Salem State University



January 4, 2021 SALEM STATE UNIVERSITYMATHEMATICS DEPARTMENTSalem, Massachusetts 01970-5353COURSE SYLLABUS, Spring 2021MATH 734LINEAR AND MULTILINEAR ALGEBRA (3 credits)Section S1:Wed. 7:00 p.m. – 9:20 p.m. in the following Zoom class: ID: 946 5579 1396Passcode: 657699One tap mobile+19292056099,,94655791396#,,,,,,0#,,657699# US (New York)Dial by your location +1 929 205 6099 US (New York)Instructor:Dr. Arthur RosenthalE-mail:arosenthal@salemstate.eduOffice:308I Sullivan Bldg.Phone: 978-542-6392Internet home page: hours:Mon. 2:30 p.m. – 4:30 p.m.; Wed. and Fri. 2:00 p.m. – 3:00 p.m.Other times by appointment or by chance.Because of policies related to Covid-19, my office hours will need to be online until further notice. I hope the following instructions will help you "visit" me during my virtual office hours:Join Zoom Meeting: Mon. 2:30 – 4:30 p.m., Wed. and Fri. 2:00 – 3:00 p.m. ID: 970 8417 1561Password: 9785426392One tap mobile+19292056099,,97084171561#,,1#,9785426392# US (New York)Dial by your location +1 929 205 6099 US (New York)Find your local number: text:Linear Algebra and Its Applications (4th ed.) by Gilbert Strang (Thomson Brooks/ Cole, 2006)Chapter Coverage:6.Positive Definite putations with Matrices8.Linear Programming and Game TheoryA.Intersection, Sum, and Product of SpacesB.The Jordan FormExaminations:2 exams in class of one hour each: Feb. 24 and March 31FINAL EXAM:Wednesday, May 5 7:00 – 9:00 p.m. Course and Grading Policies:Each of the one hour exams will count for 20% of the course grade. The cumulative final exam will count for 40% of the course grade. Homework assignments and quizzes will count for 20% of the course grade, with the relative weight given to each of these determined by the number of possible points on each of them. The number of times you inform me, before I inform the class, of a correct answer to a problem in the chapter currently being covered (according to the schedule of course topics) with an incorrect answer in the back of the text will be added to your overall average. (This means if you correct 5 problems with wrong answers in the back of the text and your overall average would have been 70%, your overall average will become 70%+5%=75%).The following table will be used to convert your overall average percent grade to a letter grade:Final Average:90-10080-8975-7970-7465-6960-6455-5950-540-49Letter Grade:AA-B+BB-C+CC-FAll exams are required. Make-ups will be given, no later than 4 pm on May 17, only if you notify me before the exam starts or as soon as possible and supply a specific reason that justifies your absence. The notification may be an email sent to arosenthal@salemstate.edu or a voicemail left at 978-542-6392. Students who miss a quiz or exam without giving me such notification have no expectation of being given a chance to make up the quiz or exam. Unavoidable conflicts may be resolved by taking parallel exams before the scheduled date, if prior notice of one week is given to the instructor. Assignments submitted late are subject to a 10% penalty if submitted before any students receive their corrected solutions. Late assignments receive no credit if submitted after any students receive their corrected solutions.It is your responsibility to attend as many classes as possible, to do all homework problems assigned in class, and to complete all course requirements. You are responsible for any topics or problems covered in class (whether or not you are present). Attendance will be spot-checked on at least three occasions. There is no explicit limit on the number of absences allowed and no explicit penalty for excessive absence. Nevertheless, there is an implicit disadvantage for excessive absence, because it could cause homework problems assigned in class to be missed or quizzes or exams to be missed. That could adversely affect your grade, unless you complied with my policy that make-ups will be given only if you notify me before the class involved or as soon as possible and supply a specific reason that justifies your absence. Requests to reschedule coursework made after the work was due will generally be declined. Each student in this section is required to have a graphing calculator comparable to a TI 83 or 84 or a laptop computer comparable to a Dell Latitude 3410. (The specifications for this computer may be found by going to ). Each student needs to be able to bring this graphing calculator or computer to any class on or after Wednesday, February 3.University Policies:1. Requirements: All students are expected to be familiar with the academic regulations, including those regarding Academic Integrity, for Salem State University as published in the