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San Jose State University Department of Mathematics Math 70 Finite Mathematics Catalog Description Systems of linear equations and inequalities, matrices, linear programming, set theory, probability theory, applications to business and to social sciences. 3 units. Prerequisite Satisfaction of the ELM requirement. Textbook Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 11th Edition, by Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen, Pearson/Prentice Hall, 2008 References A Student Solutions Manual by Barnett, Ziegler, and Byleen. Course Objectives To learn counting principles, permutations, combinations, probability, probability distribution, expectation, conditional probability, Bayes’ formula, matrices, and their applications, solving systems of linear equations and linear inequalities, linear programming, computing interest, present and future value of annuities. Student Outcomes A student should be able to 1. 2. 3. 4. 5. 6. 7. 8. 9. Use the multiplication principle for counting Compute permutations and combinations of objects with applications Compute probabilities and conditional probabilities Know Bayes’ formula and applications Do operations on matrices Compute the inverse of a matrix Solve linear systems using matrices Solve and graph systems of linear inequalities Find solutions of linear programming problems geometrically 10. Find maximum and minimum of a linear function under constraints using the simplex method 11. Compute simple interest, compound interest and annuities. Outcome Assessment Three (50-minute) exams and a comprehensive final should be given. Numerous homework problems should be assigned and sometimes graded. Quizzes may be given to evaluate continual preparation. Suggested Course Schedule Chapter 3 Sec. 1-4 Simple interest. Compound interest. Future value of an annuity. Present value of annuity. (5 hours). Chapter 4 Sec. 1-6 Systems of linear equations in two variables. Systems of linear equations and augmented matrices. Gauss-Jordon elimination. Basic matrix operations. The inverse of a matrix. Matrix equations and systems of linear equations. (12 hours) Chapter 5 Sec. 1-3 Inequalitics in two variables. Systems of linear inequalities in two variables. Geometric approach to linear programming. (4 hours) Chapter 6 Sec. 1-3 The simplex method and the dual problem. (5 hours) Chapter 7 Sec. 2-4 Sets. Basic counting principles. Permutations and combinations. (4 hours). Chapter 8 Sec. 1-5 Sample spaces, events, and probability. Union, intersection, and complement of events. Odds. Conditional probability, intersection, and independence. Bayes’ formula. Random variable, probability distribution, and expected value. (10 hours) Miscellaneous Exams/quizzes/reviews (5 hours) ------------------------------------------------------------------------------------------------------Total time allocation: 45 hours 2 Please put on your green sheet: STUDENTS WHO INTEND TO USE THIS COURSE TO SATSFY THE MATHEMATICAL REQUIREMENT FOR GENERAL EDUCATION MUST EARN A C OR BETTER. To Instructors: Since a C indicates minimal competence to continue or meet a requirement and C- indicates that the student performance is so low that the course should be repeated, your grading standards should reflect these judgments. Never change a grade from C- to C because the student needs the C. Your chair will not approve such changes and may ask for documentation of clerical errors. Updated by: Marilyn Blockus Mathematics Department, SJSU October, 2007 3