earning less than 70% are distributed mid-quarter and are also available upon request: abby.brown@sduhsd.net.

Online Progress Reports

For information about transcripts, please refer to:

Notebook

Read assigned section thoroughly at home.
List all vocabulary with definitions.
Write all theorems.
Include any other notes and examples you feel would be most helpful.
Do the class exercises in your notebook too.

You may type your notes. However, equations can be difficult to do. Also, one good learning method is to write things out for yourself.

There may be random notebook checks in class.

Note: I really expect you (the students) to do this. If I find that you are not, I reserve the right to change the class organization and/or grading system. You will, of course, be notified of any such changes.
Assignments available on Course Notes page.

Quizzes

There will be approximately one quiz per chapter.
Quizzes will be assigned as take-home worksheets and will be graded for completion.
Students should use quizzes as an opportunity to assess current understanding of the material. Textbooks, course notes, and calculators should only be used after completing as much of the quiz as possible by yourself.
Quizzes will be discussed in class the class period after they are assigned.
PDF files for quizzes available on Course Notes page.

projects

In this course students give regular, informal presentations from the problem sets. These presentations are not rigorously graded, but are included as part of the students’ participation grades. Please refer to the Calculus C and D presentation information for details about more formal presentations should we choose to do them in Linear Algebra. There will be a final project at the end of the year.

course outline

Calendar: Linear Algebra Spring 2012

Course Notes (Assignments, Quizzes, Additional Notes)

(3 semester units)

Text: Elementary Linear Algebra, Howard Anton (8th edition) (PDF Outline)

Chapter 1 — Systems of Linear Equations and Matrices

1.1   Introduction to Systems of Linear Equations
1.2   Gaussian Elimination
1.3   Matrices and Matrix Operations
1.4   Inverses; Rules of Matrix Arithmetic
1.5   Elementary Matrices and a Method for Finding A^-1
1.6   Further Results on Systems of Equations and Invertibility
1.7   Diagonal, Triangular, and Symmetric Matrices

Chapter 2 — Determinants

2.1   The Determinant Function
2.2   Evaluating Determinants by Row Reduction
2.3   Properties of the Determinant Function
2.4   Cofactor Expansion; Cramer's Rule

Chapter 3 — Vectors in 2-Space and 3-Space

3.1   Introduction to Vectors (Geometric)
3.2   Norm of a Vector; Vector Arithmetic
3.3   Dot Product; Projections
3.4   Cross Product
3.5   Lines and Planes in 3-Space

Chapter 4 — Euclidean Vector Spaces

4.1   Euclidean n-Space
4.2   Linear Transformations from Rⁿ to R^m
4.3   Properties of Linear Transformations from Rⁿ to R^m

Chapter 5 — General Vector Spaces

5.1   Real Vector Spaces
5.2   Subspaces
5.3   Linear Independence
5.4   Basis and Dimension
5.5   Row Space, Column Space, and Nullspace
5.6   Rank and Nullity

Chapter 6 — Inner Product Spaces

6.1   Inner Products
6.2   Angle and Orthogonality in Inner Product Spaces
6.3   Orthonormal Bases; Gram-Schmidt Process; QR-Decomp.
6.5   Orthogonal Matrices; Change of Basis

Chapter 7 — Eigenvalues, Eigenvectors

7.1   Eigenvalues and Eigenvectors
7.2   Diagonalization
7.3   Orthogonal Diagonalization

Chapter 8 — Linear Transformations

8.1 General Linear Transformations
8.2 Kernel and Range

We may also include some additional topics from Chapters 8, 9, and 10.