## Martin Flashman's CoursesMath 241 Elements of Linear Algebra Fall, '04TR 13:00- 14:20 SCIA 564 Self Schedule for Final Examinations

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Last updated: 08/17/2004
Assignments and recommended problems: Fall 2004
Tentative until a Due Date is designated.
 HW # Due Date Read Section Assigned Problems Additional Suggested Problems HW #1 8-31 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 9-2 §1.2 p. 25-27 #1, 2, 8, 12, 13, 16, 21, 24, 25 #4, 7, 9-11, 14-15, 20, 22, 23 HW #3 9-7 §1.3 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 9-9 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 9-14 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 HW #6 9-16 §1.6  Study Guide p. 63-64 #1, 4, 5, 7, 8, 11, 12, 14 Note: Correction for Problem 11. 80 -->C instead of   80 <---C. #2, 3, 13 HW #7 9-21 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 9-23 §1.8  StudyGuide p. 79-81 #2, 3, 6, 10, 11, 17, 18, 20, 21, 34 # 1, 4, 5, 9, 12-16, 19, 22 HW #9 9-28 p. 90-91 #1, 2, 4, 5, 10, 11, 17, 24, 35 Submit in writing:1.8 #34 #3, 6-9, 13-16, 18-23, 31, 32 HW #10 9-30 §1.10 pp97-99 Study Guide p. 101 #9, 11, 12 #1, 2, 4, 5, 8, 3, 6, 7, 10 On-Line Markov System Materials HW #11 9-30 §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 #12 10-5 §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 #13 10-12 §2.3 p. 132-133 # 3, 7, 8, 11, 14, 15, 16, 19, 27 #1, 2, 4-7, 12, 13, 17, 18 HW #14 §2.4 p. 139-141 #1, 4, 6, 10, 13, 21, 22, 25 #2, 3, 5, 7-9, 11, 12, 14 HW #15 §2.5 p. 149-151 #2, 5, 9, 16, 21, 24, 25, 26 #1, 3, 4, 6-8, 10-15 HW #16 §2.6[2.7?] p. 156-157 #2, 3, 6, 7, 9, 10, 12, 13 #1, 4, 5, 14 HW #17.1 11-2 §4.1 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 # 17.2 p.   234-236 # 7-9, 25,31, 34, #35, 36 HW  #17.3 §4.3 p. 342- 345 # 22, 25, 26, 31,33,38 #32 4.4,     4.5 error correcting codes.pdf HW #18 10-14 §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 #19 10-19 §2.9 p. 180-182 #1, 4, 6, 8, 9, 12, 14, 18, 19 #2, 3, 5, 10, 11, 13, 17 HW #20 10-21 §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 #21 10-26 §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 #22 10-28 §3.3 Determinant summary p. 209-210 #2, 5, 8, 19, 24, 25, 28, 29 #1, 3, 4, 6, 7, 9, 10, 20-23, 27, 30 HW #23 11-16 §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 #24 11-18 §5.2 p. 317-318 #2, 3, 9, 11, 16, 21, 23, 24 #1, 4-8, 10, 12-15, 17, 19, 20, 22 HW #25 11-30 §5.3 p. 325-326 #1, 4, 7, 12, 18, 22, 27, 33 #2, 3, 5, 6, 8-11, 13-17, 19-21 HW #26 12-2 §6.1 p. 382-383 #1, 4, 5, 8, 10, 13, 15, 18, 19 Submit in writing #24 #2, 3, 5-7, 9, 11, 12, 14, 16, 17, 20, 22 HW #27 12- 7 §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 #28 §6.3 p. 400-401 #1, 4, 7, 10, 12, 13, 15, 18, 22 #2, 3, 5, 6, 8, 9, 11, 14-17, 21 HW #29 §6.4 p. 407-408 #2, 5, 7, 8, 9 #1, 3, 4, 6, 10-12

