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Finite Mathematics Course Design 2000-2001 Course Information Organization: Division: Course Number: Title: Credits: Developed by: Lecture/Lab Ratio: Transfer Status: EASTERN ARIZONA COLLEGE mathematics Mat 171 Finite Mathematics 4 Ralph Selensky Lecture 4 Lab 0 ASU transfers as Mat 119 for 3 credits, U of A transfers as Mat 114, NAU transfers as Mat 119 Extended Registration Class: no CIP Code: Assessment Mode: Awareness Course: Intensive Writing Course: Prerequisites: 27.0101 Pre/Post Test (25 questions/25 points) No No 1. MAT 154 or higher with a grade of "C" or higher, or appropriate EAC Placement Test Score Educational Value: Goals: This class is recommended for business adminstration major or computer information systems transfer students. 1. Develop students mathematics concepts, techniques and their applications.The index of topics can be applied to the disciplines of business, personal finance, social and life sciences. Description: Math for social, life and management sciences. Topics covered will be of special use to business students. Includes systems of equations, set theory, matrices, probabilty, logic and other subjects. S. T. Tan. Applied Finite Mathematics. Sixth edition. Brooks / Cole Publishing, 1997. scientific calculator Textbooks: Supplies: Finite Mathematics 1 Mat 171 April '01 Competencies and Performance Standards 1. Graph linear functions and write their equations Domain--Cognitive Level--Analysis Importance--Important Difficulty--Medium Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Graph a line. • learner will graph a line. • on assigned activities b. Translate word problems into • learner can translate word • on written exam linear equations. problems into linear equations. • on a two hour cumulative final c. Find the intercepts of a given • learner can find the intercepts of exam linear equation. a given linear equation. 2. Solve linear equations in 2 or 3 variables. Domain--Cognitive Level--Application Importance--Essential Difficulty--Medium Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Solve systems of linear • learner can solve systems of • on assigned activities equations ( 2 or 3 variables) linear equations ( 2 or 3 algebraically. • on written exam variables) algebraically. b. Solve systems of linear • on a two hour cumulative final • learner can solve systems of equations (2 variables) exam linear equations (2 variables) graphically. graphically. c. Solve systems of equations • learner can solve systems of using Gauss-Jordan method (2 or equations using Gauss-Jordan 3 variables). method (2 or 3 variables). d. Perform the following operations • learner can perform the following with matricies: addition, operations with matricies: subtraction, and multiplication. addition, subtraction, and e. Calculate the inverse of a matrix. multiplication. f. Solve systems of equation by • learner can calculate the inverse using the inverse matrix. of a matrix. • learner can solve systems of equations by using the inverse matrix. 3. Solve linear programming problems graphically. Domain--Cognitive Level--Application Importance--Essential Difficulty--Medium Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Graph systems of inequalities in • learner can graph systems of • on assigned activities two variables. inequalities in two variables. • on written exam b. Determine the feasible region and • learner can determine the feasible • on a two hour cumulative exam its verticies. region and its verticies. c. Solve linear programs graphically • learner can solve linear programs by using the verticies of the graphically by using the verticies feasible region. of the feasible region. Finite Mathematics 2 Mat 171 April '01 4. Solve linear programming problems algebraically. Domain--Cognitive Level--Synthesis Importance--Essential Difficulty--High Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Maximize a linear program with • learner can maximize a linear • on assigned activities the use of the Simplex method. program with the use of the • on written exam b. Minimize a linear program with Simplex method. the use of the Simplex mehod. • on a two hour cumulative final • learner can minimize a linear exam c. Maximize or minimize non program with the use of the standard linear program using Simplex mehod. the Simplex method. • learner can maximize or minimize non standard linear program using the Simplex method. 