Math 322 (Section 005): Matrix algebra and its applications (3
credits), Spring 2007
- Office : Patterson Office Tower 763
- Office Phone : (859) 257 6793
- E-mail : oshea at ms dot uky dot edu
(please have Math 322 in the subject line)
- Office Hours : Friday 11 - 1 in POT 763.
Announcements
- Adjusted Homework for Chapter 6:
- 6.1: 9,10,13--16,19,22,23,24,27--30.
- 6.2: 3,4,9--16,23ab,24ad,26.
- 6.3: 2,3,4,7,8,11--16,21abcd,24.
- 6.4: 3--6, 9--12,17ab, 18ab.
- 6.5: 3--10,13,14,17,25.
Basic Information
Lecture : White Hall classroom building (CB) 345
TuesThurs 9:30 - 10:45
Textbook : Linear Algebra and its Applications (3rd edition)
by David C. Lay.
Topics to be covered : We will cover most of Chapters 1-6 in
the text book. Time permitting, we may possibly cover
some of Chapter 7. In addition, the text may be supplemented with
material handed out in class. See tentative schedule below.
Grading scheme : The letter grade will be determined
according to the standard scheme:
A is 90-100%, B is 80-89%, C is 70-79%,
D is 60-69% and E is 0-59%. At the instructor's
discretion, the lower bound of each grade may be lowered but
not raised. See below for a detailed breakup of how grades are
distributed.
Homework, Attendance, Quizzes and Exams
Homework and Quizzes (25% of overall grade):
- Homework will be assigned in class. You do not need to turn in homework.
- There will be a quiz at the start of class
every other Tuesday, beginning January 23. The quiz will consist of questions
directly from all homework assigned since the previous quiz.
- Because the quiz will be taken directly from the homework there will
be less time to do the questions than normal quizzes and you are expected
to write a very solid and concise exposition when answering each question.
Little or no credit will be given for only submitting "the right answer".
- The single lowest quiz score or missed quiz will not be considered when
determining your quiz grade.
- You encouraged to talk to your fellow students about the
homework and the material you are learning. However, please be sure you
write up careful solutions on your own .
- Don't cheat yourself out of enjoying the beautiful mathematics in
this course! Start the homework as early as possible and set aside at
least two hours a day for focused study on the problems.
Attendance and participation in class: Your attendance
will not be officially recorded but if you are on the border between
two grades your attendance and participation may be taken into account.
Exams (75% of overall grade): There will be two midterms
and a final exam. Midterm I (II) will roughly cover Chapters 1 & 2 (3 & 4)
- Midterm I (20% of overall grade) : Tuesday February 13 in class.
- Midterm II (20% of overall grade) : Thursday, March 22 in class.
- Final Exam (35% of overall grade):
Thursday, May 3; 8 am through 10am in CB 345.
Tentative Schedule
- Week beginning January 8:
- Orientation
- (1.1) Systems of linear equations
- Week begining January 15:
- (1.2) Row reductions and echelon forms
- (1.3) Vector equations
- (1.4) The equation Ax = b.
- Week begining January 22:
- QUIZ on Tuesday, January 23.
- (1.5) Solution sets of linear systems
- (1.7) Linear independence
- (1.8) Introduction to linear transformations.
- Week begining January 29:
- (1.9) The matrix of a linear transformation
- (2.1) Matrix operations
- (2.2) The inverse of a matrix
- Week begining February 5:
- QUIZ on Tuesday, February 6.
- (2.3) Characterizations of invertible matrices
- Review for Midterm I
- Week begining February 12:
- MIDTERM I on Tuesday, February 13.
- (3.1) Introduction to determinants
- (3.2) Properties of determinants
- Week begining February 19:
- (3.3) Cramer's rule, volume, and linear transformations
- (4.1) Vector spaces and subspaces
- (4.2) Null spaces, columns spaces, and linear transformations
- Week begining February 26:
- QUIZ on Tuesday, February 27.
- (4.3) Linearly independent sets and bases
- (4.4) Coordinate systems
- (4.5) The dimension of a vector space
- Week begining March 5:
- (4.6) The rank of a matrix
- QUIZ on Thursday, March 8
- Review for Midterm II
- Week begining March 12: NO CLASS -- SPRING BREAK .
- Week begining March 19:
- Review for Midterm II.
- MIDTERM II on Thursday, March 22.
- Week begining March 26:
- (5.1) Eigenvectors and eigenvalues
- (5.2) The characteristic equation
- Week begining April 2:
- QUIZ on Tuesday, April 3.
- (5.3) Diagonalization
- (5.5) Complex eigenvalues
- Week begining April 9:
- (6.1) Inner products
- (6.2) Orthogonal sets
- QUIZ on Thursday, April 11
- Week begining April 16:
- (6.3) Orthogonal projections
- (6.4) The Gram-Schmidt algorithm
- (6.5) Least-squares problems
- Week begining April 23:
- Week begining April 30:
- Final exam -- Thursday, May 3; 8 am through 10am in CB 345 .
