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Credit- Degree applicable
Effective Quarter: Fall 2020

##### 5 Unit(s)

 (See general education pages for the requirement this course meets.)Requisites: Prerequisite: Intermediate Algebra (MATH 109, MATH 114 or MATH 130) or equivalent. Advisory: EWRT 211 and READ 211, or ESL 272 and 273. Hours: Lec Hrs: 60.00 Out of Class Hrs: 120.00 Total Student Learning Hrs: 180.00Description: Application of linear equations, sets, matrices, linear programming, mathematics of finance and probability to real-life problems. Emphasis on the understanding of the modeling process, and how mathematics is used in real-world applications. Student Learning Outcome Statements (SLO) • Student Learning Outcome: Identify, evaluate, and utilize appropriate linear, probability, and optimization models and communicate results. • Student Learning Outcome: Compare, evaluate, judge, make informed decisions, and communicate results about various financial opportunities by applying the mathematical concepts and principles of the time value of money.

II. Course Objectives

 A. Develop, throughout the course as applicable, systematic problem solving methods
 B. Investigate linear and exponential models
 C. Investigate methods of solving linear systems using matrices; write a system of linear equations to solve applied problems; solve a system of linear equations using Gauss-Jordan elimination and interpret the result; find the inverse of a square matrix and use the inverse to solve a system of linear equations.
 D. Formulate and solve linear programming models in at least three variables.
 E. Develop the concepts of the time value of money, and compute compound interest, future and present values and periodic payments. Use these concepts to solve applied problems in finance including simple interest, annuities, sinking funds, and amortization.
 F. Examine sets, counting techniques and their applications. Find unions, intersections and complements of sets. Use Venn diagrams to solve problems.
 G. Create probability models and investigate their applications. Determine the probability of a specified event and find the conditional probability of an event.
 H. Investigate stochastic processes and Markov chains
 I. Utilize technology as an aid in exploring, analyzing, understanding and solving problems
 J. Investigate, throughout the course as applicable, how mathematics is used as a human activity around the world.

III. Essential Student Materials

 Graphing calculator

IV. Essential College Facilities

 Computer Lab (optional)

