Nassau Community College



NASSAU COMMUNITY COLLEGEDEPARTMENT OF MATHEMATICS/COMPUTER SCIENCE/INFORMATION TECHNOLOGY Course Syllabus for227457027940MAT 118Finite Mathematics 00MAT 118Finite Mathematics Course Information Title Finite Mathematics Quantitative AnalysisCredit Hours 3 CreditsNumber MAT 118Section _____________________Semester/Term _____________________Meeting time _____________________ Location Remote _______________Instructor/Contact Information Name ____________________________________________________________Office location ____________________________________________________________Office hours ____________________________________________________________Office telephone and fax numbers __________________________________________________Email address ____________________________________________________________Blackboard link ____________________________________________________________Website____________________________________________________________Other ____________________________________________________________Course Description MAT 118: Finite MathematicsPrerequisites: College Placement Test or MAT 002. Students must have satisfied all MAT, ENG 001and RDG 001 remediation requirements prior to starting the course.Description: Applications of finite mathematical models primarily to problems in business and management, Matrix operations, Markov analysis, linear programming and the simplex method, game and decision theory.Calculator Requirement: The TI-83 or TI-84 graphing calculator is required and will be used extensively throughout the course. (The TI-83 Plus and the TI-84 Silver Edition are also acceptable.) However, if the student does not already own one of the listed calculators (s) s/he is encouraged to buy the TI-84 Plus Silver Edition.MAT 118 satisfies SUNY GEN ED-GMAT; NCC GEN EDMATH. This course you have registered for is a REMOTE LEARNING class.??As per the college’s minimum requirements for instruction for remote learning, this course will be delivered using videoconferencing and BlackBoard.??????Therefore, to be able to complete this course, the following are necessary:???1.?????You will need a stable internet connection.??You will need a device that has :??audio and video capabilities???the ability to access the full capabilities of BlackBoard (i.e. upload/download files, take exams, etc)??the ability to access the full capabilities of any courseware required by your instructor. (i.e. Publisher products such as MyMathLab, WileyPlus, Development tools such as Eclipse)??the ability to access the full capabilities of the video conferencing software (i.e. ZOOM)??The college has a limited number of loaner machines.??If you feel you will need to take advantage of this program,?you may apply for a loaner machine through the portal's Launchpad under the "Student Computer Equipment Loan" link.??3.??????You must have the ability to create a single .pdf file, containing multiple pages,?with a device that can be viewed on camera while the .pdfs are being created.?????There are several free apps for the iPhone and Android including, but not limited to,?Notes for IPhone, Genius Scan and Camscanner.???4.??????You must access your NCC email regularly.? All communications will come via your NCC account.? Information will NOT be sent to other accounts.???5.???????You must become familiar with the use of BlackBoard and the various links to get help using BlackBoard.? Once you log into the Portal and follow the NCC Online link, you can access the?NCC Online Student Orientation?or access the?Support Tab?to get more help.???Instructor can choose to use HonorLock testing system for the exams. In this case please include the following statement in the syllabus:This course you have registered for is a REMOTE LEARNING class where assessments (i.e. homework, projects, quizzes, tests, etc)??will be delivered electronically.??This course will be using HONORLOCK, an online proctoring service.??The following systems specifications are needed to complete an assessment on HONORLOCK:???1.?????Operating System:??( Windows 10??OR??MacOSX 10.13 or higher??OR ChromeOS)???2.?????Browser:??????????????????( Google Chrome version 79 or higher)???3.?????Internet Speed:????????