Finite Mathematics
Edition: 1
Copyright: 2026
Pages: 90
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$75.00 USD
There are many possible topics in the area called Finite Mathematics. They cover the parts of mathematics that do not involve calculus or limits. For a book like this we have selected some, but not all, of the topics in Finite Mathematics. We start with basic set theory, including unions intersections, complements and Venn diagrams. We move on to counting techniques (combinatorics), where you will learn to count many very complicated things, e.g., the number of possible 5-card hands or the number of possible 4-digit pin numbers. We move on to elementary probability theory, where we use our counting techniques to solve probability problems. We continue our study of probability by studying random variables and the concepts of mean, variance and standard deviation. We next consider random variable with a binomial distribution or a normal distribution. We move on from probability by studying lines and linear models. We include ”least squares” lines that best fit a set of data points. After that we study systems of linear equations using the augmented matrix, row operations and the reduced row-echelon form. Finally we discuss a particular difference equation and its applications to ex ponential growth and decay, and to financial problems.
Preface
Chapter1: Sets
1. Definitions and Notation
2. Subsets
3. Unions, Intersections and Relative Complements
4. Universal Sets and Complements
5. Venn Diagrams
Chapter 2: Counting
1. n(A∪B)
2. Counting using Venn Diagrams
3. The Multiplication Principle
4. General Multiplication Principle
5. Permutations
6. Combinations
7. The Mississippi Problem
Chapter 3: Probability
1. Experiments, Outcomes and Events
2. Notion of Probability and Basic Rules
3. Equally Likely Outcomes
4. Conditional Probability and Independence
5. Bayes Rule and Tree Diagrams
Chapter 4: Random Variables
1. Probability Distributions
2. Mean or Expected Value
3. Variance and Standard Deviation
4. Binomial Distribution: Bernoulli Trials
Chapter 5: Normal Distribution
1. Standard Normal Distribution
2. Normal Distribution
3. Normal Approximation of the Binomial Distribution
Chapter 6: Lines and Linear Models
1. Equations of Lines
2. Linear Depreciation
3. Supply Curve
4. Demand Curve
5. Intersection of Lines
6. Least Squares
Chapter 7: Systems of Linear Equations
1. Augmented Matrix
2. Row Operations
3. The reduced Row-Echelon Form
4. Finding the Solutions from the reduced row-echelon form
5. Listing all the solutions
6. Word Problems
Chapter 8: A Difference Equation
1. Exponential Growth and Decay
2. Applications to Finance
Dr. Hadwin earned a Ph.D. in Mathematics from Indiana University–Purdue University Fort Wayne, an M.A. in Mathematics from the University of Wisconsin, and a B.S. in Mathematics from Michigan State University. His research interests include analysis and functional analysis, and he continues to collaborate with colleagues and publish new research. Dr. Hadwin has taught a wide range of undergraduate and graduate mathematics courses, including finite mathematics, mathematical proof, analysis, operator theory, independent study, and senior seminar.
There are many possible topics in the area called Finite Mathematics. They cover the parts of mathematics that do not involve calculus or limits. For a book like this we have selected some, but not all, of the topics in Finite Mathematics. We start with basic set theory, including unions intersections, complements and Venn diagrams. We move on to counting techniques (combinatorics), where you will learn to count many very complicated things, e.g., the number of possible 5-card hands or the number of possible 4-digit pin numbers. We move on to elementary probability theory, where we use our counting techniques to solve probability problems. We continue our study of probability by studying random variables and the concepts of mean, variance and standard deviation. We next consider random variable with a binomial distribution or a normal distribution. We move on from probability by studying lines and linear models. We include ”least squares” lines that best fit a set of data points. After that we study systems of linear equations using the augmented matrix, row operations and the reduced row-echelon form. Finally we discuss a particular difference equation and its applications to ex ponential growth and decay, and to financial problems.
Preface
Chapter1: Sets
1. Definitions and Notation
2. Subsets
3. Unions, Intersections and Relative Complements
4. Universal Sets and Complements
5. Venn Diagrams
Chapter 2: Counting
1. n(A∪B)
2. Counting using Venn Diagrams
3. The Multiplication Principle
4. General Multiplication Principle
5. Permutations
6. Combinations
7. The Mississippi Problem
Chapter 3: Probability
1. Experiments, Outcomes and Events
2. Notion of Probability and Basic Rules
3. Equally Likely Outcomes
4. Conditional Probability and Independence
5. Bayes Rule and Tree Diagrams
Chapter 4: Random Variables
1. Probability Distributions
2. Mean or Expected Value
3. Variance and Standard Deviation
4. Binomial Distribution: Bernoulli Trials
Chapter 5: Normal Distribution
1. Standard Normal Distribution
2. Normal Distribution
3. Normal Approximation of the Binomial Distribution
Chapter 6: Lines and Linear Models
1. Equations of Lines
2. Linear Depreciation
3. Supply Curve
4. Demand Curve
5. Intersection of Lines
6. Least Squares
Chapter 7: Systems of Linear Equations
1. Augmented Matrix
2. Row Operations
3. The reduced Row-Echelon Form
4. Finding the Solutions from the reduced row-echelon form
5. Listing all the solutions
6. Word Problems
Chapter 8: A Difference Equation
1. Exponential Growth and Decay
2. Applications to Finance
Dr. Hadwin earned a Ph.D. in Mathematics from Indiana University–Purdue University Fort Wayne, an M.A. in Mathematics from the University of Wisconsin, and a B.S. in Mathematics from Michigan State University. His research interests include analysis and functional analysis, and he continues to collaborate with colleagues and publish new research. Dr. Hadwin has taught a wide range of undergraduate and graduate mathematics courses, including finite mathematics, mathematical proof, analysis, operator theory, independent study, and senior seminar.