NCC Dept. of MAT/CSC/ITE



NASSAU COMMUNITY COLLEGEDEPARTMENT OF MATHEMATICS/COMPUTER SCIENCE/INFORMATION TECHNOLOGY Course Syllabus forMAT 226 Elementary Linear AlgebraCourse Information Title Elementary Linear AlgebraCredit Hours 4 CreditsNumber MAT 226Section _____________________Semester/Term _____________________Meeting time _____________________ Location _____________________Instructor/Contact Information Name ____________________________________________________________Office location ____________________________________________________________Office hours ____________________________________________________________Office telephone and fax numbers __________________________________________________Email address ____________________________________________________________Blackboard link ____________________________________________________________Website____________________________________________________________Other ____________________________________________________________Course Description MAT 226 Elementary Linear AlgebraPrerequisites: Students must have passes MAT 123 Calculus 2 with at least a C.Description: Students are presented with systems of linear equations that can be mathematical models of physical systems. A system is analyzed in a linear vector space setting by applying the fundamental laws of matrix algebra. The matrix, as a function (linear transformation), is examined which provides essential properties of the model. The basic objective is to extend the student’s knowledge of the laws of algebra for operators operating on real numbers to the algebraic laws for matrix operators operating on vectors.Calculator Requirement: A graphing calculator, the TI-86, TI-89 or TI N-spire is recommended.Learning Outcomes and Objectives? OBJECTIVES: GeneralStudents are presented with systems of linear equations that can be mathematical models of physical systems. A system is analyzed in a linear vector space setting by applying the fundamental laws of matrix algebra. The matrix, as a function (linear transformation), is examined which provides essential properties of the model. The basic objective is to extend the student’s knowledge of the laws of algebra for operators operating on real numbers to the algebraic laws for matrix operators operating on vectors.?OBJECTIVES: SpecificTo enable the student to: 1. analyze systems of linear equations that can be mathematical models of physical systems. 2. learn the structure of a linear vector space by applying the fundamental laws of linear algebra. 3. apply the laws of linear algebra to matrix operators. 4. examine the matrix as a function operating on a vector space. 5. establish a fundamental decomposition of the matrix operator.SUNY General Education Goals & Outcomes1. Linear Algebra FundamentalsStudents will be able to analyze and solve linear models by the basic linear algebra theories.Outcome1.1 Systems of Linear EquationsSolve a system of linear equations using the row reduction method.1.1.1 Basic Algebra Solution of Systems?1.2 Systems as Matrix EquationsSolve a system with vector and matrix algebra.1.2.1 Matrix Algebra Solution of Systems?2. Vector Spaces and Linear TransformationsStudents will be able to properly define and modify the format of a vector space, and then define and analyze various linear transformations.Outcome2.1 Bases and SubspacesDetermine a basis for a vector space, and derive subspaces.2.1.1 Bases of Vector Spaces?2.2 Linear TransformationsExamine eigen-properties of transformations, and then derive standard decompositions. 2.2.1 Transformations ?3. Inner Product Spaces and Spectral TheoryStudents will create an inner product space, and then derive the spectral decomposition of a linear transformation.Outcome3.1 Standard Inner Product Space DerivationsDefine an inner product space, and construct a Gram-Schmidt equivalent.3.1.1 Inner Product Space?3.2 Spectral Decomposition of a Linear TransformationTransform a matrix transformation as a spectral decomposition 3.2.1 Matrix Transformations?Mathematics A.S. Degree Goals and Outcomes1. Proof and TheoryStudents must be able to describe what a mathematical proof is and why proofs are important in mathematics. In addition, students must recognize the different types of proofs and their proofs should use appropriate notation and be complete. Deriving a formula also plays an important part of this process.Outcome1.1 Proof TypesStudents will be able to demonstrate a number of different techniques in constructing a proof, including direct proofs, indirect proofs, proofs by contraposition and proofs by induction.1.2 Prove Mathematical TheoremsStudents will be able to apply the various types of proofs using appropriate notation/arguments in order to construct a valid proof.1.3 Derive FormulasStudents will derive formulas in order to apply the mathematics they are studying.2. AlgorithmsStudents must be able to apply algorithms derived in their classes to many mathematical situations.Outcome2.1 Perform ComputationsStudents must perform numeric computations2.2 Analyze Mathematical ModelsStudents must construct and apply symbolic and graphical