( 1.5 Mbps download and 750 Kbps upload)???4.?????Webcam and Microphone?You may want to add the following paragraph for students to understand the NCC Access Program.??This course is a 3 credit course using publisher materials.??Through the NCC Access program you should have been charged $78 for this course.??For more information on this program you can visit ? TOPICS OUTLINEChapter 4. Systems of Linear Equations; Matrices4.1 Review: Systems of Linear Equations in Two Variables-Systems of linear equations in two variables-Discuss possible solutions to a linear system-Graphing systems of linear equations-Solving systems of linear equations by the substitution and elimination methods; emphasize the elimination method-Applications of the systems of linear equations4.2 Systems of Linear Equations and Augmented Matrices-Introduce matrices: coefficient matrix, constant matrix, augmented matrix-Row operations on matrices-Solving systems of linear equations using augmented matrices-Introduce row operations on a graphing calculator4.3 Gauss-Jordan Elimination-Matrices in reduced echelon form -Solving systems of three linear equations in three variables by using the Gauss-Jordan elimination method-Introduce Gauss-Jordan elimination on a graphing calculator-Emphasize mathematical modeling and applications of systems of linear equations4.4 Matrices: Basic Operations-Addition and subtractions of matrices-Product of a number and a matrix-Product of matrices-Product of matrices on a graphing calculator-Applications of the operations on matrices4.5 Inverse of a Square Matrix-Identity matrix for multiplication-Multiplicative inverse of a square matrix-Finding multiplicative inverse of a square matrix on a graphing calculator-Application of matrix inverses: cryptography4.6 Matrix Equations and Systems of Linear Equations-Basic properties of matrices-Solving matrix equations-Using matrix equations to solve systems of linear equations-Applications4.7 Leontief Input-Output Analysis-Input-output problem for two-industry economy model-Two-industry model on a graphing calculator- Input-output problem for three to n -industry economy models-Applications of input-output problemsChapter 5. Linear Inequalities and Linear Programming5.1 Linear Inequalities in Two Variables-Graphing linear inequalities in two variables-Using graphing calculator to solve linear inequalities in two variables-Applications 5.2 Systems of Linear Equations in Two Variables-Solving systems of linear inequalities graphically-Finding the corner points-Definition of bounded and unbounded regions-Applications5.3 Linear Programming in Two Dimension: A Geometric Approach-Constructing a mathematical model for a linear programming problem-General description of linear programming-Geometric method for solving linear programming problems-ApplicationsChapter 6. Linear Programming: The Simplex Method6.1 The Table Method: An Introduction to the Simplex Method-Introducing standard maximization problems in standard form-Slack variables-The table method: introducing basic solutions and basic feasible solutions-Basic and nonbasic variables-The table method: k decision variables6.2 The Simplex Method: Maximization with Problem Constraints of the Form-Initial system-Selecting basic and nonbasic variables for the Simplex method; simplex tableau-Pivot operation-Interpreting the simplex process geometrically-Applications6.3 The Dual Problem: Minimization with Problem Constraints of the Form -Formation of the dual problem-Solution of minimization problems-Applications6.4 Maximization and Minimization with Mixed Problem Constraints-Big M method: Introducing Slack, Surplus, and Artificial variables to form the modified problem-Minimization by the big M method-Larger problems: refinery applicationChapter 9. Markov Chains9.1 Properties of Markov Chains-Introduction: transition probability matrix; initial-state probability matrix-Transition and sate matrices-Powers of transition matrices; using a graphing calculator-Applications9.2 Regular Markov Chains-Stationary matrices-Regular Markov chains-Applications-Graphing calculator approximations9.3 Absorbing Markov Chains-Absorbing states and absorbing chains-Standard forms for absorbing Markov chains-Limiting matrices for absorbing Markov chains-ApplicationsChapter 10. Games and Decisions10.1 Strictly Determined Games-Fundamental principle of game theory; saddle values-Strictly determined matrix games-Nonstrictly determined matrix games-Applications10.2 Mixed Strategy Games-Nonstrictly determined games-Pure and mixed strategies-Expected value of a game-Fundamental Theorem of game theory-Solution to a 2x2 matrix game-Recessive rows and columns-Applications10.3 Linear Programming and 2x2 Games: A Geometric Approach-Invariant optimal strategies-2x2 matrix games and linear programming10.4 Linear Programming and m x n Games: Simplex Method and the Dual Problem-2x3 matrix games and linear programming-Investment analysis-ApplicationsEmphasis of Topics: Suggested topicsfor reduced emphasisSuggested topics for increased emphasis1.2.Routine methods of solving equations and inequalities. The basic concepts of probability are needed for understanding of the Markov chains 1.2Applications in every topic being covered in the course.Writing explanations for conclusions.Learning Outcomes and ObjectivesOBJECTIVES: GeneralTo give the student an understanding of basic concepts and techniques of finite mathematics and quantitative analysis, especially as its used in business and management.Specific?To study matrix