Finite Mathematics

Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. Raymond N. Greenwell earned a B.A. in Mathematics and Physics from the University of San Diego, and an M.S. in Statistics, an M.S. in AppliedMathematics, and a Ph.D. in Applied Mathematics from Michigan State University, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for four years, he moved to Hofstra University in1983, where he currently is Professor of Mathematics. Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He is currently (2002-2005) governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club¿s Inner City Outings program. Nathan P. Ritchey earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is currently a Professor of Mathematics and Chair of the Department of Mathematics and Statistics at Youngstown State University. He has published articles in economics, honors education, medicine, mathematics, operations research, and student recruitment. Nate is a Consultant/Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations. In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's "People Who Make a Difference Award," the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program. A father of four children, Nate enthusiastically coaches soccer and softball. He also loves music, playing several instruments, and is a tenor in the Shenango Valley Chorale. More information about Nate Ritchey can be found at: http://www.as.ysu.edu/~nate/.

R. Algebra Reference.


Polynomials.



Factoring.



Rational Expressions.



Equations.



Inequalities.



Exponents.



Radicals.



1. Linear Functions.


Slopes and Equations of Lines.



Linear Functions and Applications.



The Least Squares Line.



2. Systems of Linear Equations and Matrices.


Solution of Linear Systems by the Echelon Method.



Solution of Linear Systems by the Gauss-Jordan Method.



Addition and Subtraction of Matrices.



Multiplication of Matrices.



Matrix Inverses.



Input-Output Models.



3. Linear Programming: The Graphical Method.


Graphing Linear Inequalities.



Solving Linear Programming Problems Graphically.



Applications of Linear Programming.



4. Linear Programming: The Simplex Method.


Slack Variables and the Pivot.



Maximization Problems.



Minimization Problems; Duality.



Nonstandard Problems.



5. Mathematics of Finance.


Simple and Compound Interest.



Future Value of an Annuity.



Present Value of an Annuity; Amortization.



6. Logic.


Statements.



Truth Tables and Equivalent Statements.



The Conditional and Circuits.



More on the Conditional.



Analyzing Arguments and Proofs.



Analyzing Arguments with Quantifiers.



7. Sets and Probability.


Sets.



Applications of Venn Diagrams.



Introduction to Probability.



Basic Concepts of Probability.



Conditional Probability; Independent Events.



Bayes' Theorem.



8. Counting Principles; Further Probability Topics.


The Multiplication Principle; Permutations.



Combinations.



Probability Applications of Counting Principles.



Binomial Probability.



Probability Distributions; Expected Value.



9. Statistics.


Frequency Distributions; Measures of Central Tendency.



Measures of Variation.



The Normal Distribution.



Normal Approximation to the Binomial Distribution.



10. Markov Chains.


Basic Properties of Markov Chains.



Regular Markov Chains.



Absorbing Markov Chains.



11. Game Theory.


Strictly Determined Games.



Mixed Strategies.



Game Theory and Linear Programming



Tables


Table 1: Area Under a Normal Curve