Some Additional Comments
- Expectations:
This course will be taught through the lectures and
homework assignments . The lectures introduce the
concepts and hence tend to be straightforward. You will be
expected to read the appropriate chapters in the text book after each
lecture to solidify the concepts and fill in details. It is very
important to understand concepts clearly along with being able to
apply them to numerical problems. Both theory and computations
covered in the lectures can be tested on exams. All in
all, your job is to master the concepts covered in the
assigned sections of the textbook. Everything else is working to
achieve this goal and the exams aim at testing overall command of the
material and not the ability to reproduce certain specific
problems.
- Guidelines on how to write up solutions to problems:
- Assume I am your fellow student: When writing your solutions
imagine me as a fellow student who has kept up with the course but who
hasn't done this current homework. I should be able to read your
solution and understand it.
- I do not have psychic powers: I must never have to fill
in holes or guess what you're thinking. Don't assume that I will
understand where you're coming from.
- My job should be easy: If I have to read your solution
five times or spend more than 10 minutes trying to understand what
you are saying then you haven't made a strong case. Your solutions
should read like poetry, like honey dripping from the page.
- Some general comments: (some of
these were copied from Rekha R. Thomas)
- Make-up exams: :
No make up exams will be given. Please make sure that you
do not schedule other activities on the dates of exams. If you must
miss a test for medical or other very serious reasons, I will
need written documentation explaining the situation. Please let me
know as soon as possible if you cannot take a test.
- Students needing testing accomodations:
If you have university sponsored needs for special
accomodations for taking exams I am more than happy to
accomodate your requests. If this is the case, please
let me know as soon as possible and in writing and supply
me with the appropriate letters supporting your claims.
- Partial Credit: There might be several questions
on a quiz or an exam that carry no partial credit. This is usually
because of the nature of the question where a partially correct answer
may make no sense at all. For instance, a misstated theorem or definition
is just a false statement and couldn't be graded with partial credit.
It is important to learn to do computations correctly from beginning to
end or to state a theorem accurately.
- Keep records: Please hold on to all your graded
quizzes and exams until you receive your final grade. You
will be asked to produce these if there are any questions or
complications regarding records during the quarter.
- Classroom etiquette: The classroom is a learning
space where I expect everyone to behave maturely and with
respect for others. During class time, please turn off your
cellphone, place your earphones in your bag, put the newspaper
away, etc.
- Cheating and plagiarism:
Cheating will be considered as an extremely serious offense.
Homework questions for the semester
- 1.1: 3,4,7,10,11,14,26,27,29.
- 1.2: 2,10,14,15,16,17,20,21,23,24,29,30,31.
- 1.3: 4,5,6,10,12,16,17,18,20,21,24.
- 1.4: 1,2,3,4,5,7,12,13,15,16,18,19,21,22,32,33,34.
- 1.5: 2,3,6,8,11,14,16,17,24,26,27,29,30,35.
- 1.7: 5,6,7,8,11,12,15,16,17,18,19,20,22,25,26,29,31,39.
- 1.8: 3,4,7,8,9,11,15,16,19,20,24,25,29,30,31.
- 1.9: 2,3,4,7,8,12,13,14,17,18,20,25,28,33,35.
- 2.1: 1,2,4,7,8,10,12,15,17,19,20,22,27,28.
- 2.2: 3,5,6,7,8,9,10,21,22,24,25,26,29,30,31,32,37,38.
- 2.3: 1,2,3,4,5,6,7,8,11,12,13,15,17,21,22,27,28,31,32,33,34.
- 3.1: 4,6,8,9,10,13,15,16,and 19 through 30 inclusive.
- 3.2: 7,8,9,10,12,13,16,19,20,24,25, and 28 through
36 inclusive.
- 3.3: 3 through 8 and 11,12,17,18.
- 4.1: 1 through 18, and 21 and 22.
- 4.2: 2,3,4,8,10,11,12,17,18,20, and 22 through 28.
- 4.3: 3 through 6, 9 through 16, 19, 22,23,24,29,30.
- 4.4: 2,3, 7 through 13, and 16.
- 4.5: 3,4, 7 through 13, 16 through 20, 25,26.
- 4.6: 3 through 8, 11 through 15, 17, 19 through 22, and 27 through 30.
- 5.1: 3,4,7,8,9,10,15,16,18,19,20,21,22,23,24.
- 5.2: 2,4,11,12,13,14,16,18,19,22,25.
- 5.3: 1,2,3,4.
- 5.3: 5,6,9,10,13,14, 23---28.
- 5.5: 1---4, 9---16.
- 6.1: 9,10,13--16,19,22,23,24,27--30.
- 6.2: 3,4,9,10,17--20,23--28.
- 6.3: 2,3,4,7,8,11--18,21.
- 6.4: 3--12,17ab, 18ab.
- 6.5: 3--10,13,14,17,25.