Linear Algebra

Spring 2015

CRN 21692
MW 10:30-11:50, UGLC 208; 3 credit hours

Other resources

• article ("The Growing Importance of Linear Algebra in Undergraduate Mathematics", Alan Tucker, The College Mathematics Journal, Vol. 24, No. 1. (Jan., 1993), pp. 3-9) about the history of linear algebra; the bottom of page 5 and top of page 6 (the third and fourth pages of the article) briefly describe the origin of matrix multiplication. [Note: the link will only work from UTEP computers, or other computers that have access to JSTOR.]
• blog post "Mathematics Professors and Mathematics Majors' Expectations of Lectures in Advanced Mathematics"
• author's website for the book, including Table of Contents and two sample chapters, ordering information and more.
• Major theorems for midterm exam
• Major theorems for final exam
• Syllabus in pdf
• Homework guidelines in pdf
• Camscanner, a useful tool for scanning (and then emailing) homework; free versions for iOS, Android, Windows Phone.

Syllabus

Instructor: Dr. Art Duval

Please feel free to come by my office any time during scheduled office hours. You are welcome to visit at other times, but in that case you might want to make an appointment, just to make sure that I will be there then. You can make an appointment simply by talking to me before or after class, by calling me at my office or at home, or by sending e-mail.

You may also ask any questions directly via phone or e-mail. If I'm not in when you call, please leave a message on the voice-mail or answering machine with your name, number, and a good time for me to call you back. I will try to respond to your phone or e-mail message as soon as possible.

Prerequisites:

MATH 3325, or an equivalent course where you learn the basics of writing proofs.

COURSE OBJECTIVES:

Upon successful completion of the course, you will be able to prove (and occasionally discover) theorems in linear algebra, at the level of abstraction of linear transformations and vector spaces; other major topics include eigenvalues/eigenvectors and inner product spaces. You will know, understand, and be able to apply, prove, and explain major results in this area. You will be better able to independently read advanced mathematics.

Note:

In contrast to Matrix Algebra (Math 3323), we will be focusing on proofs and theory instead of applications (though theory lies closer to applications in linear algebra than it does in, say, analysis), vector spaces instead of R^n, and linear transformations instead of matrices. Otherwise, many topics will look familiar.

Textbook:

Linear Algebra Done Right, 3rd ed., Sheldon Axler, Chs. 1-6, 8. We will generally spend one to two class periods per section (see Table of Contents), though parts of Chs. 1, 2, and 4 should be review, and we will go a little faster through these. We will skip some sections, as announced in class.

You will spend a substantial amount of time outside of class reading the textbook. The course will be structured to encourage and support you in this endeavor. In-class activities will center around our making use of what you have read outside of class.

Homework and Participation:

For each section of material we encounter, there will be three kinds of homework, as follows (more details are on a separate handout):
You will read the section carefully, write responses to reading questions, create some of your own questions, and reflect. The written part of this assignment will be due before we discuss the material in class.
Warmup exercises (10%):
On the day of our class discussion over the material, we will discuss easier warmup exercises. You will prepare your answers, in writing, before class, and the class will share answers in small groups or whole class discussions.

I expect everyone to attend and participate actively in class, in particular to speak up during class discussion with questions and ideas, and to work well with others. Your active participation in class will constitute a substantial part of this part of your grade for the course.

Main exercises (30%):
After our class discussion over the material, you will turn in clearly-written solutions to harder homework problems. These will generally be due weekly.

Graduate students taking this class will be assigned additional main exercises, in accordance with university policy.

Written assignments (for all three kinds of homework) will not be accepted after they are due, except in extenuating circumstances that you explain to me as soon as possible. Incomplete homeworks will be accepted, though, so please turn in whatever work you have completed when homework is due. You are encouraged to work together on your homework, but you must write up your solutions by yourself.

Exams:

Midterm (15%):
The midterm will cover all material we have discussed to that point, and will be on
Wed., 18 Mar.
Final (25%)
The final exam will be comprehensive over all material we discuss in class. The final will be on
Fri., 15 May, 10:00 a.m.-12:45 p.m.

Makeup tests can be given only in extraordinary and unavoidable circumstances, and with advance notice.

POLICIES:

It is UTEP's policy, and mine, for all suspected cases or acts of alleged scholastic dishonesty to be referred to the Office of Student Conduct and Conflict Resolution for investigation and appropriate disposition. See Section II.1.2.2 of the Handbook of Operating Procedures.

Attendance:

Due to the course structure, attendance is mandatory. There is no particular penalty for missing a particular class, but you cannot get a good participation grade if you miss too many classes. I will usually "excuse" an absence if you tell me about it in advance, or, in cases of emergencies, as soon as possible afterwards. My goal is for class meetings and activities to complement, rather than echo, the textbook, and thus for every class to be worth attending.

Drop date:

The deadline for student-initiated drops with a W is Monday, April 6. After this date, you will not be able to drop the class (as per the Dean's office). Furthermore, a grade of incomplete is only for extraordinary circumstances, such as a missed exam.

I hope everyone will complete the course successfully, but if you are having doubts about your progress, I will be happy to discuss your standing in the course to help you decide whether or not to drop. You are only allowed three enrollments in this course, and students enrolled after Fall 2007 are only allowed six withdrawals in their entire academic career, so please exercise the drop option judiciously.

Courtesy:

We all have to show courtesy to each other, and the class as a whole, during class time. Please arrive to class on time (or let me know when you have to be late, and why); do not engage in side conversations when one person (me, or another student) is talking to the whole class; turn off your cell phone (or, for emergencies, at least set it to not ring out loud), and do not engage in phone, email, or text conversations during class.

Disabilities:

If you have, or suspect you have, a disability and need an accommodation, you should contact the Center for Accommodations and Support Services (CASS) at 747-5148, cass@utep.edu, or Union East room 106. You are responsible for presenting to me any CASS accommodation letters and instructions.

Exceptional circumstances:

If you anticipate the possibility of missing large portions of class time, due to exceptional circumstances such as military service and/or training, or childbirth, please let me know as soon as possible.