Oza, A.

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New Jersey Institute of TechnologyDigital Commons @ NJITMathematical Sciences Syllabi NJIT SyllabiFall 2019MATH 337-017: Linear AlgebraA. OzaFollow this and additional works at: https://digitalcommons.njit.edu/math-syllabiThis Syllabus is brought to you for free and open access by the NJIT Syllabi at Digital Commons @ NJIT. It has been accepted for inclusion inMathematical Sciences Syllabi by an authorized administrator of Digital Commons @ NJIT. For more information, please contactdigitalcommons@njit.edu.Recommended CitationOza, A., "MATH 337-017: Linear Algebra" (2019). Mathematical Sciences Syllabi. 124.https://digitalcommons.njit.edu/math-syllabi/124MATH 337: Linear AlgebraFall 2019 Course SyllabusNJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciencestakes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means thatthere must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or anyform of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligatedto report any such activities to the Instructor.COURSE INFORMATIONCourse Description: Matrices, determinants, systems of linear equations, vector spaces, linear transformations,eigenvalues, eigenvectors, and related topics.Number of Credits: 3Prerequisites: MATH 112 with a grade of C or better or MATH 133 with a grade of C or better.Course-Section and InstructorsCourse-Section InstructorMath 337-001 Professor P. MilojevicMath 337-007 Professor C. FrederickMath 337-009 Professor P. MilojevicMath 337-013 Professor W. ChoiMath 337-017 Professor A. Oza Math 337-029  Professor E. MichalopoulouMath 337-101  Ammicht, EgbertOffice Hours for All Math Instructors: Fall 2019 Office Hours and EmailsRequired Textbook:Title Linear Algebra and its ApplicationsAuthor LayEdition 5thPublisher PearsonISBN # 978-0321982384University-wide Withdrawal Date:The last day to withdraw with a W is Monday, November 11, 2019. It will bestrictly enforced.COURSE GOALSCourse ObjectivesLearn about matrices, determinants, applications to solving linear system of equations, matrix factorization,eigenvalues and eigenvectors, Gram-Schmidt process.Cover relevant applications in economics, science and engineering to illustrate the utility of learning thesetopics.Use mathematical software, in problem solving, to allow the solution of more complex problems and providevisualization of the same.Course OutcomesPrepare students for further study in theoretical courses such as differential and difference equations and leastsquares analyses.To enable students to use linear algebra use for numerical solvability of many problems.Students are prepared for applying linear algebra to many practical applications in fields like economics,computer science, physics, engineering, archeology, demography, relativity, etc.POLICIESDMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department ofMathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policiesvery seriously and enforces them strictly.Grading Policy: The final grade in this course will be determined as follows:Quizzes and Projects 25%Common Midterm Exam I 20%Common Midterm Exam II 20%Final Exam 35%Your final letter grade will be based on the following tentative curve.A 90 - 100 C 60 - 69B+ 85 - 89 D 50 - 59B 75 - 84 F 0 - 49C+ 70 - 74Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read andfully understand the Math Department’s Attendance Policy. This policy will be strictly enforced. Absences fromclass will inhibit your ability to fully participate in class discussions and problem solving sessions. Tardiness toclass is very disruptive to the instructor and students and will not be tolerated. Students might be withdrawnfrom the class or receive an "F" because of absences.MATLAB: MATLAB is a mathematical software program that is used throughout the science and engineeringcurricula. Several MATLAB assignments will be given out. These assignments have been designed to help youlearn how to use this software in order to visualize many of the concepts taught in class.Projects: It is vital that you complete the required assignments by the specified dates.Quiz Policy: A short quiz based on the homework problems will be given weekly.Exams: There will be two common midterm exams held during the semester and one comprehensive commonfinal exam. Exams are held on the following days:Common Midterm Exam I October 2, 2019Common Midterm Exam II November 13, 2019Final Exam Period December 14 - 20, 2019The time of the midterm exams is 4:15-5:40 PM for daytime students and 5:45-7:10 PM for evening students.The final exam will test your knowledge of all the course material taught in the entire course. Make sure youread and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and followthe required steps under the DMS Examination Policy found here:http://math.njit.edu/students/policies_exam.phpCellular Phones: All cellular phones and other