# Introduction to Linear Algebra (Honors)

#### Basic Information

• Manil Suri, Math/Psych 419, (410) 455-2311, suri@umbc.edu,
office hours: MW 3:30-4:30. Also by appointment.
• Lectures: MW 1:00-2:15, Meyerhoff Chemistry 256
• Text: “Linear Algebra and its applications” by David C. Lay (4th edition)
• Prerequisites: Math 141,151,155 or 380

#### 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

The honors version will, firstly, include a more general treatment of topics (for example, more general vector spaces, rather than concentrating mainly on R^n). Secondly, we will include some proofs, which will help to better understand and absorb the theorems (and also prepare you a little for Math 301, if that’s in your future). Most importantly, we will place less emphasis on performing computational exercises by hand. Instead, we will make use of the computer program MATLAB, which will allow us to handle larger, more realistic systems and apply the concepts we learn to the solution of more “real-life” problems. (In particular, the computer assignments are not included in a non-honors class.) We will also begin to get an understanding of how some of the ideas in this course pervade almost all branches of mathematics, as well as other related and unrelated fields.

Please be advised that this is a “hard-core” honors course, significantly more challenging than the non-honors version. Although you will benefit through more personalized attention (max class size is 20), you should make sure you have enough time, energy and motivation to put into the class. 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.

#### Learning Goals

This course has the following goals.

• Knowledge-based: Knowledge of key definitions such as vector space, basis, linear independence, rank, eigenvalue, eigenvector, which are essential components of the language of mathematics. (Homework, tests and the final are geared towards this and the goal below.)
• Technique-based: Usage of the above to decompose and analyze problems (such as solving linear systems).
Proof-based: Enhancing your arsenal of techniques to prove mathematical theorems. (Sample examples in class, and some selected HW problems will assist in this.)
• Computational: Introduction to Matlab, a computational tool that you will find valuable in other courses as well. (Computer HW projects will help in this and the goal below.)
• Applications: Using theoretical results in applied “real-life” examples, to see how they come into play.
• Big Picture: Extensions to other mathematical subjects, generalizations and limitations. Broad scope of intrinisic ideas and their appearance in other fields. (I will give a powerpoint presentation on this when we cover basis functions.)

#### Syllabus

We will cover the following sections (subject to modifications):

• 1.1-1.5
• 1.7-1.9
• 2.1-2.3
• 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 (e.g. 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. Problems will be assigned via Blackboard (under ‘Homework.’)

1. PAPER AND PENCIL HW Problems (Denoted HW P1, HW P2,.. etc): These will include both PRACTICE and CREDIT problems.

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.

CREDIT problems will be graded for credit. (Note: Only selected problems will be graded, not every one you submit!) The problems for sections completed in any given week will be due the next week, on Wednesday. Any difficulties with HW problems should be brought up in class on Mondays or at my office hours.

2. MATLAB problems (Denoted HW M1, HW M2,…etc). These will require MATLAB to complete. They will be announced in class and posted on Blackboard.

• There will also be a few CHALLENGE problems (denoted C1, C2, etc) which MUST be attempted and turned in. These will lead to additional credit.
• TESTS will be given twice in the semester. The dates will be announced well in advance. Problems will be similar to the HW problems. Sample tests will be handed out in advance.
• FINAL This will be cumulative. It will be held on Wed, Dec 17, from 1-3 pm in our regular classroom. 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.

• Paper/Pencil Homework: 15%
• MATLAB Homework: 15%
• Tests: 40%
• Final: 30%
• CHALLENGE HW scores will be added on top of this (at least an additional 5% potentially)
• Cut-offs: A: 90%, B: 80%, C: 65%, D: 55%

#### MATLAB

Matlab is available on UMBC computers (and also can be purchased in student versions). You should also be able to access Matlab free of charge remotely on your home computer or laptop, using these directions.The document Getting started with MATLAB (look down near the middle of the page) 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 (upto #13, for now), and you should complete this by yourself (ask me in class if problems occur).

(Also see Introduction to Matlab. Follow “Getting started with Technology” tab, and then click on topmost link.)

#### Study Suggestion

The author, David Lay, has various study aids on the website webpage. For example, you might find the “Transparency Masters” useful. 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.

#### Important Dates

Wed, Sep 10 is the last date to drop a class without a W on your transcript. Tue, Nov 11 is the last date to drop this class with a grade of W. Please do not hesitate to talk to me if you need some guidance on how to proceed regarding these dates.
On Tue, November 4, UMBC is presenting a play on mathematics which I would like everyone to attend. More details later, but please mark it on your calendar. Please talk to me the week before in case you are unable to attend.