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Advanced Linear Algebra
Math 462 - Fall 2009 - Section 15224
California State University Northridge
Bruce E. Shapiro, Ph.D.
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Subject to Change. Last Revision: 28 Sept 2009.

PDF syllabus   Lecture Notes   Using Latex   Homework Exercises   Impact of Budget Crisis
Step-by-Step Latex installation instructions for Vista     Schedule
 
Announcements

Wed Dec 9: Study Day, No Class

Final Exam: Monday December 14, 8:00 PM

Download a draft of "Introducing Latex" notes by BES.

Here are some other (probably more) useful Latex Notes

Get a List of Latex Math Symbols

Get the official Latex Users Guide

Get a Latex Command Summary

Get the Latex Wiki Book

 

Class Location:

Class Time:

Class Number:

Instructor:

Email:

Office Hours:

Chaparral 5114 (What? Where's that?)

Mon/Wed 7:00-8:15 PM

15224

Bruce E Shapiro Ph.D

bruce.e.shapiro at csun.edu

Monday 5:30-6:30, Wed 3:30-4:30 Bookstore Atrium.
[Click 4 Map]
Class Web Page: http://www.beshapiro.com/math462/
Students are responsible for checking the web page regularly for announcements and homework assignments.
Class Description from catalog: picture of CSUN catalog cover Prerequisite: Math 262; MATH 320.

Finite dimensional vector spaces, linear transformations, matrix polynomials, canonical forms.
 

The Real Pre-requisites (what I expect to you to know coming in to the class):

Image of Woman Teaching Geometry, from a medieval translation of Euclid's Elements. Linear Algebra: I would exepct you thave some familiarity with the following: real vectors in 2 and 3 dimensions; length of a vector (know how to compute it); dot products (know how to compute it); scalar multiplication (know what the difference between a scalar and a vector is and how to multiply them); basis vectors (know what they are; you probably called them i, j, and k); linear dependence/linear independence (know what it means); matrix multiplication; determinants (know what they are and how to calculate up to 3x3); matrix transpose and inverse; eigenvalues and eigenvectors (know what they are and how to calculate them up to 3x3). All of these things are covered in Math 150 A/B, 250 and 262, so if you've had them at CSUN you'll be fine.

Proving: This class is primarly theoretical, meaning you will have to do a lot of proofs. The whole class will be basically theorem-proof. This is why 320 is a prereq. You should have some experience proving theorems and be fairly comfortable with the concept of proofs.
 
Student Learning Outcomes:
Upon completing this class, the student should be able to:

  • Do better at solving math problems than this (see picture)
 
Topics Covered:

The following subjects will be covered (not necessarily in this order):

  1. Using Latex
  2. Vector Spaces
  3. Subspaces, Sums, Direct Sums
  4. Span, Dimension, Linear Independence
  5. Linear Maps, Range, Null-space, Invertibility
  6. Matrices of Linear Maps
  7. Polynomials, real and complex roots
  8. Eigenvalues and Eigenvalues
  9. Inner Product Spaces
  10. Operators on Inner Product Spaces
  11. Trace and Determinant
 

Grading Policy:

There will be approximately four or five homework sets and a final exam on Mon. Dec. 14 at 8:00 PM. They count equally (i.e., the final exam has the same weight as one homework set). Homework should be typeset using Latex and should be clearly written (explain steps in an easy to follow sequence). Your grade will be reduced by 3 points for each unexecused absence.
 

Attendance:

Is required and your grade will be penalized if you miss too many classes. Your grade will be reduced 3 points (out of 100) for each unexecused absence.
Remember to sign in during every class.
 

Textbook:

Cover Image of Axler's Book Axler, Sheldon. Linear Algebra Done Right, Second Edition, Spring, 1997, ISBN 0-387-98258-2
[ Find a copy to buy ]
[ Publisher's Web Site ]
[ Author's web site ]
MSRP: $39.95 (paperback) $74.95 (hardcover)
 

Cookies:

 I encourage students to bring snacks to share with me and the rest of the class.
 

Student Conduct

Students are expected to conduct themselves in accord with university policies on Student Conduct and Academic Dishonesty. Violation of this code could be punishable by a failing grade in the class or removal from the university, as determined by Dean of Students.

I require students to sign an affirmation that they will abide by the student conduct code (and not cheat in this class) and to reaffirm this contract at each exam. If you are uncomfortable signing this affirmation you should not enroll in this class.

The student conduct code is posted at: http://www.csun.edu/a&r/soc/studentconduct.html and is in the University Catalog, Appendix C.

View the Student Conduct Code


Download the University Catalog, Appendix C, Student Conduct Code, in pdf format..
 

You are no doubt aware of the California's budget deficit and economic crisis. The CSU (California State University System) is facing a $585 million dollar reduction in funding. The cut to CSUN is in the tens of millions of dollars. By cutting back on salaries for faculty, administrators, managers, staff workers, maintenance workers, nurses, instructors, librarians, etc., our campus can make up a part of this shortfall. This is in addition to significant tuition increases and cuts to classes. All of these are ways this campus is trying to deal with the reality of the budget cuts to CSUN.

Most of the workers mentioned above are covered by a "furlough" plan, which means the workers will see a ~10% reduction in pay over the school year and a corresponding reduction in their workload. This semester you will see the whole campus closed on designated days. Each faculty member will also have nine furlough days during the semester. During these furlough days faculty cannot do any work (for the university): no returning or taking of phone calls, no reading emails, no grading papers, no teaching, no meeting with students, nothing.

You are paying more for your education now than ever before but note that these new rules for faculty mean that your instructors may have to cancel or reschedule some class meetings; may not get papers back as quickly as in the past; some assignments may not be collected or checked at all; may have to reduce office hours; and may have to omit material from some classes.

As you know this crisis has also meant that many course sections cannot be offered, have limited seats available and/or classes have been canceled.

This situation is outrageous and heart breaking for us. We want you to have the best academic preparation possible, but that goal is becoming more difficult to reach given the economic realities we all face.

We encourage you to step up and get involved in your higher education, your future, and the future of California. Contact your state legislators and tell them what you think. Contact our Governor. Attend the rallies and events that will occur on campus this semester. Join the Students for a Quality Education (SQE) group on campus. Take action! By taking action, we can make change!

Go to leginfo.ca.gov/yourleg.html to find out who your assembly and legislative representatives are.

 
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