  
Description  
 Set theory, basic combinatorial analysis, introduction to probability, linear equations and inequalities, introduction to linear programming and the simplex method, introduction to matrix algebra with applications, Markov chains, game theory and mathematics of finance.


Course Objectives  
 The student will be able to:
 Determine the equation of a line, graph linear equations, and solve applications problems in business, science, and social science using linear models.
 Solve systems of linear equations graphically, using algebraic methods, and with matrices; solve applications problems in business, science, and social science using these methods.
 Understand matrix arithmetic and matrix algebra, and use it to solve applications problems in business, science, and social science.
 Model linear programming problems by constructing an appropriate linear program, and solve linear programming problems using both graphical methods and the simplex algorithm.
 Compute compound and simple interest, future and present value of an annuity and payments on a loan, and use the equations of finance to solve applications problems.
 Solve problems using sets and basic counting principles.
 Compute probabilities, including conditional probability, probability of independent events, using Baye's formula, and for binomial experiments.
 Solve problems using Markov Chains.
 Solve problems in game theory.
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Interpret mathematical solutions.

Special Facilities and/or Equipment  
  Graphing Calculator
 When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Determine the equation of a line, graph linear equations, and solve applications problems in business, science, and social science using linear models.
 Coordinate systems and graphs
 Slopes and equations of straight lines
 Linear modeling with one line
 Solve systems of linear equations graphically, using algebraic methods, and with matrices; solve applications problems in business, science, and social science using these methods.
 Graphing method
 The substitution method
 The elimination method
 GaussJordan reduction
 Understand matrix arithmetic and matrix algebra, and use it to solve applications problems in business, science, and social science.
 Matrix addition
 Matrix multiplication
 Matrix algebra
 Inverse of a matrix
 Model linear programming problems by constructing an appropriate linear program, and solve linear programming problems using both graphical methods and the simplex algorithm.
 Linear inequalities in two variables
 The linear program for a linear programming problem
 Graphical methods
 The Simplex Algorithm
 Nonstandard and minimization problems
 Duality
 Applications to business, science, and social science
 Compute compound and simple interest, future and present value of an annuity, and payments on a loan; use the equations of finance to solve applications problems.
 Interestīsimple and compound
 Annuities
 Amortization of loans
 Applications involving the equations of finance
 Solve problems using sets and basic counting principles.
 Sets and Venn diagrams
 The multiplication principle
 Permutations and combinations
 Application problems using sets and basic counting principles
 Compute probabilities, including conditional probability, of independent events, using Baye's formula, and for binomial experiments.
 Sample spaces
 Calculating probabilities of events
 Discrete random variables and expected value
 Conditional probability and independence
 Baye's theorem
 Binomial experiments
 Solve problems using Markov Chains.
 Transition matrix
 State vectors
 Regular Markov chains
 Application problems using Markov chains
 Solve problems in game theory.
 Games and strategies
 Mixed strategies
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Application problems from business, economics, social science, and science
 Proper notation
 Interpret mathematical solutions.
 Explain the significance of solutions to application problems.

Methods of Evaluation  
  Written homework
 Quizzes and tests
 Proctored comprehensive final examination

Representative Text(s)  
 Waner S., Constenoble S. Finite Mathematics. 6th ed. Brooks/Cole Publishing Company, 2013.

Disciplines  
 Mathematics


Method of Instruction  
 Lecture, Discussion, Cooperative learning exercises.


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: Homework problems covering subject matter from text and related material ranging from 30  60 problems per week.
Students will need to employ critical thinking in order to complete assignments. Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB. Worksheets: Problems and activities covering the subject matter.Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
