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# FINITE MATHEMATICS

COURSE DESCRIPTION: This course is for students interested in business, social and managerial sciences. Topics include introduction to basic concepts and techniques of those areas in mathematics which deal with finite sets. Topics include linear programming, probability theory, matrix manipulations, Markov Chains, game theory and optimization problems.

OBJECTIVES: Upon successful completion of this course, students should be able to:
•Perform matrix manipulations, including: addition, subtraction, and multiplication (both scalar and matrix);
•Write matrix inverses;
•Solve matrix equations, write algebraic equations in matrix form, and switch between algebraic and matrix forms; solve the matrix equation
AX = B by Gaussian elimination;
•Solve linear programming problems by graphing and the simplex algorithm;
•Model stochastic processes; determine if a transition matrix is regular; calculate and interpret the equilibrium vector;
•Do the basics of 2-person zero-sum games, including: payoffs, saddle points, dominance, and strategy for 2*2, 2*n, and m*2 games.

ATTENDANCE: You will start with 300 points for attendance and punctuality; 200 regular points and 100 bonus points. Late arrivals or early departures cost 1 point per minute (up to 50 on a given day) and absences cost 50 points each. Dropping off books and immediately leaving, or leaving as soon as class has begun, does NOT count as an arrival; you are present when you are seated and ready to work. The foregoing deductions apply regardless of the reasons for your lateness or absence (that’s why I offer bonus points).

Course material will be posted on line using the Desire2Learn course management system; this can include, but is not limited to, written and video material as well as assigned problems. You are required to log on to D2L daily and participate in course activities; failure to do adequate work in any module will count as an absence. See me promptly if you do not understand the material.

As per the college's attendance policy, I reserve the prerogative to withdraw or issue a failing grade to any student who misses more than the equivalent of one week of classes. If you cannot attend this class regularly, you should drop it and sign up for a section that fits into your schedule.

HOMEWORK: You will receive homework assignments throughout the semester. I will not grade them; however, they are a tool to ensure that you can do the work covered in class, so do not skip this step. I will review homework problems as necessary. See me promptly if you do not understand the material.

EXAMINATIONS: There will be three unit examinations and a two-day final examination. The final examination is cumulative and mandatory for all students.

If you have a conflict with a scheduled exam date, you may arrange to take your exam on an earlier date if and only if you give me at least 24 hours’ notice. Make-up exams are given solely at my discretion and only for extenuating circumstances beyond your control; they will be different and slightly more difficult than those given, and will cost points. Documentation must be provided in either case.

FINAL GRADES: Grading will depend solely on your own performance in this class. The breakdown is as follows:

 Attendance – Regular 200 Unit Examinations (3 at 400 points each) 1,200 Final Examination 600 Regular Points 2,000 Attendance – Bonus 100 Total Available Points 2,100

 Points Letter Grade At least 1,800 A At least 1,700 B+ At least 1,600 B At least 1,500 C+ At least 1,400 C At least 1,300 D+ At least 1,200 D Below 1,200 F

You are guaranteed the minimum grade for which you qualify.

## OTHER INFORMATION

REQUIRED MATERIALS: You will need to bring #2 pencils (inexpensive mechanical ones are best), a notebook, graph paper as necessary, your textbook, and a calculator (see next item).

CALCULATORS: Graphing calculators will be required. You may use the TI-80, TI-81, TI-82, TI-83, TI-84, TI-85, TI-86, or the “Plus” versions of these models. The TI-84 is my first preference, followed by the TI-86. These are the only models I will support. You may not use cell phones or any device with a computer algebra system. It is up to you to obtain my approval before relying on a device other than those I recommend. If you fail to bring an approved calculator to an examination, you will be out of luck.

DISRUPTIONS: Pagers and cell phones are to be turned off at all times. If anyone wishes to reach you in an emergency, he or she should call the Mathematics Department at 851-6737. If there is no answer, he or she should call 851-6571. The staff at either office will get a message to you quickly. If you need to constantly text or make calls, take another class.

Disruptive behavior will result in a warning, a yellow card, and a loss of 25 points. A second offense will be followed by removal from class as per the student handbook, a red card, and a loss of 50 points. Anyone earning two red cards in a semester will be referred to the Dean of Students for disciplinary action.

ETHICAL BEHAVIOR: As in other courses, cheating, plagiarism, and other forms of academic dishonesty will not be tolerated. Any such acts will be dealt with swiftly and appropriately.

DISABILITIES: If you are a student who has a disability and need reasonable accommodations, then please speak to me privately outside of class. If you have specific questions about obtaining these services, you can contact a special-needs counselor. For assistance, call the Counseling Center at 851-6250. If you do not submit documentation identifying your needs to me, then you are not eligible for these accommodations. I need advance notice to make appropriate arrangements, especially for examinations.

PROBLEMS: Please do not hesitate to ask questions or to discuss problems with me. Make an appointment with me as soon as you feel the need to do so. The time to be concerned about your performance and course grade starts at the beginning of this course, not the end!

Good luck to you in your studies!

## COURSE SYLLABUS

TEXTS: [R] Finite Mathematics, Sixth Edition; Rolf, Howard L.; Thomson Learning, Inc.; ©2005.

[L] Quantitative Approaches to Management, Eighth Edition, Chapters 11-12; Levin, Richard I., David S. Rubin, Joel P. Stinson, and Everette S. Gardner, Jr.; McGraw-Hill, Incorporated; ©1992.

SUPPLEMENT: [C] Linear Programming, Chapter 2; Chvátal, Vašek; W. H. Freeman and Company; ©1983. I will provide this supplement.

 Module Dates Class Date Section(s) Topic(s) 1 27 Jan- 9 Feb 27 Jan [R] 2.1-2.4 Systems of Linear Equations; The Gauss-Jordan Method and Elementary Matrix Operations 2 27 Jan- 9 Feb 3 Feb [R] 2.5-2.6 Matrix Multiplication; Matrix Inverses 3 Feb- 9 Feb Unit Examination #1 Review (On Line) 10 Feb Unit Examination #1 (Covers Modules 1-2) 3 11 Feb- 23 Feb 17 Feb [R] 3.1-3.2 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 4 18 Feb- 2 Mar 24 Feb [R] 3.3, [C] Solving Linear Programming Problems Graphically and Algebraically 5 25 Feb- 9 Mar 3 Mar [R] 4.1-4.4 The Simplex Method: Standard Maximization Problems; Duality; Mixed Constraints 3 Mar- 9 Mar Unit Examination #2 Review (On Line) 10 Mar Unit Examination #2 (Covers Modules 3-5) 6 11 Mar- 23 Mar 17 Mar [R] 7.1-7.5 Basic Probability; Conditional Probability and Independent Events 7 18 Mar- 30 Mar 24 Mar [R] 7.6-7.7 Bayes’ Rule; Markov Chains 24 Mar- 30 Mar Unit Examination #3 Review (On Line) 31 Mar Unit Examination #3 (Covers Modules 6-7) 8 1 Apr- 20 Apr 14 Apr [R] 9.1-9.2 Two-Person Zero-Sum Games: Pure and Mixed Strategies 9 15 Apr- 27 Apr 21 Apr [L] 11.1-11.3, 12.1-12.2 Transportation Problems; PERT/CPM 10 22 Apr- 4 May 28 Apr [L] 12.5-12.8 Maximal Flow and Minimum Spanning Tree; Shortest-Route Problems; Dynamic Programming 29 Apr- 11 May 5 May Final Examination Review (In Class and On Line) 12 May Final Examination – Day 1 14 May Final Examination – Day 2