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For Freshmen/Sophomore-level, 1 term or 1 quarter courses in Finite Mathematics in the departments of business, economics, social sciences, or life sciences. This mid-level text covers mathematics of finance, linear algebra, linear programming, probability, and descriptive statistics, with an emphasis on cross-discipline principles and practices. Designed to be student friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.
Table of Contents
I. A LIBRARY OF ELEMENTARY FUNCTIONS.
1. A Beginning Library of Elementary Functions.
Functions. Elementary Functions: Graphs and Transformations. Linear Functions and Straight Lines. Quadratic Functions. Chapter 1 Review. Chapter 1 Group Activities.
2. Additional Elementary Functions.
Polynomial and Rational Functions. Exponential Functions. Logarithmic Functions. Chapter 2 Review. Chapter 2 Group Activities.
II. FINITE MATHEMATICS.
3. Mathematics of Finance.
Simple Interest. Compound Interest. Future Value of an Annuity; Sinking Funds. Present Value of an Annuity; Amortization. Chapter 3 Review. Chapter 3 Group Activities.
4. Systems of Linear Equations; Matrices.
Review: Systems of Linear Equations in Two Variables. Systems of Linear Equations and Augmented Matrices. Gauss-Jordan Elimination. Matrices: Basic Operations. Inverse of a Square Matrix. Matrix Equations and Systems of Linear Equations. Leontief Input-Output Analysis. Chapter 4 Review. Chapter 4 Group Activities.
5. Linear Inequalities and Linear Programming.
Systems of Linear Inequalities in Two Variables. Linear Programming in Two Dimensions--A Geometric Approach. A Geometric Introduction to the Simplex Method. The Simplex Method: Maximization with Problem Constraints of the Form *. The Dual; Minimization with Problem Constraints of the Form *. Maximization and Minimization with Mixed Problem Constraints. Chapter 5 Review. Chapter 5 Group Activities.
6. Probability.
Basic Counting Principles. Permutations and Combinations. Sample Spaces, Events, and Probability. Union, Intersection, and Complement of Events; Odds. Conditional Probability, Intersection, and Independence. Bayes' Formula. Random Variables, Probability Distribution, and Expectation. Chapter 6 Review. Chapter 6 Group Activities.
7. Data Description and Probability Distributions.
Graphing Data. Graphing Quantitative Data. Measures of Central Tendency. Measures of Dispersion. Bernoulli Trials and Binomial Distributions. Normal Distributions. Chapter 7 Review. Chapter 7 Group Activities.
8. Games and Decisions.
Strictly Determined Games. Mixed Strategy Games. Linear Programming and 2 x 2 Games--Geometric Approach. Linear Programming and m x n Games--Simplex Method and the Dual. Chapter 8 Review. Chapter 8 Group Activities.
9. Markov Chains.
Properties of Markov Chains. Regular Markov Chains. Absorbing Markov Chains. Chapter 9 Review. Chapter 9 Group Activities.
APPENDICES.
A. Basic Algebra Review.
Self-Test on Basic Algebra. Sets. Algebra and Real Numbers. Operations on Polynomials. Factoring Polynomials. Operations on Rational Expressions. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Linear Equations and Inequalities in One Variable. Quadratic Equations.
B. Special Topics.
Sequences, Series, and Summation Notation. Arithmetic and Geometric Sequences. The Binomial Theorem.
C. Tables.
Table I: Area Under the Standard Normal Curve. Table II: Basic Geometric Formulas.
Answers. Index. Library of Elementary Functions. Applications Index.