## Martin Flashman's CoursesMath 241 Elements of Linear Algebra Spring, '07MWF 10:00- 10:50 SH 128

Last updated: 1/15/2007

Assignments and recommended problems: Spring 2007
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 Read Section Assigned Problems Additional Suggested Problems HW #1 1-22/24 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 1/26 p. 25-27 #1, 2, 8, 12, 13, 16, 21, 24, 25 #4, 7, 9-11, 14-15, 20, 22, 23 HW #3 1/29*31 §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 1/31* 2/2 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 2/5*2/7 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 2/7*2/9 §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 HW #7 2/9*2/12 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 2/14/*16 §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 2/19*21 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 2/23*26 §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 2/26*28 §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 3/5 § p. 132-133 # 3, 7, 8, 11, 14, 15, 16, 19, 27 #1, 2, 4-7, 12, 13, 17, 18 HW #12.5 3/7 §1.10 pp97-99 Study Guide p. 101 #9, 11, 12 On-Line Markov System Material HW # 13 3/9*19 §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 #13.5 3/19 §1.10 pp93-96 p99 #1, 2, 4, 5, 8, 3, 6, 7, 10 HW #14 3/19*21 §2.9 p. 180-182 #1, 4, 6, 8, 9, 12, 14, 18, 19 #2, 3, 5, 10, 11, 13, 17 HW #15 3/23 §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 3/26*28 §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 3/28*30! §3.3 Determinant summary Proof ot Thrm 6 on BB p. 209-210 #2, 5, 8, 19, 24, 25, 28, 29 #1, 3, 4, 6, 7, 9, 10, 20-23, 27, 30 HW #18 4/4 §4.1 More v.s. examples on BB 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 4/4*6*9 p.   234-236 # 7-9, 25,31, 34 #35, 36 HW #20 4/11 §4.3 p. 342- 345 # 22, 25, 26, 31,33,37 #32 HW #21 4/13*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 #22 4/18 §5.2 p. 317-318 #2, 3, 9, 11, 16, 21, 23, 24 #1, 4-8, 10, 12-15, 17, 19, 20, 22 HW # 23 4/20*23 §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 4/25 §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 #25 4/27*30 §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 5/2? §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 possible assignments. For use in the future! :) §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

 Monday Wednesday Friday Week 1 1.1-1.2 1-15 MLK DAY No Class Introduction and Motivation Solving 2 by 2  systems. Continuation: Solving Systems of linear equations. Week 21.2-1.4? 1-22 Introduction to matrices. Being Systematic. Gauss-Jordan Method using row operations Vector Equations and Linear combinations Begin Vector-Matrix Arithmetic and equations. Week 31.4, 1.5 1- 29 Discussion of proofs. Application to polynomial curve fitting? Vector-Matrix Arithmetic and equations Solutions AND Linear combinations "Inner product." Homogeneous and Non-homogeneous systems Week 4 1.6-1.8 2-5 Applications Spanning and Linear dependence Linear Independence Week 5 1.8, 1.9 2-12 Linear Transformations Matrices and LT's More on LT's [Abstract definition] Connection with matrices. Week 6 2.1-2.3 2-19 More on LT's 1:1 and onto. Properties of Matrix algebra. More Matrix algebra-Matrix Inverse. Week 7 Midterm Exam #1 Self-Scheduled March 1 Covers weeks 1-6.2.2,2.3 2-26 More Matrix Algebra- Inverse More on Matrix Inverse Invertibility and Independence, Spanning, etc.  Invertible Linear Transformations Week 82.8, 2.9, 2.3, (2.6, 2.7?) 3-5 Applications(Linear Difference- Migration-Markov) Begin Subspaces. Null Space and Column Spaces of a matrix. BASES Week 9 3-12 ... Spring Break   NO Classes! Week 10 3.1,3.2 3-19  Dimension Rank of a matrix. Bases and Linear Transformations Rank and nullity More Inverse results.  Begin Determinants  Calculating determinants by cofactor expansion Properties of determinants  Products and Inverses Week 11 3.3, 3-26 Applicatons of Determinants Cramer's Rule, geometry of determinants. Determinants, Linear Transformations and Areas Proof of Product Property [Permutations and determinants?] 3-30CC Day  No classes Week 12 4.1, 4.2, 4.3,  (4.4,4.5,4.6)? 4-2 Begin Abstract Vector Spaces Linear Transformations Kernel(Null Space) and range More VS examples. Subspaces and spanning Rank and Nullity.  More Linear transformations: T+aU, TU Geometry of LT's Week 13 Exam II 5.1, 5.2 4-9 More on Linear  Transformations, Null Space, Range, Independence, Basis, and Differential equations. Eigenvalue/vector of a matrix, Linear transformation More eigenstuff. Week 14 5.2,5.3, 4.9 4-16 Diagonalizable Matrices/transformations. Applications of  diagonalization. Stochastic Matrices. Comments on diagonalizable matrices. Inner products and more on transformations Week 15 6.1, 6.2 4-23 Inner products Orthogonal and orthonormal bases Finish Orthonormal bases, Orthogonal transformations and distance. Week 16 6.3, 6.4 4-30 Gram- Schmidt - orthonormal bases. General inner product spaces. Geometry and Lin. Operators, Transformations Breath! :) Symmetric Matrices, Transpose,Trace? Week 17 Review Session: Sunday 4-6pm Lib 56 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 in the Reality Quizzes Folder. Self Schedule for Final Examinations Tues. May 8 10:20-12:10 FH 125 Wed. May 9 10:20-12:10 SH 128 * (as per Exam Schedule) Wed. May 9 12:30-14:20 SH 116 Fri. May 11 10:20-12:10 FH 125OR Special Appointment Final Exam Week

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Spring, 2007                                  COURSE INFORMATION          M.FLASHMAN
MATH 241  Elements of Linear Algebra
OFFICE: Library 1                                                                                     PHONE:826-4950

Office Hours: M-F 12:30-13:30 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 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 3 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.)