representations of functions. ?3. ApplicationsStudents must be able to construct, analyze and interpret mathematical models and how they apply to real-life situations throughout their coursework.Outcome3.1 Construct Mathematical ModelsStudents must construct an appropriate mathematical model in order to solve to a problem.3.2 Analyze Mathematical ModelsStudents must analyze a mathematical model in order to present results.3.3 Communicate ResultsStudents must communicate their analysis of mathematical models in multiple ways: orally, graphically, using tables and formulas.?4. Ancillary Computer SkillsStudents must develop computer/programming skills and apply these skills in constructing and finding solutions to mathematical models.Outcome4.1 Appropriately Use TechnologyStudents must use technology appropriately to analyze mathematical problems and determine solutions.4.2 Analyze ProgramsStudents must be able to identify and understand programming specific terminology. This includes the ability to trace through a program to determine what the program does.4.3 Write ProgramsStudents must be able to write methods and understand/apply arrays of objects.?????Instructional Methods This course is taught using a variety of instructional methods including lecture, class discussion and examinations. Textbook and Materials Required textbook: Linear Algebra and Its Applications, 5th Edition, by David C. Lay, Steven R. Lay, Judy J. McDonald, Published by Addison Wesley, 2014References: 1.Determinants and matrices, by A.C. Aitken, Read Books Ltd, 2016.2. Elementary linear algebra, 3rd edition, by Paul C. Shields, Worth, 1980. 3. Linear algebra - An introductory approach, by W.W. Curtis, Allyn and Bacon, l974. 4. Algebra, by W.L. Ferrar, Oxford University Press, l970.5. Introduction to linear algebra, by M. Marcus and H. Minc, MacMillan, l965.6. Methods of applied mathematics, by F.B. Hildebrand, Prentice-Hall, l965.7. Foundations of linear algebra, by A.I. Malcev, Freeman, l963.Student Responsibilities /Course PoliciesInstructors need to complete the following for their specific policies. It is recommended that in class exams are required.Participation __________________________________________________________________Homework ____________________________________________________________________Online discussions ______________________________________________________________Projects ______________________________________________________________________Group work (include information on effective group procedures) _____________________________________________________________________________________________________Exams/quizzes _________________________________________________________________Attendance/lateness policy _____________________________________________________Missed exams/ quizzes policy_____________________________________________________Extra credit ___________________________________________________________Academic Dishonesty & PlagiarismAcademic dishonesty, which includes plagiarism and cheating, will result in some form of disciplinary action that may lead to suspension or expulsion under the rules of the Student Code of Conduct. Cheating can take many forms including but not limited to copying from anotherstudent on an examination, using improper forms of assistance, or receiving unauthorized aid when preparing an independent item of work to be submitted for a grade, be it in written, verbal or electronic form. Anyone who assists or conspires to assist another in an act of plagiarism or anyother form of academic dishonesty may also be subject to disciplinary action.Plagiarism is a particular type of academic dishonesty that involves taking the words, phrases or ideas of another person and presenting them as one's own. This can include using whole papers and paragraphs or even sentences or phrases. Plagiarized work may also involve statistics, labassignments, art work, graphics, photographs, computer programs and other materials. The sources of plagiarized materials include but are not limited to books, magazines, encyclopedias or journals; electronic retrieval sources such as materials on the Internet; other individuals; or paper writing services.A student may be judged guilty of plagiarism if the student:(a) Submits as one's own an assignment produced by another, in whole or in part.(b) Submits the exact words of another, paraphrases the words of another or presents statistics, lab assignments, art work, graphics, photographs, computer programs and other materials without attributing the work to the source, suggesting that this work is the student's own.Allegations of student plagiarism and academic dishonesty will be dealt with by the appropriate academic department personnel. It is the policy of Nassau Community College that, at the discretion of the faculty member, serious acts will be reported in writing to the Office of the Dean of Students, where such records will be kept for a period of five years beyond the student's last semester of attendance at the College. These records will remain internal to the College and will not be used in any evaluation made for an outside