## Martin Flashman's CoursesMath 241 Elements of Linear Algebra Fall, '09 TR 14:00- 15:20 Art 27

Last updated: 8/24/2009

Assignments and recommended problems: Fall 2009
Tentative until a Due Date is designated.
*Early or Just in time:
When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work
.

HW #

Due Date

Assigned Problems

HW #1

8/27-9/1

A Note to Students
§1.1

p. 11-12

#1, 4, 7, 10, 13, 14, 15, 20, 24

#2, 3, 8, 9, 11, 12, 16-19, 21-23

HW #2 9/1-3

§1.2
Check out

p. 25-27

#1, 2, 8, 12, 13, 16, 21, 24, 25

#4, 7, 9-11, 14-15, 20, 22, 23

HW #3 9/8

p. 37-39

#1, 5, 8, 10, 11, 14, 17, 20, 27

#2-4, 6, 7, 9, 12, 13, 15, 16, 18, 19, 21-26

HW #4
9/10

p. 47-49

#1, 6, 7, 10, 12, 14, 19, 22, 23

#2-5, 8, 9, 11, 13, 15-18, 20, 21, 24-26

HW #5
9/15

p. 55-56

#2, 3, 6, 9, 12, 14, 15, 18, 24

#1, 4, 5, 7, 8, 10, 11, 13, 16, 17, 19, 20-23, 33, 34

Quiz #1
Covers 1.1,1.2 and 1.3
HW #1, #2, and #3

HW #6
9/22

§1.6  Study Guide

p. 63-64

#1, 4, 5, 7, 8, 11, 12, 14
[Note for 3rd edition: Correction for Problem 11 - made in the updated version: 80 -->C instead of   80 <---C.

#2, 3, 13

Quiz #2

Covers 1.3 and 1.4
HW #3 and #4

HW #7
9/22-24

p. 71-72

#2, 5, 8, 10, 13, 16, 18, 21, 28, 33

#1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 19, 20, 22-27, 34-38

HW #8
9/29 - 10/1
§1.8  StudyGuide    p. 79-81    #2, 3, 6, 10, 11, 17, 18, 20, 21, 34
# 1, 4, 5, 9, 12-16, 19, 22
Quiz #3

Covers 1.5 and 1.6
HW #5 and #6

HW #9
9/29- 10/1

p. 90-91

#1, 2, 4, 5, 10, 11, 17, 24, 35
Submit in writing:1.8 p 81: #34

#3, 6-9, 13-16, 18-23, 31, 32

Quiz #4

Covers 1.7 and 1.8
HW #7 and #8

HW #10
10/6

§2.1

p. 116-117

#2, 3, 5, 7, 10, 12, 16, 17, 22, 27

#1, 4, 6, 8, 9, 11, 13, 15, 28

HW #11
10/6-8
§2.2 and start 2.3  p. 126-127  #4, 7, 11, 14, 18, 19, 22, 24, 31, 35   #1-3, 5, 6, 8-10, 13, 15-17, 20, 21, 23, 29, 30, 32
HW #12
10/13-15

§

p. 132-133

# 3, 7, 8, 11, 14, 15, 16, 19, 27

#1, 2, 4-7, 12, 13, 17, 18

Midterm Exam #1 Self-Scheduled Tuesday evening 10/13 and Wednesday 10/14
Try to come 5 minutes before your starting time

Covers Material from HW # 11 and related sections. see Sample Exam on Moodle.

HW #15 10/15-20
§3.1
p. 190-191 #1, 4, 8, 9, 11, 17, 37, 38 #2, 3, 5-7, 10, 12-16, 18-30, 39, 40
HW #16 10/22
§3.2 p. 199-200 #5, 7, 10, 12, 18, 19, 23, 26, 29, 34 #1-4, 6, 8, 9, 11, 13-17, 20-22, 24, 25, 27, 28, 31-33, 35, 36
HW #17 10/22-27
§3.3
Determinant
summary
Proof of Thrm 6 on Moodle
p. 209-210 #2, 5, 8, 19, 24, 25, 28, 29 #1, 3, 4, 6, 7, 9, 10, 20-23, 27, 30
HW #18 10/29-11/3
§4.1
More v.s. examples on Moodle
p. 223-225 #2, 3, 5, 6, 8, 10, 11, 19, 20, 21, 24, 32 #1, 4, 7, 9, 12-18, 22, 23, 33
HW #19 11/5 -12
Changed 11/10
p.   234-236  # 7-9, 25,31, 34 #35, 36
HW #12.5 11/12
§1.10 pp97-99
Study Guide
p. 101 #9, 11, 12 On-Line Markov System Material
HW #20 11/12-17
§4.3 p. 342- 345 # 22, 25, 26, 31,33,37 #32
Midterm Exam #2 Self-Scheduled 11/17 evening- 11/18
Try to come 5 minutes before your starting time:

Covers Material from HW # 12 to 20 ( and related sections). see Sample Exams on Moodle.

HW #21 12/1-3
§5.1 p. 308-309 #1, 4, 8, 10, 13, 22, 25, 26, 27 #2, 3, 5-9, 11, 12, 14-21, 23, 24
HW #22 12/3
§5.2 p. 317-318 #2, 3, 9, 11, 16, 21, 23, 24 #1, 4-8, 10, 12-15, 17, 19, 20, 22

HW # 23 12/8-10
§5.3 , Optional 5.4 p. 325-326 #1, 4, 7, 12, 18, 22, 27, 33 #2, 3, 5, 6, 8-11, 13-17, 19-21
HW #24 12/10
§6.1 p. 382-383 #1, 4, 5, 8, 10, 13, 15, 18, 19
#2, 3, 5-7, 9, 11, 12, 14, 16, 17, 20, 22
HW #25 12/10
§6.2 p. 392-393 #2, 5, 7, 10, 12, 14, 20, 21, 23 #1, 3, 4, 6, 8, 9, 11, 13, 15-19, 22, 24
HW #26 12/10???

§6.3

§6.4

p. 400-401 1, 4, 7, 10, 12, 13, 15, 18, 22 2, 3, 5, 6, 8, 9, 11, 14-17, 21
Backlog of previous course assignments. Not assigned in Fall, 2009 :)

HW #13.5

§1.10 pp93-96 p99
#1, 2, 4, 5, 8, 3, 6, 7, 10

HW # 13

§2.8
p. 173-175 #2, 3, 5, 6, 7, 10, 18, 21, 25 #1, 4, 8, 9, 11-17, 19, 20, 22-24, 26
HW #14

§2.9

p. 180-182

#1, 4, 6, 8, 9, 12, 14, 18, 19

#2, 3, 5, 10, 11, 13, 17

§2.4

p. 139-141

#1, 4, 6, 10, 13, 21, 22, 25

#2, 3, 5, 7-9, 11, 12, 14

§2.5

p. 149-151

#2, 5, 9, 16, 21, 24, 25, 26

#1, 3, 4, 6-8, 10-15

§2.6[2.7?]

