Below, I discuss
Linear Algebra and Its Applications, by David Lay.
Optional: The Study Guide for Linear Algbebra and Its Applications, ISBN 0-201-64847-4. There are (or will be) two copies of this on reserve in the library. Take a look at it, and if you decide you'd like to order it, the book store will order it for you for you, I believe.
At the very basic level, Linear Algebra is concerned with solving systems of linear equations like
2x + 3y + 2z = 10 x - 6y + 2z = 2At first glance, this may seem simple or even boring, and you can't imagine how we're going to spend an entire semester on this topic. You may not be surprised to find that it turns out that people run into systems of equations like these (sometimes with many more equations and variables) all the time. What you may indeed be surprised at is how interesting the prospect of solving systems of equations is! For one thing, these seemingly mundane algebraic questions have very deep geometric interpretations. We will be able to play the algebraic and geometric views against each other to gain insights and build intuition about both. Fundamental to developing this intuition is an understanding of the relationship between matrices and linear transformations, which are special types of maps from n-space to m-space.
The interconnections among systems of linear equations, matrices, and linear transformations provide a framework for applications to vastly different areas. Some of the applications we will look at this semester include applications to population dynamics, computer graphics, and the long-term behavior of dynamical systems.
Course Organization and Expectations:
As you probably already know, math is best learned by doing, not by watching. Therefore, the class will be structured to combine some time spent on lectures to introduce material or to emphasize particular topics with much time spent on in-class work. The class meetings are not intended to be a complete encapsulation of the course material --there will be material in the text for which you are responsible that we will not cover in class.
As you probably began to learn in Calculus, being able to do problems similar to those in the book is not really what math is all about, although it is certainly necessary. Really learning mathematics involves being able to solve problems that are different from anything you've ever seen and communicating the results. Solving new problems requires starting a problem even if you don't know how to finish it, being able to think of and try several different approaches, and being able to easily translate from English to ``math'' and back again. Communicating mathematics of course goes in both directions -- not only to you have to be able to read and write clear and concise mathematics, but you have to be able to understand it when it's communicated to you.
To help you gain in your abilities to dive into mathematics and to communicated mathematics, the course will emphasize problem-solving, and reading, speaking, and writing mathematics.
Thus in addition to the usual homework problems, quizzes, and exams, you will also be reading the textbook (and answering questions on the reading), working in groups, and doing two projects which will consist of larger, more open-ended problems.
As mentioned above, one of the goals of this class is that you become comfortable reading mathematical material.
Before each class meeting, you will read the material that we will be discussing that day. To give you credit for your efforts, I will post questions on the web that cover each day's reading. You will send the responses to those questions by 8am of the day they are due.
See the guidelines for submitting reading assignments .
You can get to the appropriate chapter's web page from the course's web page.
These reading assignments are required, and will be graded out of 2 points each: 2 points if you respond in full (whether correctly or not) and 1 point for a partial response. Late responses will not be accepted. I expect to drop each person's lowest three score at the end of the semester. People who do not miss any reading assignments will receive a small amount of extra credit.
Weekly problem sets will alternate between being done individually and in groups. Problem sets will be due most Wednesdays at the beginning of class. You should begin each new problem set on Wednesday afternoon and work on it throughout the week, as these problem sets represent a week's worth of learning.
Your assignments will be posted on the web, and can be found through links toward the bottom of the course web page.
Consult the Guidelines for Homework Presentation for information on how your problem sets should look.
|Late problem sets will not be accepted!|
To give you an opportunity to solve problems that are more realistic--problems which do not necessarily have one ``right'' answer, which can be approached in a variety of ways, and which take several days of pondering to solve --you will work on two group projects this term.
The due dates are (tentatively) listed on the syllabus.
One of the main goals of the projects is that you learn to communicate mathematics precisely, both verbally with your group and in writing. The reports should be written in complete sentences explaining the results and major ideas involved. Every member of the group is responsible both for understanding the mathematics of the project and for the clarity and quality of the explanation in the report. You may not divide the mathematics in any significant way, but you may divide the writing of the report in whatever way is agreeable to the group. Everyone should completely understand the whole of the paper and each member should proofread the entire paper for consistency and typos.
Late projects are only accepted in extreme circumstances, and usually with penalties.
Quizzes and Exams:
The takehome exams will have some problems that are similar, but not identical, to homework exercises. However, most of the exam problems will ask you to combine your knowledge of several different topics from the course. You can ask me as many questions as you want about the exams, but you may not discuss the exams in any way with anybody except me.
The quizzes will be short and on very specific topics. They will be mostly computational, but you may also need to state definitions or theorems precisely. I will tell you the exact topics that each quiz will cover.
See the Tentative Syllabus for the dates of the exams and quizzes. The final will also be a take-home exam, and will be due at 2pm on December 14th.
I expect to use the weights below, although I reserve the right to change my mind if the semester does not go as expected.
|Two Takehome Exams||30%|
I expect you to abide by the Honor Code. Below are some guidelines on what constitutes violations of the honor code in this class.
Reading assignments: You may discuss the questions with your classmates, but you must enter the responses yourself, in your own words.
Homework and Projects: You may work with anybody you want. You may use any references that help you figure out how to do the problem on your own; you may not use any references (people, old homework or projects, books, the web, for instance) which tell you how to solve it or lead you to the solution. You must understand how to do every problem, and you must cite references if you've received assistance from any source. When doing group projects or group problem sets, you may not divide the mathematics into different parts--you must do them all together, and you must make sure every member of your group understands every part. Exams: All of the exams are take-home exams. The only person you may discuss the exam with is me. You may use calculators, Maple, and your text. You may not look in other texts for solutions, or look at any exams from previous Linear Algebra classes.
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278