individual or agency unless there is a disciplinaryaction determined by a formal ruling under the Student Code of Conduct, in which case only those records pertaining to the disciplinary action may apply. A student whose alleged action is reported to the Office of the Dean of Students will be notified by that office and will have the rightto submit a letter of denial or explanation. The Dean will use his/her discretion in determining whether the alleged violation(s) could warrant disciplinary action under the Student Code of Conduct. In that case the procedures governing the Code of Conduct will be initiated.Copyright statement: The Higher Education Opportunity Act of 2008 (HEOA) requires the College to address unauthorized distribution of copyrighted materials, including unauthorized peer-to-peer file sharing. Thus, the College strictly prohibits the users of its networks from engaging in unauthorized distribution of copyrighted materials, including unauthorized peer-to-peer file sharing. Anyone who engages in such illegal file sharing is violating the United States Copyright law, and may be subject to criminal and civil penalties. Under federal law, a person found to have infringed upon a copyrighted work may be liable for actual damages and lost profits attributable to the infringement, and statutory damages of up to $150,000. The copyright owner also has the right to permanently enjoin an infringer from further infringing activities, and the infringing copies and equipment used in the infringement can be impounded and destroyed. If a copyright owner elected to bring a civil lawsuit against the copyright infringer and ultimately prevailed in the claim, the infringer may also become liable to the copyright owner for their attorney's fees and court costs. Finally, criminal penalties may be assessed against the infringer and could include jail time, depending upon the severity of the violation. Students should be aware that unauthorized or illegal use of College computers (such as engaging in illegal file sharing and distribution of copyrighted materials), is an infraction of the Student Code of Conduct and may subject them to disciplinary measures. To explore legal alternatives to unauthorized downloading, please consult the following website: Resources Web sites____________________________________________________________Library services____________________________________________________________Labs and learning centers: MATH CENTER REQUIREMENTIf needed, students are encouraged to avail themselves of further study and/or educational assistance available in the Mathematics Center located in B-l30. These activities and use of the resources provided are designed to help the student master necessary knowledge and skills.Study groups ____________________________________________________________Extra help options____________________________________________________________Assessments and Grading MethodsProvide a clear explanation of evaluation, including a clear statement on the assessment process and measurements. Be explicit! Include format, number, weight for quizzes and exam, descriptions of papers and projects as well as how they will be assessed and the overall grading scale and standards. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Americans with Disabilities Statement & Non-Discrimination Statement (NCC Required)"If you have a physical, psychological, medical, or learning disability that may?have an impact on your ability to carry out the assigned coursework, I urge you to?contact the staff at the Center for Students with Disabilities (CSD), Building U,?(516)572-7241, TTY (516)572-7617.? The counselors at CSD will review your concerns and determine to what reasonable accommodations you are entitled as covered by the Americans with Disabilities Act and section 504 of the Rehabilitation Act of 1973.? All information and documentation pertaining to personal disabilities will be kept confidential.”Course Schedule and Important DatesProvide a detailed list of meeting dates, topics, assignments, and due dates for all exams, scheduled quizzes, papers, projects, assignments, labs, etc. Use a grid format to help students easily read and understand the information. Class NumberDateTopic1/2Chapter 1: Linear Equations in Linear AlgebraSections 1.1-1.53/4Chapter 1: Linear Equations in Linear Algebra Sections 1.7-1.95/6Chapter 2: Matrix Algebra, Sections 2.1, 2.2Chapter 3: Determinants, Sections 3.1-3.27/8Review Chapters 1-3 Exam 19/10Chapter 4: Vector SpacesSections 4.1-4.211/12Chapter 4: Vector SpacesSections 4.3-4.413/14Chapter 4: Vector SpacesSections 4.5-4.715/16Review Chapter 4 Exam 217/18Chapter 5: Eigenvectors and EigenvaluesSections 5.1-5.3 10/20Chapter 5: Eigenvectors and EigenvaluesSections 5.4-5.5 21/22Review Chapter 5 Exam 323/24Chapter 6: Orthogonality and Least SquaresSections 6.1, 6.725/26Chapter 7: Symmetric Matrices and Quadratic FormsSections 7.1, 7.427/28Chapter 7: Symmetric Matrices and Quadratic Forms, Sections 7.2Review Chapters 6, 729/30Review additional sectionsExam 4Fall 2019 ................
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