p. 156-157

#2, 3, 6, 7, 9, 10, 12, 13

#1, 4, 5, 14

4.4,     4.5

error correcting codes.pdf

#2, 3, 5-7, 9, 11, 12, 14, 16, 17, 20, 22

§6.2

p. 392-393

#2, 5, 7, 10, 12, 14, 20, 21, 23

#1, 3, 4, 6, 8, 9, 11, 13, 15-19, 22, 24

§6.4

p. 407-408

#2, 5, 7, 8, 9

#1, 3, 4, 6, 10-12

 Tuesday Thursday Week 1 1.1-1.2 8/25Introduction and Motivation Solving 2 by 2  systems. Continuation: Solving Systems of linear equations. Week 2 1.2-1.3 9/1 Solving Systems of linear equations. Introduction to matrices. Being Systematic. Gauss-Jordan Method using row operations Vector Equations and Linear combinations Begin Vector-Matrix Arithmetic and equations. Week 3 1.3, 1.4, 1.5 9/8 Solutions AND Linear combinations Vector-Matrix Arithmetic and equations "Matrix Inner product." [Discussion of proofs.] Proof of  Theorem 4 ("equivalences") Start Homogeneous and Non-homogeneous systems Week 4 1.5-1.8 9/15 Homogeneous and Non-homogeneous systems Applications Application to polynomial curve fitting Spanning and Linear dependence Linear Independence Week 5 1.8, 1.9 9-22 Linear Transformations Matrices and LT's More on LT's [Abstract definition] Connection with matrices. Week 6 2.1-2.2 9-29 More on LT's 1:1 and onto. Properties of Matrix algebra. Week 7 2.2,2.3 10-6 -Matrix Inverse. More Matrix Algebra- Inverse  Invertibility and Independence, Spanning, etc Week 8 Midterm Exam #1 Self-Scheduled 10/13 evening+10/14 Covers weeks 1-7. 2.8, 2.9, 2.3, (2.6, 2.7?) 10-13 The Big theorems: Invertibility and Independence, Spanning, etc.  Invertible Linear Transformations Begin Determinants Calculating determinants by cofactor expansion Properties of determinants Products and Inverses Permutations and determinants? Week 9 3.1,3.2 10-20 More Properties and Applicatons of Determinants Cramer's Rule  Proof of Product Property Geometry of determinants. Determinants and Areas 10-22 Finish determinants Linear Transformations and Area Week 10 3.3, 4.1, 4.2 10/27  Integration? More Inverse results. 10/29Begin Abstract Vector Spaces Linear Transformations Week 11 4.1-4.3 11/3More VS examples. Begin Subspaces. Linear Transformations Kernel(Null Space) and range Null Space and Column Spaces of a matrix. Week 12  2.8, 2.9  (4.4,4.5,4.6)? 5.1, 5.2 11/10 Reading: Applications(Linear Difference- Migration-Markov) More on Linear  Transformations, Null Space, Range, Subspaces and spanning BASES Dimension Rank of a matrix. Bases and Linear Transformations Rank and nullity Independence, Basis,  Eigenvalue/vector of a matrix, Linear transformation? Week 13 Exam II 11-17/18 Self-scheduled! 11/17 review for exam. Stochastic Matrices. Bases and coordinates. Week 14 Thanksgiving Break Week 15 5.2, 5.3 12/1 Coordinates, linear transformations and matrices. Eigenstuff and Differential equations. Diagonalizable Matrices/transformations. Eigenvalues and  Complex numbers. Comments on diagonalizable matrices. Week 16 4.9 6.1, 6.2, 6.3, 6.4 12/8 Applications of  diagonalization. Inner products Orthogonal vectors and complements. Orthogonal and  Orthonormal bases, Orthogonal transformations and distance. Gram- Schmidt - orthonormal bases. General inner product spaces. Geometry and Lin. Operators, Transformations More Linear transformations: T+aU, TU? Geometry of LT's Breath! :) Symmetric Matrices, Transpose,Trace? Week 17 Review Session: Sunday 4:00- 6:00 PM Come to BSS 308. Sample Final Exam Questions will be available on Moodle by Dec 10. Final Exam Week Final Exam Sign-up! Sign up for your self-scheduled FINAL EXAM You can sign up by responding to the sign-up on Moodle Self Schedule for Final Examinations Final Exam Week 17 Final Examination Self scheduled choices: Mon: 12/14 10:20 SH 128 Tues: 12/15 15:00 Art 27 Thurs.: 12/17 10:20 SH 128 Fri: 12/18 10:20 SH 128

Back to Martin Flashman's Home Page :) Back to HSU Math. Department :}

Fall, 2009                                 COURSE INFORMATION          M.FLASHMAN
MATH 241  Elements of Linear Algebra
OFFICE: BSS 356                                                                                     PHONE:826-4950

Office Hours (Tent.): MTRF 12:30-1:30 AND BY APPOINTMENT or chance!

E-Mail: flashman@humboldt.edu         WWW: http://flashman.neocities.org/
***Prerequisite:MATH 205 or 210 (Allowed for Concurrent enrollment) (Permission given for three completed semesters or 4 quarters of Calculus)