5. Calculate the mathematics of finance. Domain--Cognitive Level--Application Importance--Essential Difficulty--Medium Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Calculate compound interest. • learner can calculate compound • on assigned activities b. Calculate annunities. interest. • on written exam c. Produce an amortization table. • learner can calculate annunities. • on a two hour cumulative final d. Produce a sinking fund chart. • learner can produce an exam amortization table. • learner can produce a sinking fund chart. • Finite Mathematics 3 Mat 171 April '01 6. Understand sets and set operations. Domain--Cognitive Level--Synthesis Importance--Essential Difficulty--High Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Demonstrate the correct use of • learner demonstrates the correct • on assigned activities set notation and terminology use of set notation and within given sets. • on written exam terminology within given sets. b. Draw venn diagrams of given • on a two hour cumulative final • learner can draw venn diagrams sets. exam of given sets. c. Determine the union, • learner can determine the union, intersection, and/or complement intersection, and/or complement of given sets. of given sets. d. Determine the number of • learner can determine the number elements in a finite set. of elements in a finite set. e. Use the multiplication principle • learner uses the multiplication to determine the number of ways principle to determine the of performing several tasks in number of ways of performing succession. several tasks in succession. f. Calculate the number of • learner can calculate the number combinations of n distinct of combinations of n distinct objects taken r at a time in a objects taken r at a time in a given set. given set. g. Calculate the number of • learner can calculate the number permutations of n distinct of permutations of n distinct objects taken r at a time in a objects taken r at a time in a given set. given set. 7. Calculate probabilities. Domain--Cognitive Level--Application Importance--Essential Difficulty--High Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Define experiment, event, sample • Define experiment, event, sample • on assigned activities space, and probability. space, and probability. • on written exam b. Compute the probability of an • Compute the probability of an event. • on a two hour cumulative final event. exam c. Recognize mutually exclusive • Recognize mutually exclusive events and independent events. events and independent events. d. Compute the probability of • Compute the probability of combined events. combined events. e. Use the rules of probability to • Use the rules of probability to solve more advanced probability solve more advanced probability problems. problems. Finite Mathematics 4 Mat 171 April '01 8. Investigate logic. Domain--Cognitive Level--Analysis Importance--Essential Difficulty--Medium Criteria--Criteria - Performance will Conditions--Competence will be Learning Objectives: be satisfactory when: demonstrated: a. Define the logical connectives: • learner define use of propositions • on assigned activities conjunction, disjunction, exclusive disjunction, negation, • learner define use of connective • on written exam conditional, and biconditonial. • learner calculate truth tables • on a two hour cumulative final b. Construct truth tables for the exam • learner define use of conditional logical connectives. connective c. Define the order of operation of • learner define use of the logical connectives. biconditional connective d. Apply the laws of logic. • learner use laws of logic e. Determine the validity of an • learner illustrate arguments argument. f. Represent logical statements with networks. Types of Instruction Classroom Presentation Grading Policy Evaluation Methods: Each instructor has th flexability to develop evaluative procedures within the following parameters. 1. Written exams must represent at least 60 % of the final grade. 2. Final exam represent at least 20 % of the final grade. 3. The post test is to be embedded in the final exam and must represent at least 10 % of the final grade. 4. Other activities may represent at most 20 % of the final grade. Grading Scale: Grade A B C D F Requirement 90 - 100% 80 - 89% 70 - 79% 60 - 69% below 60% Finite Mathematics 5 Mat 171 April '01 Learning Plans Learning Plan 1-- Finite Math Overview: Finite Math teaches mathematical concepts, techniques and their application. Their application can be applied to the discipline of business, personal finance, social and life science. 1. 2. 3. 4. 5. 6. 7. 8. Graph linear functions and write their equations Solve linear equations in 2 or 3 variables. Solve linear programming problems graphically. Solve linear programming problems algebraically. Calculate the mathematics of finance. Understand sets and set operations. Calculate probabilities. Investigate logic. Competency: Competency: Competency: Competency: Competency: Competency: Competency: Competency: Learning Activities: _____1. listen to a lecture and take notes _____2. participate in a class discussion _____3. read the assigned section in the text _____4. demonstrate a procedure for others _____5. work on assigned problems individually _____6. collaborate with others on assigned problems _____7. correct mistakes on homework and exams Performance Assessment Activities: _____1. complete assigned activities _____2. complete written exam _____3. complete a final exam Finite Mathematics 6