Math 118
Linear Algebra
Section 1

Syllabus

Fall 2004

Time:

MWF 11:30 am - 12:20 pm

Place

Wilson 411

Instructor

Professor Hotchkiss

Office

Wilson 419

Office Phone

572-5575

Home Phone

562-1658 No calls after 10 pm, please.

E-mail

photchkiss @ wsc.ma.edu

            

This is a great way to get in touch with me.

Office Hours

   .1cm

Monday	2:30 - 4:00 pm
Wednesday	2:30 - 3:30 pm
Thursday	1:30 - 3:00 pm
and by appointment

Text

Elementary Linear Algebra 2nd Edition by Nicholson

THE COURSE

Linear Algebra is one of the fundamental tools of mathematics. Almost every branch of mathematics uses techniques from Linear Algebra in an essential manner. The term Linear Algebra has two meanings. It describes the algebra needed to simultaneously solve a set of linear equations. Linear Algebra also refers to the study of collections of objects that satisfy certain conditions. These two ``definitions" may seem to be completely unrelated, but in fact the tools and underlying ideas used in each area are the same. In this course we will study the tools and ideas that are used in each aspect of Linear Algebra.

As with calculus, we will use the Rule of Four:

Concepts should be investigated and understood in algebraic, numeric, graphical and verbal (written) representations. Moreover appreciation of the relationships between these representations is essential to the development of conceptual understanding of mathematics.

GOALS

   

• To learn about the nature of linear algebra and some of its applications.
• To improve your mathematical reasoning.
• To improve your ability to read and write mathematics.

HOMEWORK

The problems that are assigned for each section are meant to be representative of what you should be learning. It is extremely critical that you work on the homework problems when they are assigned, as they will help you understand the concepts and techniques that we are studying. Putting them off will cause you to fall behind and can lead to a failing grade! While many of these problems will be routine computational problems, some of them will be more detailed and non-routine and may take upwards of an hour to solve; you should not be discouraged by this. If you are struggling with a problem, sometimes it is helpful to put it aside for a while and then come back to it later. If you can not solve a problem you need to ask about it, either in class or during office hours. When you ask a question about a problem it will be most helpful if you can indicate what progress you have made and where exactly your difficulties lie. You should keep neat detailed solutions in a section of your notebook. After doing the assigned problems, I expect you to read the unassigned problems, and if you haven't mastered the topic in an unassigned problem, attempt the problem. While I will not regularly collect the problems assigned, it will be assumed that you are doing them. I also urge you to regularly study and work on the homework together.

WeBWork

WebWork is an online system for assigning and grading homework problems that we will be using this semester. The URL is http://hosted.webwork.rochester.edu/webwork2/WSC_ma0118.

Each Monday you will be assigned several problems based on the material we covered the previous week that will be will be due the following Monday. You will log in to the site (your user id and password will be assigned shortly) to get your assignment. You can then print the problems so you can work on them and when you are finished you will log back on and submit your answers online. The system will immediately tell you whether your answer is correct, and you may resubmit a solution to a problem as many times as needed (up to the due date) to get the answer correct. While I strongly encourage you to work together on these, each problem on your problem set will be slightly different from everybody elses, so you can not just copy the answer from someone else in the class.

PROBLEM SETS

Two of the goals of this course are to improve your mathematical reasoning and your reading and writing of mathematics. Being able to understand and use correct mathematical reasoning and communicate your work is at the heart of mathematics. Of course the best ways to learn these skills is to do them, and so I will regularly assign several problems that are to be handed in the following week. These are graded homeworks so you should do these on your own. You can expect, at sometime during the semester, to be stumped by a problem. You should direct any questions about these problems to me; do not hesitate to get help from me during office hours or other times. Your practice at mathematical writing and reasoning in this course will provide a ground work for any mathematics course you take later.

