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Introduction to Linear Algebra (Honors)

 

Math 221H (Spring 2004)
Instructor: Manil Suri
http://www.math.umbc.edu/~suri/math221H.html

Basic Information

  • Manil Suri, Math/Psych 419, (410) 455-2311, suri@math.umbc.edu,
    office hours: MW 4-5. Also by appointment.
    Lectures: MW 2:00-3:15, SS 101
    Text: "Linear Algebra and its applications" by David C. Lay (3rd edition)
    Prerequisites: Math 141,151,155 or 380. (Permission Required)

Overview

This course introduces you to linear algebra, with applications. The course starts simply enough, with a discussion of systems of m linear equations in n unknowns, and the connection with vectors and matrices. However, it then becomes more abstract, dealing with more general vector spaces and their properties. Certain aspects of the course, such as determinants and the calculation of eigenvalues are quite straightforward and computational, while others, such as the definitions of basis, dimension, linear independence and linear dependence, are more conceptual. Fortunately, there are several excellent "real-life" applications which give a good idea of the practicality and usefulness of the material. Since this is a challenging course, it is essential to keep up with what is being done in class - it would be very difficult to "catch up" if you get behind.

Honors Component

Since the course is being taught at an honors level, we will be paying more attention to proofs than the non-honors version of this course. There will be less emphasis placed on performing computational exercises by hand, and more emphasis on homework that is more conceptually interesting. We will make use of MATLAB, so that several of the assignments will be computer-based.

Please be advised that this is going to be a challenging course. The standard formula for math courses is that you should expect to spend three hours outside class on the material and assignments for every hour you spend in class. For an honors course like this one, you should expect to spend even more time outside class.

Syllabus

We will cover the following sections:

  • 1.1-1.5
  • 1.7-1.9
  • 2.1-2.3, 2.7
  • 3.1-3.3
  • 4.1-4.6
  • 5.1-5.3
  • 6.1-6.3.

In addition, selected applications will be covered from other sections (such as 1.6), and Sections 5.4,5.5,6.4,6.5 may be covered as time permits.

Tests and Homework

  • HOMEWORK is an essential part of the course. There will be two types of problems assigned.

    PRACTICE problems will be similar to the ones worked out in detail at the end of each section (and also the true/false questions in each section). These will not be collected for grading, and will generally be odd-numbered problems, for which answers are usually available at the back of the book. Any difficulties with these problems should be brought up in class or at my office hours. The problems in the mid-term test and the final will be similar to these problems.

    CREDIT problems will be of both paper/pencil and computer type. These will be graded for credit. They will be assigned at the end of each section, but collected approximately once every two to three weeks. Problems assigned and due dates will be available from my webpage, http://www.math.umbc.edu/~suri/hw.html


    TESTS will be given twice in the semester, on Mar 3 and Apr 19. These dates are subject to change.
    FINAL This will be cumulative. The final will be held in SS 101 on Wednesday, May 12, from 1 to 3 pm. All tests and the final are closed book.
    MAKE-UPS for tests will only be allowed under emergency circumstances with written documentation and prior approval if possible. If you miss something, contact me immediately (i.e. on that day) via e-mail (or phone).

Grading

  • Homework: 22%
  • Tests: 44%
  • Final: 34%
  • Cut-offs: A: 90%, B: 80%, C: 65%, D: 55%

MATLAB

All students are expected to have computer accounts (see the UMBC webpage for starting up). Matlab is available on UMBC computers, and also can be purchased in student versions.

The handout distributed during the first lecture, Getting started with MATLAB has a series of exercises which will help you learn the basics of MATLAB that we will need. We will be only using fairly elementary commands, and you should complete this by yourself (ask me in class if problems occur).

Study Suggestion

I will sometimes be using the notes that go along with this text, prepared by the author, David Lay. These are available under "Transparency Masters" on his webpage. Also available on this webpage are various review materials, and the first chapter of a study guide. If you miss a lecture, please have a look at the transparency master for that lecture. You might also want to read up a section ahead to get an overview of what we will be covering. To do well in tests and the final, I recommend that you attempt ALL the problems at the back of each chapter we cover.

Academic Conduct

Unless announced by me otherwise, credit homework problems must be done alone. This includes computer assignments turned in for credit. Please apprise me of any collaboration on homework turned in for credit. There is a thin line between discussing ideas related to a credit problem (which may be permissible) and actually solving the problem collaboratively. I reserve the right to ask you to reproduce proofs and computer computations in my presence if I feel this line has been crossed. Also, please note the standard policy statement that follows.

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, or the UMBC Policies section of the UMBC Directory.