V. Expanded Description: Content and Form

 A. Develop, throughout the course as applicable, systematic problem solving methods
 1 devise a strategy or plan
 2 organize information, including identification and definition of known and unknown quantities
 3 translate into mathematical format
 4 apply mathematical tools to formulate a solution
 5 clearly communicate the solution
 a. state the solution
 b. interpret the results in the context of the problem
 B. Investigate linear and exponential models
 1 produce linear graphs
 a. review Cartesian coordinates
 b. graph linear equations and linear inequalities
 c. investigate properties of parallel and perpendicular lines
 2 construct linear equations
 3 apply the linear equations and linear systems to solve problems involving
 a. fixed and variable costs
 b. cost and revenue functions and break-even analysis
 c. supply and demand functions and equilibrium point
 d. comparison pricing models
 4 Define properties and characteristics of exponential functions
 a. Properties of the graphs of exponential functions
 b. Solve applied problems involving exponential models
 5 Define properties and characteristics of logarithmic functions
 a. Define the logarithmic function as the inverse of the exponential function
 b. Solve exponential equations using logarithms
 c. Solve applied problems involving logarithmic models
 C. Investigate methods of solving linear systems using matrices; write a system of linear equations to solve applied problems; solve a system of linear equations using Gauss-Jordan elimination and interpret the result; find the inverse of a square matrix and use the inverse to solve a system of linear equations.
 1 define matrix
 a. entries and size of a matrix
 b. row and column matrices
 c. augmented matrix
 d. representation of data in matrix form
 2 perform matrix operations
 b. matrix multiplication
 3 apply Gauss-Jordan method to solve linear systems
 a. define elementary row operations
 b. perform operations on augmented matrices to obtain reduced row echelon form
 c. write solutions to linear systems
 1 identify consistent and inconsistent systems
 2 differentiate between independent and dependent consistent systems
 4 define identity matrix and find inverse matrices
 a. calculate inverse of a non-singular matrix using row operations
 b. write system of linear equations in matrix form
 c. use inverse matrix to solve systems that have unique solutions
 5 solve application problems involving consistent and inconsistent systems
 a. application problems resulting in no solution or many solutions
 b. setting up models requiring matrix multiplication in mixture problems such as
 1 batching process, product allocation and nutritional models
 2 cryptography
 3 Leontief input-output economic models
 D. Formulate and solve linear programming models in at least three variables.
 1 set up a linear programming optimization model
 a. distinguish between minimization and maximization problems
 b. formulate objective function
 c. formulate constraints
 2 solve linear programs using geometric approach
 a. draw feasibility region
 b. identify critical points
 c. determine optimal solution
 d. interpret solution
 3 solve linear programs using the simplex method
 a. construct initial simplex tableau by adding slack variables
 b. perform pivot operations to obtain maximum solution
 c. use the dual problem to solve minimization problems
 d. interpret solution
 E. Develop the concepts of the time value of money, and compute compound interest, future and present values and periodic payments. Use these concepts to solve applied problems in finance including simple interest, annuities, sinking funds, and amortization.
 1 compare and calculate simple and compound interest
 a. effective interest rate
 b. present and future values for lump sums
 2 develop compound interest models for annuities
 a. present value of an annuity; amortization
 b. future value of an annuity; sinking funds
 3 apply financial models to real world problems such as
 a. mortgages and loans
 b. savings plans
 c. leasing
 d. capital expenditures
 e. bonds
 F. Examine sets, counting techniques and their applications. Find unions, intersections and complements of sets. Use Venn diagrams to solve problems.
 1 investigate sets and their properties
 a. subsets
 b. complements
 c. unions and intersections
 d. Venn Diagrams
 e. De Morgan's Laws
 2 utilize counting techniques
 a. fundamental principles of counting
 1 multiplication rule
 b. permutations
 1 permutations involving distinct elements
 2 circular permutations
 3 permutations involving indistinguishable elements
 c. combinations
 1 combinations involving a single set
 2 combinations involving several sets
 3 apply counting techniques to solve problems such as
 a. consumer surveys, investing, student reading habits
 b. book displays, seating, pin numbers, coin tosses, telephone numbers, radio station call letters, license plates
 c. committee selection, menu selection, card hands, bus or taxi routing, quality control, lottery
 G. Create probability models and investigate their applications. Determine the probability of a specified event and find the conditional probability of an event.
 1 define probability as a non-deterministic (stochastic) model
 a. construct sample spaces
 b. assign probabilities to outcomes in sample space.
 2 determine probability of events
 a. equally likely events
 b. mutually exclusive events
 c. complementary events
 d. compound events
 1 using tree diagrams
 2 using counting techniques
 3 explore conditional probability and independent events
 a. tree diagrams
 b. contingency tables
 c. Bayes' Formula
 4 use binomial probability model to solve problems involving Bernoulli trials
 5 calculate and interpret expected value
 6 apply probability techniques to solve problems such as
 a. birthday problem
 b. poker hands and other gambling problems
 c. quality control
 d. sweepstakes
 e. opinion polls
 f. reliability of medical tests
 g. batting averages
 H. Investigate stochastic processes and Markov chains
 1 define a Markov chain
 a. states and iterations
 b. transition probabilities
 c. multiple iterations
 d. initial state vector
 2 define regular Markov chains
 a. equilibrium state as a long term iteration
 b. fixed probability vector
 3 define absorbing Markov chains
 a. canonical form
 b. expected number of iterations until absorption
 4 apply Markov chains to solve problems such as
 a. consumer buying trends both short term and long term
 b. political party preferences
 c. market share
 d. gambler's ruin problem
 e. genetics
 f. insurance risks
 I. Utilize technology as an aid in exploring, analyzing, understanding and solving problems
 1 Use graphing calculators, spreadsheets or desktop applications to graph straight lines in solving problems involving
 a. slopes
 b. equations of lines
 c. linear programming using geometrical approach
 2 Use graphing calculators, spreadsheets or desktop applications to manipulate matrices in solving problems involving
 a. Gauss-Jordan method in system of equations
 b. Matrix inverse method in system of equations
 c. Simplex method in linear programming
 d. Markov chains
 e. Game theory
 3 Use graphing calculators, spreadsheets or desktop applications for mathematics of finance in solving problems involving
 a. compound interest
 b. annuities and sinking funds
 c. present values of annuities and installment payments
 4 Use graphing calculators, spreadsheets or desktop applications for computing factorials, combinations, and permutations in problems involving
 a. counting techniques
 b. probability
 c. binomial distribution
 J. Investigate, throughout the course as applicable, how mathematics is used as a human activity around the world.
 1 the use and development of mathematical concepts throughout history. Some possibilities are:
 a. investigate the number e in continuous compounding
 b. research Dr. George Dantzig's contribution in the development of linear programming and computers
 c. research Indian scientist Narendra Karmakar's contribution to linear programming
 d. apply Wassily Leontief's Nobel prize winning economic models
 e. explain the Law of 72 in continuous compounding as used by various cultures as those of Egypt, India, the Arabic cultures, China and Europe
 f. European and Chinese origins of Pascal's Triangle
 2 applications that are of historical and/or contemporary interest. Some possibilities are:
 a. utilize mathematical modeling to predict real-life occurrences in fields such as physical sciences, social science, astronomy, management, and economics
 b. study the recent use of matrices as a natural way to organize data in the fields of management, natural science and social science, as well as, to solve problems that arise in these fields, from inventory control to models of a nation's economy
 c. investigate the use of probability in areas as diverse as gambling, medical testing, industrial testing, insurance policy analysis, weather forecasting and financial planning.
 d. employ expected value (mathematical expectation) in its widespread application to the decision making process in business, economics and operations research
 e. analyze the conflict situations and their corresponding strategies for decision making the relatively recent branch of mathematics called game theory See Multicultural Handout for developmental sequence for additional activities