WORK GROUPS

Group work will be an important part of this course. Most of the time we will be working in small groups during class and I strongly encourage you to work in groups of 3 or 4. I will not assign these groups because you will need to find people whose schedule is compatible with your own. You should sit with your groups every day as we will be doing group work quite often. The purpose of this is twofold. First, working in groups is essential in any job and second, working in groups is excellent opportunity to stop and think (and therefore learn) about what we are doing- with the added benefit of having someone to help work out those things you are not clear about.

GRAPHING CALCULATORS

One of most critical tools this semester will be the Graphing Calculator. If you are a mathematics major, or are considering majoring in mathematics, you will need to purchase a Voyage 200 (recommended) or a TI-89. You can purchase these through TechLine Inc., either online at http://www.tech-line-inc.com or over the phone (1-800-777-3635). The Voyage 200 and TI-89's contain a Computer Algebra System (CAS) and as far as I know, no other brands contain a CAS. These calculators will be invaluable as you go through our program. If you are not a mathematics major, you should still buy the TI-89. While these also contain a CAS, they do not have some of the software that the Voyage 200's have. We will be using the calculator both in and out of class on a regular basis, so you will need to bring it to class with you every day.

EXAMS

In addition to the problem sets, there will be three in class exams on September 29, November 8 and December 3. The final exam will be December 17 from 2:30 - 4:30 pm. Calculators will be allowed and will be almost essential. If there is any conflict with either exam please notify me ahead of time, at least a week if possible. There will be no make-ups given except in extenuating circumstances.

ATTENDANCE

You are expected to attend class each day and are responsible for all material covered in class (which may at times include material not covered in the text). I will take attendance every day and you are allowed no more than three unexcused absences.

SCALE

The (minimum) scale on all graded material will be the following straight scale.

95-100	A
90-94	A-
87-89	B+
84-86	B
80-83	B-
77-79	C+
74-76	C
70-73	C-
67-69	D+
64-66	D
60-63	D-
below 60	F

Curves are not considered until the course grades are being assigned.

GRADES

Course grades will be determined using the following percentages:  

Exams	40%
Problem Sets	20%
WebWork Assignments	20%
Final exam	20%

A ``borderline grade'' may be raised to account for class attendance and participation.

TENTATIVE SCHEDULE

WEEK	TOPIC	SECTION
1	Introduction and Matrices	1.1
2	Solving Simultaneous Equations	1.2, 1.3
3	More on Simultaneous Equations, Matrix
	Multiplication and Inverses	1.3 - 1.5
4	Inverses, Elementary Matrices, LU Factorization	1.5 - 1.7
5	Exam 1
	Determinants	2.1
6	More on Determinants and Inverses	1.9
7	Columbus Day
	Diagonalization and Eigenvalues	2.3
8	Vector Geometry	3.1, 3.2
9	Lines, Planes and the Cross Product	3.3, 3.5
10	Matrix Transformations	3.4
11	Exam 2
	Subspaces of \BbbRn	4.1
12	Linear Independence	4.2
13	Dimension	4.3
	Thanksgiving Break
14	Rank	4.4
	Exam 3
15	Orthogonality and Projections and Approximations	4.5, 4.6
16	Review

TIPS

   

• Read through your notes and the section(s) to be discussed before you come to class. It is not necessary that you understand everything you read, but it will help you know where you might have difficulties.
• A full understanding of the homework in a good indication of potential to perform well on the examinations. Since the homework is based on the class material and the pertinent sections in the book, both class attendance and reading is your best help. The homework assigned is the least amount of problems you should be doing. If you have difficulty with a problem, be sure to find a similar problem to do after you think you have a firm grasp of the ideas. Also go over text examples and other examples done in class.
• Ask questions as they come up in class. If there is a theoretical question, be sure to get it answered before we move into another section. The day before an exam is not adequate time for information to sink in.
• Try to follow along as the problems are being done in class. In fact, you may try to do the problem yourself as I am doing it on the board. This should solidify your understanding of the material.

ADDENDUM

   

• This syllabus is subject to change with prior notification.