University catalog. In addition, each student is responsible for completing all course requirements and for keeping up with all that goes on in the course (whether or not the student is present).2. Equal Access: The Salem State University 2020–2021 catalog states, “Salem State University is committed to providing equal access to the educational experience for all students in compliance with Section 504 of The Rehabilitation Act and The Americans with Disabilities Act and to providing all reasonable academic accommodations, aids and adjustments. Any student who has a documented disability requiring an accommodation, aid or adjustment should speak with the instructor immediately. Students with Disabilities who have not previously done so should provide documentation to and schedule an appointment with the Disability Services Office (phone 978-542-6217 or e-mail disability-services@salemstate.edu), and obtain appropriate services.” 3. Academic Integrity: The School of Graduate Studies assumes that all students attend Salem State with serious educational intent and expects them to be mature, responsible individuals who will exhibit high standards of honesty and personal conduct in their academic life. All forms of academic dishonesty are considered to be serious offenses against the University community. The University will apply sanctions when student conduct interferes with the University’ s primary responsibility of ensuring its educational objectives. All members of the Salem State academic community have a responsibility to ensure that scholastic honesty and academic integrity are safeguarded and maintained. Cheating, plagiarism, and collusion in dishonest activities are unfair, demoralizing, and demeaning to all of us. They diminish the learning experience not only for the perpetrators, but also for the entire community. It is expected that Salem State graduate students will understand and subscribe to the ideal of academic integrity and that they will bear individual responsibility for their work. Materials (written or otherwise) submitted to fulfill academic requirements must represent a student’s own efforts.4. COVID-19 pandemic statement: Students must comply with the Coronavirus Disease 2019 (COVID-19) Health and Safety Protocols for the 2020 - 2021 Academic Year. This includes wearing masks in class and on campus in public spaces, practicing physical distancing where possible, including in class, engaging in a daily symptom check, notifying Counseling and Health Services at 978-542-6413 if they have any symptoms associated with COVID-19, and not coming to campus or to an in-person class if they have any of the symptoms related to COVID-19, until cleared by the Student Life Wellness Area. Students who have documented disabilities that may prevent them from complying with these policies are required to contact the Disability Services Office.5. Critical Emergency Policy: In the event of a university declared critical emergency, Salem State University reserves the right to alter this course plan. Students should refer to salemstate.edu for further information and updates. The course attendance policy stays in effect until there is a university declared critical emergency. In the event of an emergency, please refer to the alternative educational plans for this course which will be sent by email. Students should review the plans and gather all required materials before an emergency is declared. Course Prerequisite:Linear Algebra, comparable to our Math 414 or 704Course Description:Suggested topics are: canonical forms for matrices and linear transformations, quadratic forms, principal axis theorem, tensor products, exterior and symmetric algebras.Last Day to Withdraw from the Course:The last day on which withdrawal from the course is permitted with a “W” grade is Friday, April 16.Math/ Computer Lab:Free tutoring and a variety of mathematics software packages are available in the Math/ Computer Lab, SB306. Hours will be posted, and are expected to be from 10 a.m – 5 p.m. on Monday - Thursday and from 9 a.m. – 3 p.m. on Friday during most of the semester. Please go to for more details, because all tutoring is expected to be done remotely this semester.Global Goals:To increase the student's understanding of the basic concepts of linear algebra.To make the student aware of the crucial importance of linear algebra to many fields in engineering, science, probability, statistics, computer science and economics.To enhance the student's ability to reason mathematically.To enable the student to appreciate the beauty of linear algebra and its value.To be able to solve simple problems involving linear algebra by hand and more complicated problems