algebra, Markov analysis, linear programming techniques, and game theory.?To acquaint students with computers and/or calculators that have matrix-handling capabilities. Computer Software such as DERIVE, MAT 118 software, and calculators such as the TI-83, TI-84, or TI-85 may be incorporated in the course.SUNY General Education Goals & Outcomes1. Draw Inferences from Mathematical ModelsStudents will demonstrate the ability to and draw inferences from mathematical models such as formulas, graphs, tables, and schematics.Outcome1.1 Mathematical InterpretationStudents will interpret variables, parameters, and other specific information within a mathematical model.?1.2 Draw InferencesStudents will draw inferences about the situation being modeled mathematically.?1.3 Verbal InterpretationStudents will verbally interpret the results of their analysis of the mathematical model.?2. Represent Mathematical InformationStudents will demonstrate the ability to represent mathematical information symbolically, visually, numerically and verbally.Outcome2.1 Mathematical InformationStudents will employ the appropriate representation to display the mathematical information.?2.2 Mathematical TerminologyStudents will clearly define variables? draw, scale and label graphs? use correct mathematical terminology and/or language.?3. Employ Quantitative MethodsStudents will demonstrate the ability to employ quantitative methods such as arithmetic, geometry, or linear programming to solve problems.Outcome3.1 Identify Quantitative MethodsStudents will be able to identify a specific numeric, algebraic, or linear programming method(s) needed to solve a problem .?3.2 Applying Quantitative MethodsStudents will apply the method identified, and correctly solve the problem.?4. Check Mathematical Results for ReasonablenessStudents will demonstrate the ability to estimate and check mathematical results for reasonableness.Outcome4.1 EstimationStudents will estimate and justify a mathematical result to a problem.?4.2 ReasonablenessStudents will articulate a justification for the estimate using a clearly defined logical plan.?5. Recognize LimitsStudents will demonstrate the ability to recognize the limits of mathematical methods.Outcome5.1 Real Life ComparisonStudents will describe how the results of the mathematical model may differ from the real-life situation it is modeling.?5.2 Mathematical AssumptionsStudents will articulate the assumptions made in developing a mathematical model. Instructional Methods This course is taught using a variety of instructional methods including lecture, class discussion, and small group work when applicable. Textbook and Materials Required textbook: Finite Mathematics for Business, Economics, Life Sciences and Social Sciences, 14th Ed. by Barnet, Ziegler, and Byleen. Published by PearsonRelevant software is available at World/utilsindex.htmlStudent 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 Methods Provide 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 NumberDateTopic1/2Orientation Section 4.1 Review: Systems of Linear Equations in Two VariablesSection 4.2 Systems of Linear Equations and Augmented Matrices 3/4Section 4.3 Gauss-Jordan EliminationSection 4.4 Matrices: Basic Operations5/6Section 4.5 Inverse of a Square MatrixSection 4.6 Matrix Equations and Systems of Linear EquationsSection 4.7 Leontief Input-Output Analysis7/8ReviewTest #1 on chapter 49/10Section 5.1 Linear Inequalities in Two VariablesSection 5.2 Systems of Linear Inequalities in Two VariablesSection 5.3 Linear Programming in Two Dimensions: A Geometric Approach11/12Section 6.1 The Table Method: An Introduction to the Simplex MethodSection 6.2 The Simplex Method: Maximization with Problem Constraints Of the Form 13/14Section 6.2 The Simplex Method: Maximization with Problem Constraints Of the Form Section 6.3 The Dual Problem: Minimization with Problem Constraints Of the Form 15Section 6.3 Problem: Minimization with Problem Constraints Of the Form Section 6.4 Maximization and Minimization with Mixed Problem Constraints16/17ReviewTest #2 on chapters 5 and 618/19Review probability 8.1 – 8.5 as needed for Markov chainsSection 9.1 Properties of Markov ChainsSection 9.2 Regular Markov Chains20/21Cont. Section 9.2 Regular Markov ChainsSection 9.3 Absorbing Markov Chains22/23Section 10.1 Strictly Determined Games Begin Section 10.2 Mixed-Strategy Games24/25Section 10.2 Mixed-Strategy GamesBegin Section 10.3 Linear Programming and 2 x 2 Games: A Geometric Approach26Section 10.3 Linear Programming and 2 x 2 Games: A Geometric ApproachSection 10.4 Linear Programming and m x n Games: Simplex Method and the Dual Problem27/28Review Test # 3 on chapters 8, 9, and 1029/30Review Cumulative final exam The course outline is approved for Fall 2020, Winter 2021, Spring 2021, Summer 2021 ................
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