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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 associate 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 mathematics 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 Rensselear 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.
Preface
1. Linear Equations and Straight Lines
1.1 Coordinate Systems and Graphs
1.2 Linear Inequalities
1.3 The Intersection Point of a Pair of Lines
1.4 The Slope of a Straight Line
1.5 The Method of Least Squares
Chapter Project: Break-Even Analysis
2. Matrices
Systems of Linear Equations with Unique Solutions
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 A Linear Programming Application
3.2 The Fundamental Theorem of Linear Programming
3.3 Linear Programming
Chapter Project: Shadow Prices
4. The Simplex Method
4.1 Slack Variables and the Simplex Tableau
4.2 Maximum Problems
4.3 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, SampleSapces, 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 Representation 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
Chapter Project: Two Items of Interest
11. Difference Equations and Mathematical Models
11.1 Introduction to Difference Equations
11.2 Difference Equations and Interest
11.3 Graphing Difference Equations
11.4 Mathematics of Personal Finance
11.5 Modeling with Difference Equations
Chapter Project: Connections to Markov Processes
12. Logic
12.1 Introduction to Logic
12.2 Truth Tables
12.3 Implication
12.4 Logical Implication and Equivalence
12.5 Valid Argument
12.6 Predicate Calculus
12.7 Logic Circuits
Chapter Project: A Logic Puzzle
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