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Finite Mathematics is a comprehensive yet flexible text for students majoring in business, economics, life science, or social sciences. Its varied and relevant applications are designed to pique and hold student interest, and the depth of coverage provides a solid foundation for students’ future coursework and careers. Built-in, optional instruction for the latest technology—graphing calculators, spreadsheets, and WolframAlpha—gives instructors flexibility in deciding how to integrate these tools into their course. Thousands of well-crafted exercises–a hallmark of this text–are available in print and online in MyLab™ Math to enable a wide range of practice in skills, applications, concepts, and technology.
In the 12th Edition, new co-author Steve Hair (Pennsylvania State University) brings a fresh eye to the content and MyLab™ Math course based on his experience in the classroom. In addition to its updated applications, exercises, and technology coverage, the revision infuses modern topics such as health statistics and content revisions based on user feedback. The authors relied on aggregated student usage and performance data from MyLab™ Math to improve the quality and quantity of exercises.
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Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming. He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.
David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an emeritus professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.
Martha Siegel holds a BA from Russell Sage College, attended Rensselaer Polytechnic Institute as a special student, and received her PhD at the University of Rochester. From 1966 until 1971 she taught at Goucher University in Baltimore. Since 1971 she has been a professor at Towson State University, also in Maryland. Professor Siegel has been on the writing team of this book since the fifth edition and is also the co-author of a precalculus reform book.
Steven Hair holds a BS from Virginia Tech and a PhD from Penn State University. He is currently a lecturer and course coordinator at Penn State, where he develops traditional and digital content for finite math and precalculus courses. In his free time, Steven enjoys spending time with his family, playing the saxophone, and fly fishing.
Preface
1. Linear Equations and Straight Lines
1.1 Coordinate Systems and Graphs
1.2 The Slope of a Straight Line
1.3 The Intersection Point of a Pair of Lines
1.4 The Method of Least Squares
Chapter Project: Break-Even Analysis
2. Matrices
2.1 Systems of Linear Equations with Unique Solutions
2.2 General Systems of Linear Equations
2.3 Arithmetic Operations on Matrices
2.4 The Inverse of a Matrix
2.5 The Gauss-Jordan Method for Calculating Inverses
2.6 Input-Output Analysis
Chapter Project: Population Dynamics
3. Linear Programming, A Geometric Approach
3.1 Linear Inequalities
3.2 A Linear Programming Problem
3.3 Fundamental Theorem of Linear Programming
3.4 Linear Programming
Chapter Project: Shadow Prices
4. The Simplex Method
4.1 Slack Variables and the Simplex Tableau
4.2 The Simplex Method I: Maximum Problems
4.3 The Simplex Method II: Nonstandard and Minimum Problems
4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems
4.5 Duality
Chapter Project: Shadow Prices
5. Sets and Counting
5.1 Sets
5.2 A Fundamental Principle of Counting
5.3 Venn Diagrams and Counting
5.4 The Multiplication Principle
5.5 Permutations and Combinations
5.6 Further Counting Techniques
5.7 The Binomial Theorem
5.8 Multinomial Coefficients and Partitions
Chapter Project: Pascal's Triangle
6. Probability
6.1 Experiments, Outcomes, Sample Spaces, and Events
6.2 Assignment of Probabilities
6.3 Calculating Probabilities of Events
6.4 Conditional Probability and Independence
6.5 Tree Diagrams
6.6 Bayes' Theorem, Natural Frequencies
6.7 Simulation
Chapter Project: Two Paradoxes
7. Probability and Statistics
7.1 Visual Representations of Data
7.2 Frequency and Probability Distributions
7.3 Binomial Trials
7.4 The Mean
7.5 The Variance and Standard Deviation
7.6 The Normal Distribution
7.7 Normal Approximation to the Binomial Distribution
Chapter Project: An Unexpected Expected Value
8. Markov Processes
8.1 The Transition Matrix
8.2 Regular Stochastic Matrices
8.3 Absorbing Stochastic Matrices
Chapter Project: Doubly Stochastic Matrices
9. The Theory of Games
9.1 Games and Strategies
9.2 Mixed Strategies
9.3 Determining Optimal Mixed Strategies
Chapter Project: Simulating The Outcomes of Mixed-Strategy Games
10. The Mathematics of Finance
10.1 Interest
10.2 Annuities
10.3 Amortization of Loans
10.4 Personal Financial Decisions
10.5 A Unifying Equation
Chapter Project: Two Items of Interest
11. Logic
11.1 Introduction to Logic
11.2 Truth Tables
11.3 Implication
11.4 Logical Implication and Equivalence
11.5 Valid Argument
11.6 Predicate Calculus
11.7 Logic Circuits
Chapter Project: A Logic Puzzle
12. Difference Equations and Mathematical Models (Online at www.pearsonhighered.com/mathstatsresources)
12.1 Introduction to Difference Equations
12.2 Difference Equations and Interest
12.3 Graphing Difference Equations
12.4 Mathematics of Personal Finance
12.5 Modeling with Difference Equations
Chapter Project: Connections to Markov Processes
Appendix A. Areas Under the Standard Normal Curve
Appendix B. The TI-83/84 Plus Graphing Calculators
Appendix C. Spreadsheet Fundamentals
Appendix D. Wolfram Alpha
Answers to Odd-Numbered Exercises
Index
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