electronic devices must be switched off and put away during allclass times.ADDITIONAL RESOURCESMath Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Fall 2019 Hours)Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporaryaccommodations for undergraduate, graduate and visiting students at NJIT.If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director ofDisability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster HallRoom 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing youraccommodations will be required.For further information regarding self identification, the submission of medical documentation and additionalsupport services provided please visit the Disability Support Services (DSS) website at:https://www.njit.edu/studentsuccess/accessibility/Important Dates (See: Fall 2019 Academic Calendar, Registrar)Date Day EventSeptember 3, 2019 T First Day of ClassesSeptember 13, 2019 M Last Day to Add/Drop ClassesNovember 11, 2019 M Last Day to WithdrawNovember 26, 2019 T Thursday Classes MeetNovember 27, 2019 W Friday Classes MeetNovember 28 - December 1, 2019 R - Su Thanksgiving RecessDecember 11, 2019 W Last Day of ClassesDecember 12 & 13, 2019 R & F Reading DaysDecember 14 - 20, 2019 Sa - F Final Exam PeriodCourse Outline*APPLICATION SECTIONS IN REDWeek Subjects Section and Recommended Exercises1 Systems of Linear Equations 1.1: 2, 4, 10, 15, 18, 24, 29Row Reduction and Echelon Form 1.2: 2, 4, 8, 11, 13, 18, 20Vector equations 1.3: 2, 5, 9, 11, 13, 17, 242 Matrix Equations 1.4: 2,4,5,9,17Solutions of Linear Systems 1.5: 1,4,6,8,11,15,233 Application to Chemistry (brief) 1.6: 7,9Linear Independence 1.7: 1,4,6,7,14,16,31Linear Transformations 1.8: 2,4,7,9,13,154 Matrix form of Linear Transformations 1.9: 5,7,10,15,18,22Matrix Operations 2.1: 4,7,9,16,23Inverse of a Matrix 2.2: 3,6,9,26,29,325 Exam ReviewCOMMON MIDTERM #1 WEDNESDAY - OCTOBER 2, 2019Invertible Matrices 2.3: 2,6,9,11,13,14,416 LU Factorization 2.5: 2,4,5,8,11,15,17Application to Computer Graphics (brief) 2.7: 1,2,5Introduction to Determinants 3.1: 3,8,9,12,22,24,25,287 Properties of Determinants 3.2: 1,4,6,9,21,22,25,26Cramer's Rule 3.3: 2,5,8,11,16Vector Spaces and Subspaces 4.1: 8,24,30,388 Null Spaces and Columns Spaces 4.2: 2,4,14,20,24Linear Maps 4.3: 4,5,10,14,15,21Dimension of a Vector space 4.5: 2,4,6,9,13,15,189 Rank 4.6: 1,2,5,9,13,17,18Application to Markov Chains (Brief) 4.9: 2,4,6, 8,1010 Eigenvalues and Eigenvectors 5.1: 3,7,9,13,15,17,20 The Characteristic Equation 5.2: 4,7,9,13,15,16,20,2111 Exam Review  COMMON MIDTERM #2 WEDNESDAY - NOVEMBER 13, 2019Diagonalization 5.3: 2,4,6,7,8,12,17,21 Complex Eigenvalues 5.5: 4,5,13,1412 Inner Product, Length, and Orthogonality 6.1: 1,8,10,12,14,15,16,20Orthogonal Sets 6.2: 1,4,8,12,16,1720,23Orthogonal Projections 6.3: 2,4,6,8,10,12,14,1613 The Gram-Schmidt Procedure 6.4: 1,4,8,9,12Inner Product Spaces 6.7: 1,2,4,6,8Diagonalization of Symmetric Matrices 7.1: 1-10,14,17,22,2614 Quadratic Forms 7.2: 2,5,7,10,13,21Exam ReviewMATLAB Projects for M337:Linear Algebra, Fall 2019Visit the textbook website for supplementary materials including a guide to getting started with Matlab. Foradditional help, the math department has Matlab TA’s. Click for locations and times when they are available.The first thing you need to do is to install the LayData toolbox on the computer where you will be using it. Hereare the steps. I will assume that you have Matlab installed or are using Matlab on a campus PC.Download the LayData Toolbox.Uncompress the file and move the unzipped directory to the location on your computer where you want it.Add the toolbox to the Matlab search path. To do this run Matlab, and at the >> prompt, type pathtool to bringup the path management window. Click Add Folder, and select the folder containing the toolbox. Be sure tosave it.Subject Week Due NotesGetting Startedwith MATLABSeptember17, 2019Section 14: Some recent versions of Matlab use New -> Script instead of New ->M-file. Do install the Laydata programs and set the path as described in section 16for next assignment.DO NOT HAND IN.Practice RowOperations andReducedEchelon formand refOcotber 1,2019Note that there are two separate short assignments here.LowerTriangularMatricesOctober22, 2019Problem (1c) and (2b) ask you to prove a result about lower triangular matrices. Ifyou have trouble doing this in general, try it first with \(2\times2\) lowertriangular matrices, then \(3\times3\) until you see the pattern. For generalMatrices, try using the \(\Sigma\) notation for the \((i,j)\) entry of a matrixproduct.Using backslashto solve Ax=bNovember5, 2019LUFactorizationNovember26, 2019Updated by Professor P. Milojevic - 8/28/2019Department of Mathematical Sciences Course Syllabus, Fall 2019

MATH 337-017: Linear Algebra

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MATH 337-017: Linear Algebra

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