# Fall 2006 Math 314 Section 6 Home Page

Welcome to the Math 314, Section 006 (formerly Section 005), Aplied Linear Algebra, home page. You're probably here for information, so let's start with the vital statistics of the course.

### Essential Information

• Announcements Announcements about current class activities.
• Class Policy Statement
• Course Syllabus
• Assignments Assignments and due dates.
• Class Materials Some useful course materials for this course, including a printable copy of the Class Policy Statement and Syllabus are here in our home directory.
• Notes and FAQ Notes and answers to questions about class matters that students have asked. Check this periodically for the most current information. Also, check the class discussion board for information.
• Lecture Notes You'll find an outline of our activities and some extra notes here.
• Textbook Our course textbook. You'll find an errata sheet on this page -- be sure to check it periodically. In fact, help out and report any textbook errors to me!

### Applied Linear Algebra Course Resources

Tons of information can be found on the WWW. Go to your favorite search engine (like the Google or Yahoo site listed on my home page) and try searching on "matrix theory". See how many web pages you hit and visit a few interesting looking sites.

## Notes and FAQ

11/25/06: Our schedule for the rest of the semester...
Here it is:

Monday, November 27: Exam 3, usual place and time.
Tuesday, November 28: Cover Sections 6.1 and 6.2.
Thursday, November 30: Cover Sections 6.2 and 6.3, but only do the Gram-Schmidt algorithm in 6.3.
Tuesday, December 5: Cover Section 6.4.
Thursday, December 7: Review and class evaluations.
Monday, December 11: Final exam in AvH 12, 10:00 am to 12:00 noon.
I've been asked to explain what significant digits of an approximation to a number mean. Eventually, we'll need to know, so here goes: to get the number of significant digits, first *subtract* (rather than just looking at the numbers) the two (may as well be larger - smaller), then find the position of the leading digit of the error relative to the position of leading digit of the exact answer. (We're thinking in fixed point representation in this discussion.) If the difference in that position is less than 5, then number of significant digits is one less than that position, else two less.

For example if 1.006 and .996 are used to approximate 1, calculate 1.006 - 1 = 0.006. Notice I put the zero in front of the decimal to start counting from the right position. There is nonzero digit at the 4th position, counting from the (base 10) position of the leading digit of 1, and the size of this digit is greater than 5, so this approximation has 2 significant digits. On the other hand, 1 - .995 = 0.005, which again has a nonzero digit in the 4th position, and the size of the digit is at most 5, so .995 has 3 significant digits as an approximation to 1. BTW, it's also perfectly correct to say that each answer has one significant digit, though this doesn't give all the available information. Hope this helps.

## Class Policy Statement

Course: Math 314 - Section 006, Applied Linear Algebra (Matrix Theory)

Place/Time: 12 AvH, 9:30-10:45 TR, Fall 2006

Preq: Math 208 or 107H or equivalent.

Objectives: This is a multifaceted course whose goals are to help students achieve competence in the following areas:

• Matrix/vector arithmetic and algebraic manipulations.
• Abstract reasoning in the context of matrix theory and linear algebra.
• The use of matrix and vector concepts in mathematical modeling.
• Numerical experimentation in the context of linear algebra.
Instructor: Dr. Thomas Shores

Telephone: Office 472-7233 Home 489-0560

Email: tshores1@math.unl.edu

Office Hours: Monday 10:00-11:30, Tuesday 11:00-13:00, Thursday 12:00-13:30, Friday 8:30-10:30, and by appointment. Office: 229 AvH

Class Attendance: Is required. If absent, it is incumbent upon the student to determine what has been missed as soon as possible. It is advisable to consult with the instructor.

Homework/Projects: Everyone is expected to master the syllabus homework assignments. These will not be graded, but many exam questions will be modeled on them, and it is guaranteed that at least one question on each exam will come directly from these problems. Students are strongly encouraged to work them and ask questions about them in and outside of class. There will be one group project for honors contractors, and several smaller individual homework/project assignments for everyone. Our computing platform is the CAS Maple which is available on all math computers. Students will be given an account in the Mathematics Computer Lab for computer related exercises and can obtain written lab instructions in the lab itself. Current information about the course will be available on the web (via the314 homepage or my home page). Using the web is strongly recommended for keeping track of due dates for homework collections and other current activities in the course.

Reading Assignment: Read the sections of the text as, or before, they are covered in class lectures. This is a standing assignment throughout the semester.

Grade: Three 90 minute exams at a time to be determined will be given and these will account for 100 points each. The final exam will count 150 points. All exams are closed book with calculators. The small homework/projects will account for 50 points (honors contractors will also have one group project worth an additional 50 points.) The final grade will be based on these 500 (550) points.

Final Exam: Will be comprehensive. To be given on Monday, December 11, 10:00-12:00 noon in 12 AvH.

Grades of "I", "W" or "P": These grades will be given in strict accordance with University policy. (See any Schedule of Classes for the relevant information and dates.)

Keep This Information!!!

## Syllabus for Math 314, Section 6, Fall 2006

• TEXT: Applied Linear Algebra and Matrix Analysis, Thomas Shores, Springer-Verlag, New York, 2007.
The times listed below are approximate, and may be adjusted as the semester progresses.