• TEXT Linear Algebra and It's Applications, 3rd Edition Update, by David C. Lay. (Addison-Wesley, 2006)
• Catalog Description: Linear systems, matrices, determinants, linear independence, bases, eigenvalues, and eigenvectors.
• SCOPE: The course covers an introduction to the core concepts of linear algebra and some applications to both mathematical and non-mathematical problems. Key connections are made between systems of linear equations, matrices, vectors, and transformations while developing some related fundamental theory and algorithms. The text sections that will be covered include Sections 1.1 - 2.3,2.8, 2.9,3.1 - 3.3, 4.1 - 4.9,5.1 - 5.5, 6.1-6.4. Other sections may be covered as time permits.
• TESTS AND ASSIGNMENTS: There will be several tests in this course. There will be several reality check quizzes, two midterm exams and a comprehensive final examination.
• We will use the HSU Moodle for some on-line reality quizzes.
• Homework assignments are made regularly. They should be done neatly. We will be using Moodle  to grade homework. Record your homework results on Moodle at least 45 minutes before class of the due date.  I will discuss this further at the first class meeting. Problems from the assignments will be discussed in class based on the Moodle report on submitted homework. Homework assignments will be used in determining the 150 course points.
• Midterm Exams will be self-scheduled and announced at least one week in advance.
• THE FINAL EXAMINATION WILL BE SELF SCHEDULED.
• The final exam will be comprehensive, covering the entire semester.
• MAKE-UP TESTS WILL NOT BE GIVEN EXCEPT FOR VERY SPECIAL CIRCUMSTANCES! It is the student's responsibility to request a makeup promptly.
• *** DAILY ATTENDANCE SHOULD BE A HABIT! ***
• GRADES: Final grades will be determined taking into consideration the quality of work done in the course as evidenced primarily from the accumulation of points from tests and various  assignments. The final examination will be be worth either 200 or 300 points determined by the following rule:

• The final grade will use the score that maximizes the average for the term based on all possible points .
 Reality Quizzes 100 points 2 Midterm Examinations 200 points Homework 150 points Final Examination 200 or 300 points Total 650 or 750 points
• The total points available for the semester is 650 or 750. Notice that only 400 or 500 of these points are from examinations, so regular participation is essential to forming a good foundation for your grades as well as your learning.

• MORE THAN 3 ABSENCES MAY LOWER THE FINAL GRADE FOR POOR ATTENDANCE.

Students with Disabilities: Persons who wish to request disability-related accommodations should contact the Student Disability Resource Center in House 71, 826-4678 (voice) or 826-5392 (TDD). Some accommodations may take up to several weeks to arrange. http://www.humboldt.edu/~sdrc/
Add/Drop policy: ** See the University rules and dates related to the following:
• No drops will be allowed without "serious and compelling reasons" and a fee after this date.
• No drops allowed after this date.
• Students wishing to be graded with either CR or NC should make this request  using the web registration procedures.
Students are responsible for knowing the University policy, procedures, and schedule for dropping or adding classes. http://www.humboldt.edu/~reg/regulations/schedadjust.html
Emergency evacuation: Please review the evacuation plan for the classroom (posted on the orange signs) , and review http://studentaffairs.humboldt.edu/emergencyops/campus_emergency_preparedness.php for information on campus Emergency Procedures. During an emergency, information can be found campus conditions at: 826-INFO or http://www.humboldt.edu/emergency
Attendance and disruptive behavior: Students are responsible for knowing policy regarding attendance and disruptive behavior: http://studentaffairs.humboldt.edu/judicial/attendance_behavior.php

• Technology: The computer or a graphing calculator can be used for many problems.
We may use MATRIX.  Matrix by John Kennedy is designed particularly to help learn many linear algebra applications using matrices on any PC. MATRIX can be obtained from me or downloaded from the Math Archives
We may also use Maxima - which you can download free from http://maxima.sourceforge.net. This is a very powerful and useful tool for doing much mathematics - including linear algebra.
Another resource we may use is
http://www.scilab.org/ :The open source platform for numerical computation.
Graphing calculators are welcome and highly recommended. Students wishing help with any graphing calculator should plan to bring their calculator manual with them to class. I will be able to loan to any student in the class an HP48G calculator. Students wishing help with any graphing calculator should plan to bring their calculator manual with them to class. Computer software would also be useful. If you would like to purchase one or have one already, let me know. I will try to help you with your own technology during office hours or by appointment (not in class).
• Here are some on-line tools:
• Still in development!  I may suggest using some of the Linear Algebra Interactive Exercises from WIMS at wims.unice.fr .
• The link register on-line at WIMS  allows you  to register yourself to the class. (The class password is "flash" for the registration.)