Finite Mathematics & Its Applications, 13th Edition © 2023
Larry Goldstein | David Schneider | Martha Siegel
Finite Mathematics and Its Applications, 13th Edition is packed with diverse applications that hold student interest. Built-in, optional instruction for the latest technology gives instructors flexibility for integrating tools like graphing calculators, spreadsheets and Wolfram|Alpha® into their courses. Thousands of well-crafted exercises enable a wide range of practice in skills, applications, concepts and technology. Its adaptable, student-oriented approach enables independent learning and study, while demonstrating how concepts apply to future careers.
Hallmark features of this title
- Relevant, varied applications illustrate finite math in daily life. Personal finance topics include traditional and Roth Individual Retirement Accounts (IRAs,) consumer loans, mortgages and more.
- Exercises to meet all student needs: Now Try Exercises appear after select examples, as an instructor might stop in class to ask students to try a problem. Fundamental Concept Check Exercises and Chapter Review Exercises prepare students for exams.
- Integrating Technology features within sections incorporate technology including graphing calculators, spreadsheets and Wolfram|Alpha®.
- Help text shown in blue within examples helps students understand key algebraic and numerical transitions.
- Check Your Understanding problems at the end of each section prepare students for the exercise sets.
New and updated features of this title
- Greatly increased video coverage adds and updates 40 example videos, bringing the total to 240. Videos were produced and incorporated for a modern and clear presentation of the examples. These refreshed videos are integrated into MyLab problems as learning aids and in the MyLab Video & Resource Library.
- Updated and improved exercises and applications, focusing on currency of data and topics, continue to draw students into the material and inspire learning. Hundreds of exercises have been improved and many exercises added to this revision.
- New Integrated Review helps bolster prerequisite skills if needed. Skills Check assessment in each chapter pinpoints topics students need to review. Personalized homework asks them to practice only those topics requiring extra help, and Integrated Review videos and worksheets offer more instruction on those topics.
- Expanded suite of Interactive Figures: Created in GeoGebra, these illustrate key concepts, can be manipulated by users, and can be used in lectures or independently by students.
- New Mindset Videos and assignable, open-ended exercises encourage students to maintain a positive attitude, value their ability to grow, and view mistakes as learning opportunities.
- New Personal Inventory Assessments promote self-reflection and engagement with topics such as stress management, motivation, and time management.
- New Early Alerts in Performance Analytics identify struggling students. Instructors can email students individually or by group to provide feedback.
- New section-level Enhanced Assignments provide spaced practice of previously learned concepts and contain personalized prerequisite skills exercises for gaps identified in the chapter-level Skills Check Quiz. Learning aids are turned off for some exercises to ensure students understand how to work them independently.
PART ONE
1. LINEAR EQUATIONS AND STRAIGHT LINES
1.1 Coordinate Systems and Graphs
1.2 The Slope of a Line
1.3 The Intersection Point of a Pair of Lines
1.4 The Method of Least Squares
Chapter Summary and Chapter Review Exercises
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 Summary and Chapter Review Exercises
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 Summary and Chapter Review Exercises
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 Summary and Chapter Review Exercises
Chapter Project: Shadow Prices Revisited
PART TWO
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 Summary and Chapter Review Exercises
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 Summary and Chapter Review Exercises
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 Summary and Chapter Review Exercises
Chapter Project: An Unexpected Expected Value
PART THREE
8. MARKOV PROCESSES
8.1 The Transition Matrix
8.2 Regular Stochastic Matrices
8.3 Absorbing Stochastic Matrices
Chapter Summary and Chapter Review Exercises
Chapter Project: Doubly Stochastic Matrices
The Theory of Games
9.1 Games and Strategies
9.2 Mixed Strategies
9.3 Determining Optimal Mixed Strategies
Chapter Summary and Chapter Review Exercises
Chapter Project: Simulating The Outcomes of Mixed-Strategy Games
PART FOUR
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 Summary and Chapter Review Exercises
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 Summary and Chapter Review Exercises
Chapter Project: A Logic Puzzle
12. DIFFERENCE EQUATIONS AND MATHEMATICAL MODELS (ONLINE)
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 Summary and Chapter Review Exercises
Chapter Project: Connections to Markov Processes
APPENDICES
1. Areas Under the Standard Normal Curve
2. The TI-83/84 Plus Graphing Calculator
3. Spreadsheet Fundamentals
4. Wolfram Alpha
Learning Objectives
Index of Applications
Index
Larry Goldstein
Princeton, University of Pennsylvania, Drexel University
Larry Goldstein has received several distinguished teaching awards, given more than 50 conference and colloquium talks and addresses, and written more than 50 books in math and computer programming. He received his PhD at Princeton and his Bachelor of Arts (BA) and Master of Arts (MA) at the University of Pennsylvania. He also teaches part time at Drexel University.
David Schneider
Oberlin College, MIT, University of Maryland
David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from Massachusetts Institute of Technology (MIT). He is currently an emeritus professor of mathematics at the University of Maryland. He has authored 8 widely used math texts, 14 highly acclaimed computer books, and 3 widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the British Broadcasting Corporation (BBC.)
Martha Siegel
Russell Sage College, Rensselaer Polytechnic Institute, University of Rochester, Goucher University
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 5th Edition and is also the co-author of a precalculus reform book.
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