VI. Assignments

 A. Reading of text explanations and examples
 B. Written assignments which may include
 1 Problem solving exercises from the text that include both computational and concept based questions
 2 Problems requiring written explanations of key concepts, analysis of problem solving strategies and use of mathematical vocabulary
 3 Projects such as labs or "big problems" that require research or data collection
 4 Problem journals
 5 Portfolios
 6 Assignments using supplemental software on a computer
 C. Class participation which may include
 1 Collaborative activities
 2 Oral presentations

VII. Methods of Instruction

 Lecture and visual aids Discussion and problem solving performed in class Quiz and examination review performed in class Homework and extended projects Collaborative learning and small group exercises Collaborative projects

VIII. Methods of Evaluating Objectives

 A. A minimum of three one hour exams or two exams and a project. The exams will be composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class.
 B. Periodic quizzes and/or problem solving assignments from the text will be evaluated for accuracy and completion in order to asses student's comprehension of material covered in lecture and to provide feedback to students on their progress. Questions may also require the student to communicate ideas and conclusions in short essay format
 C. Other written assessments (optional) will be evaluated for accuracy, completeness and proper used of techniques and methods discussed in class. Assessments may also require the student to communicate ideas and conclusions in short essay format.
 D. Two hour comprehensive final examination composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format.

IX. Texts and Supporting References

 A. Examples of Primary Texts and References
 1 Barnett, Ziegler, and Byleen, "Finite Mathematics for Business, Economics, Life Sciences and Social Sciences", 13th edition. Prentice Hall, 2015
 2 Sekhon, Rupinder and Bloom, Roberta, "Applied Finite Mathematics", Third Edition. 2016.
 3 Sullivan, "Finite Mathematics, An Applied Approach", 11th ed. Wiley, 2011
 B. Examples of Supporting Texts and References
 1 Stefan WaStefan Warner and Steven R. Costenoble (March 2000) "Finite Mathematics Online Resources". http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tcfinitep.html
 2 GameTheory.Net (May 2004) "A Resource for Educators and Students of Game Theory". http://www.gametheory.net
 3 Eric W. Weisstein. (2004) "Linear Programming." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LinearProgramming.html
 4 David K Levine, Department of Economics, UCLA , "Zero Sum Game Solver" http://levine.sscnet.ucla.edu/Games/zerosum.htm
 5 Math Medics, L.L.C. (1999-2004) S.O.S. "Mathematics" (Search for relevant topics such as Matrices, Linear programming, Markov Chains) http://www.sosmath.com
 6 Drexel University (1999-2004) "The Math Forum" http://mathforum.org/
 7 Narasimhan, Revathi, (2003), Kean University, "Math Online: Using Excel in Finite Math and Business Calculus" http://www.kean.edu/~rnarasim/excel/excel.html
 8 Eric W. Weisstein. (2004) "Pascal's Triangle." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PascalsTriangle.html
 9 Laura Ackerman Smoller, Associate Professor of History, Adjunct Associate Professor of Medical Humanities, University of Arkansas at Little Rock, "Applications: Web Based Precalculus" http://www.ualr.edu/~lasmoller/pascalstriangle.html