 Tuesday Thursday Week 1 1.1-1.2 9-24 Introduction and Motivation Solving 2 by 2  systems. Continuation: Introduction to matrices.Being Systematic. Gauss-Jordan Method using row operations Week 2 1.3-1.4 8-31 Gauss-Jordan Method using row operations Vector Equations and Linear combinations Application to polynomial curve fitting? Discussion of proofs. Begin Vector-Matrix Arithmetic and equations. Week 31.4, 1.5 9-7 Vector-Matrix Arithmetic and equations Solutions AND Linear combinations "Inner product." Applications Week 4 1.6-1.8 9-14 More applications  [Spanning and Linear dependence.] Linear Independence Week 5 1.8, 1.9 9-21 Linear Transformations Matrices and LT's More on LT's 1:1 and onto. Week 6 2.1-2.3 9-28 Applications(Linear Difference- Migration-Markov) Properties of Matrix algebra. Matrix Inverse. Applications More on Matrix Inverse. Week 7 Midterm Exam #1 Self-Scheduled Wednesday 10-68:00- 12:30 Room 102 5:00 - 8:30pm Lib 56 Covers weeks 1-6.2.3, 2.8 10-5 Invertibility and Independence, Spanning, etc. 10-7 Invertible Linear Transformations Begin Subspaces. Null Space and Column Spaces of a matrix. Week 82.8, 2.9, 2.3, (2.6, 2.7?) 10-12 BASES Dimension Rank of a matrix. Bases and Linear Transformations Rank and nullity Week 9 3.1,3.2 10-19 More Inverse results.  Begin Determinants Calculating determinants by cofactor expansion Properties of determinants Products and Inverses [Permutations and determinants?] Week 103.3,4.1, 4.2, 4.3 10-26Applicatons of Determinants Cramer's Rule Subspaces and Linear Transformations Begin Abstract Vector Spaces Subspaces and spanning Linear Transformations  Kernel(Null Space) and range More VS examples. Week 11 4.4,4.5,4.6 11-2 Rank and Nullity. Finish Rank More Linear transformations: T+aU, TU Geometry of LT's Week 12 Exam II 5.1, 5.2 11-9 Eigenvalue/vector of a matrix 1:1 the Nullspace, and inverse functions Week 13 5.2,5.3, 4.9 11- 16 More eigenstuff. Diagonalizable Matrices/transformations. Applications of  diagonalization. Stochastic Matrices. BREAK 11-23 No class No Class Week 14 6.1, 6.2, 6.3, 6.4 11-30 Comments on diagonalizable matrices. Inner products and more on transformations Orthonormal bases Finish Orthonormal bases, Orthogonal transformations, distance and Isometries General inner product spaces. Week 15 12-7 Geometry and Lin. Operators, Transformations Symmetric Matrices, Transpose,Trace Breath & Review for Final Week 16 12-13 to 12-17 Final Exam Week

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Fall, 2004                                  COURSE INFORMATION          M.FLASHMAN
MATH 241
OFFICE: Library 48                                                                                     PHONE:826-4950
Hours (Tent.):  MTRF: 14:30-15:20 AND BY APPOINTMENT or chance!

E-Mail: flashman@humboldt.edu         WWW: http://www.humboldt.edu/~mef2/
***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, by David C. Lay. (Addison-Wesley, 2003)
• 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 Blackboard for on-line reality quizzes.
• Homework assignments are made regularly. They should be done neatly. We will be using Blackboard  to grade homework. Record your homework results on Blackboard at least 15 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 Blackboard report on submitted homework. Homework assignments will be used in determining the 100 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 150 points 2 Midterm Examinations 200 points Homework 100 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 2 ABSENCES MAY LOWER THE FINAL GRADE FOR POOR ATTENDANCE.
** See the course schedule for the dates related to the following:
• No drops will be allowed without "serious and compelling reasons" and a fee.
• Students wishing to be graded with either CR or NC should make this request by using the web registration procedures.

• Technology: The computer or a graphing calculator can be used for many problems. We will 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.
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.)
• Then the link WIMS Class Home Page will bring you (those who have registered) to the homepage of the class.

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