Text: Linear Algebra, 3rd edition, by Fraleigh & Beauregard, Addison-Wesley, 1995
Students Solution Guide
Instructor's Solutions Manual (for instructor use only)
MTH 2053 is intended to serve several purposes: (a) introduce
students to the fundamental concepts of linear algebra, (b) demonstrate
applications of these concepts, and (c) allow students to become
more familiar with the nature of definition and proof in mathematics.
Linear Algebra is also feeling the effects of graphing calculators
and computer packages. We encourage the use of calculators or
computers in order to perform routine computations in order to
give students more time on abstract concepts. Those who enroll
in this course are majoring primarily in mathematics, engineering,
physics, or computer science, planning to transfer theses credits
to UT (as M311) or to another four-year institution.
Prerequisites: The usual prerequisite for linear algebra
is completion of the calculus sequence, MTH 2154 (Calculus III).
Occasionally students who have demonstrated "mathematical
maturity" may enroll with a less formal mathematics background
after obtaining the consent of a mathematics department advisor.
Such students should be familiar with vector notation and dot
product. Also, it is not uncommon for students to be simultaneously
enrolled in Linear Algebra and Calculus III.
Syllabus: The course covers chapters 1-7 of the text and
appendix A-1 (induction). A suggested course outline is as follows:
| 16-Week Semester | 6-Week Semester | |
| Week | Sections | Sections |
| 1 | 1.1, 1.2, 1.3 | 1.1-1.6 |
| 2 | 1.4, 1.5 | 1.7, 2.1, 2.2, 2.3, 2.4* |
| 3 | 1.6, 1.7, 1.8* | 3.1-3.5 |
| 4 | Test #1 (Chap. 1), 2.1 | Induction, 4.2, 4.3, 5.1 |
| 5 | 2.2, 2.3, 2.4* | 5.2, 5.3*, 6.1, 6.2 (6.3, 6.4, 6.5**) |
| 6 | 3.1, 3.2 | 7.1, 7.2, Summary, Exam |
| 7 | 3.3, 3.4 | |
| 8 | 3.5, Test #2 (Chap. 2 &3) | |
| 9 | Induction, 4.2 | |
| 10 | 4.3, 5.1 | |
| 11 | 5.2, 5.3* | |
| 12 | Test #3 (Chap. 4 & 5), 6.1 | |
| 13 | 6.2, 6.3** | |
| 14 | 6.4**, 6.5** | |
| 15 | 7.1, 7.2 | |
| 16 | Review, Test #4 (Chap. 6 & 7) |
The sections marked with a "*" are optional. Consider
including them if you have time. You may find other interesting
sections in the text that you want to cover instead. There
is some flexibility based upon the time you have available. The
sections marked with "**" are also optional. You might
consider moving on to sections 7.1 and 7.2 after 6.2 and then
covering the first two or three sections in Chapter 8 on quadratic
forms or possibly skipping on to Chapter 10. Again there is some
flexibility allowed based upon your interest and time constraints.
Exams and Grading; Exams should check student understanding
on a broad front. Plan to include questions regarding: definitions,
computational problems, and proofs similar to those discussed
in class and assigned on homework. Proofs are initially difficult
for beginning linear algebra students, but they make remarkable
improvement later in the course. Homework should be graded. One
plan is to collect homework at each exam and grade a few selected
problems that count as 20% of the exam grade.
Attendance: You should keep track of attendance and you
may drop students who miss more than four classes. Be sure students
have in writing on the first class day that you might drop them
for more than four absences. Some students who stop attending
expect their instructor to fill out a withdrawal form for them.
Your first day handouts should indicate that you will not
be responsible for withdrawing students. In general, require students
to take care of their own paperwork. You should announce your
policy in writing on your first-day handout.
Incompletes: Incompletes should be given rarely. One should
consider an incomplete grade (I) only for a student who has taken
all exams, is passing, and has a personal tragedy occur after
the last date to withdraw which prevents course completion.
First-Day Handout for Students: You should provide a first-day
handout to your students that provides information of the following:
(a) name of the text
(b) prerequisite
(c) syllabus and projected course timetable
(d) testing timetable and grading policies
(e) homework policy
(f) withdrawal policy for excessive absences
(g) incomplete policy
(h) your name, office number, office hours, and office phone