involving linear algebra using a computer.To realize why many mathematicians consider the software package MATLAB (available on the computers in the Math Lab) to be the outstanding software for linear algebra, and be able to use it to solve some problems.Learning Objectives: The student will be able to:Perform numerical linear algebra with the help of the software program MATLAB or OCTAVE.Test whether a matrix is positive definite and understand the significance of whether it is.Find the matrix of a quadratic form and the principal axes of the quadratic form.Classify quadratic forms as positive definite, negative definite or indefinite.Analyze quadratic forms geometrically and determine whether they correspond to ellipsoids.Find the singular value decomposition of a matrix and be able to apply it to such applications as image processing and finding the pseudoinverse of a matrix.Understand computational issues that arise when solving Ax = b and how the condition number of A affects the sensitivity of the solution to small changes in the data.Use computationally efficient algorithms such as the QR algorithm to find eigenvalues of a matrix.Use the simplex method to solve linear programming problems.Find the sum, cartesian product and tensor product of two vector spaces.Find the Jordan canonical form of a matrix..Course Requirements for Assessment:AssessmentScheduled DatesLearning ObjectivesPercent of GradeHomeworkDue Dates on most Wednesdays1–1120%Test 1February 241–720%Test 2March 317–920%Cumulative Final ExamMay 51–1140%Tentative Schedule of Course Topics:WeekTopicsSections in Text1Minima, maxima and saddle points of a quadratic form; tests for positive definiteness.6.1, 6.22Singular value decomposition.6.33Minimum principles; the finite element method.6.4, 6.54Computations with matrices; matrix norm and condition number.7.1, 7.25Computation of eigenvalues; the QR algorithm.7.36Iterative methods to solve Ax = b.7.47Linear programming; the simplex method.8.1, 8.28The Dual problem.8.39Network models.8.410Game theory8.511Intersection, sum, cartesian and tensor product of two vector spaces.Appendix A12The Jordan canonical form.Appendix B13The $25,000,000 Eigenvector: The Linear Algebra behind Google.(3) in bibliography14Review15Final ExamBibliography:Anton, Howard and Chris Rorres, Elementary Linear Algebra: Applications version, 11th ed., Wiley, Hoboken, New Jersey, 2014.Bretscher, Otto, Linear Algebra with Applications, 5th ed., Pearson Education, Upper Saddle River, New Jersey, 2019.Bryan, Kurt and Tanya Leise, The $25,000,000 Eigenvector: The Linear Algebra behind Google, SIAM Review, 48, 2006, pp. 569-581 (available at ).Cheney, Ward and David Kincaid, Linear Algebra: Theory and Applications, 2nd ed., Jones and Bartlett Learning, Sudbury, Mass., 2012.Friedberg, Stephen H., Arnold J. Insel and Lawrence E. Spence, Linear Algebra, 5th ed., Pearson Education, Upper Saddle River, New Jersey, 2018.Goodaire, Edgar G., Linear Algebra: Pure and Applied, World Scientific, Hoboken, New Jersey, 2014.Johnson, Lee W., R. Dean Riess and Jimmy T. Arnold, Introduction to Linear Algebra, 5th ed., Pearson, New York, NY, 2018.Kolman, Bernard and David R. Hill, Elementary Linear Algebra with Applications, 9th ed., Pearson, New York, NY, 2018.Larson, Ron, Elementary Linear Algebra, 8th ed., Cengage Learning, Boston, Mass., 2017.Lax, Peter D., Linear Algebra and its Applications, 2nd ed., Wiley, Hoboken, New Jersey, 2007.Lay, David C., Steven R. Lay and Judi J. McDonald, Linear Algebra and its Applications, 6th ed., Pearson Education, Boston, Mass., 2020.Leon, Steven J., Linear Algebra with Applications, 9th ed., Pearson Education, Upper Saddle River, New Jersey, 2015.Lindfield, George R. and John E. T. Penny, Numerical Methods Using MATLAB, 4th ed., Elsevier, London, 2019.Math Archives, (Web site).Math Forum, (Web site).The Math Works, Inc., MATLAB and Simulink Student Version (Release 2020b), available from (Web site).Octave repository, (Web page for a freeware program very similar to MATLAB).Poole, David, Linear Algebra: A Modern Introduction, 4th ed., Cengage Learning, Stamford, CT, 2015.Sadun, Lorenzo A., Applied Linear Algebra: The Decoupling Principle, 2nd ed., American Mathematical Society, Providence, R.I., 2008.Spence, Lawrence E., Arnold J. Insel and Stephen H. Friedberg, Elementary Linear Algebra: A Matrix Approach, 2nd ed., Pearson Education, New York, NY, 2018.Texas Instruments calculator home page, (calculator software).Williams, Gareth, Linear Algebra with Applications, 9th ed., Jones and Bartlett Learning, Burlington, Mass., 2019.Wolfram-Alpha web resource, (Web site). ................
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