 WEEK DATES SECTION PROBLEMS

 1 Aug 21-25 1.1 p. 8, #1ab, 2c, 3, 5, 9, 13 1.2 p. 19, #1, 2abc, 3abc, 5, 7ab, 9, 12abc, 16, 17, 24 1.3 p. 30, #1ab, 3ab, 4ab, 5abd, 7, 9a

 2 Aug 28-Sep 1 1.3 p. 30, #13, 15a, 18 1.4 p. 42, #1abcd, 2ab, 5abc, 6ab, 7, 11a, 16, 17, 19

Friday, September 1: last day to withdraw and not have the course appear on your transcript.

 3 Sep 4 Labor Day Sep 5-8 2.1 p. 60, #1, 3ab, 5ac, 6ab, 9, 11, 16, 17c 2.2 p. 68, #1ac, 2ab, 3, 5, 7ab, 9, 13abc, 14ab, 17, 19, 27

 4 Sep 11-15 2.3 p. 85, #1bc, 3, 5, 9, 11 2.4 p. 98, #1acef, 5, 7, 8, 9, 11, 14, 15, 17, 20, 26, 27

 5 Sep 18-22 2.5 p. 112, #1abd, 3c, 4a, 5abc, 9, 13ab, 17, 21, 24 2.6 p. 126, #1ac, 3, 7ac, 9abc, 11abc, 14ab, 21, 22

 6 Sep 25-29 EXAM 1 3.1 p. 158, #2, 3, 6, 7, 11, 13, 17, 21, 24, 28 3.2 p. 168, #1, 2, 5, 6, 11, 13, 15, 17, 18

 7 Oct 2-6 3.3 p. 180, #1ab, 3-5 (just ab), 9, 10, 11, 13, 21 3.4 p. 190, #1-6 (just ab), 8, 9, 13, 17

 8 Oct 9-13 3.5 p. 196, #1, 3, 6, 7, 9, 11, 12, 13 3.6 p. 206, #1, 3d, 5abc, 7a, 8a, 9, 14

Friday, October 13: last day to change your grade option to or from ``Pass/No Pass''.

 9 Oct 16-17 (no class) Fall Break Oct 18-20 4.1 p. 225, #1abd, 2abd, 3ac, 5, 7, 17

 10 Oct 23-27 4.2 p. 236, #1ab, 3ab, 4ab, 6, 9a, 10a, 11, 15 4.3 p. 246, #1ab, 3, 4, 5, 7, 11, 14

 11 Oct 30-Nov 3 EXAM 2 3.7 p. 212, #1, 3, 5, 8 5.1 p. 261, #1ace, 3ace, 5, 7ace, 11, 13, 15, 17, 19

 12 Nov 6-10 5.2 p. 270, #1, 3abc, 7, 10, 11, 14, 17 5.3 p. 280, #1acd, 3b, 4a, 5abd, 8, 11, 13, 15

Friday, November 10: last day to withdraw from the course and receive a grade of W.

 13 Nov 13-17 5.4 p. 286, #1ad, 3ab, 5, 7, 9, 12, 13 6.1 p. 311, #1, 3a, 4b, 7, 9, 13

 14 Nov 20-21 6.2 p. 320, #1, 3, 5, 9, 11a, 13a, 19, 22 Nov 22-24 Thanksgiving Vacation

 15 Nov 27-Dec 1 EXAM 3 6.3 p. 331, #1ab, 3a, 5ab, 7, 9, 14, 15 6.4 p. 341, #1, 3, 5, 7a, 9, 12

 16 Dec 4-8 optional TBA REVIEW

Final Exam: The final exam is a comprehensive exam given on Monday, December 11, 10:00-12:00 noon in 12 AvH.

Department Grading Appeals Policy: The Department of Mathematics and Statistics does not tolerate discrimination or harassment on the basis of race, gender, religion or sexual orientation. If you believe you have been subject to such discrimination or harassment, in this or any math course, please contact the department. If, for this or any other reason, you believe that your grade was assigned incorrectly or capriciously, appeals may be made to (in order) the instructor, the department chair, the departmental grading appeals committee, the college grading appeals committee and the university grading appeals committee.

## Assignments

1. (Points: 10, Due: September 21)
Use Maple to do the calculations of Exercises 10 and 12 in Section 2.3 of the text. Turn in your appreviated and edited printout and a hand-sketched (or otherwise) picture of the graph in 12. You will find MapleWorksheet#2 quite helpful.
2. (Points: 10, Due: November 7)
Get a copy of MapleWorksheet#2 and read the assignment at the end of it. You might work through a new copy of the notebook, since I have included commands that you will find helpful for this assignment.
3. (Points: 10, Due: November 9)
Fix your errors in Exam 2 on a separate exam sheet (a copy is available in our home directory.) You must do the work yourself and may use notes or text (or see me for help.) The percentage of corrected missed points will determine your score on this assignment. Here are a few tips: For #1, see Examples 3.38, 3.39, 3.40 and Note 3.2. For #2, see Examples 3.13, 3.14. For #3, see Example 3.24. For #4, see Example 2.53 and for #5, see Examples 3.19(b) and 3.35(b).
4. (Points: 10, Due: November 30)
Get a copy of MapleWorksheet#3 and work through it. The assignment is at the end of the worksheet. Note: In Exercise 11, "three state" should be "three stage".

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