A Survey of Mathematics with Applications

Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy.

Christine Abbott received her undergraduate degree in mathematics from SUNY Brockport and her graduate degree in mathematics education from Syracuse University. Since then she has taught mathematics at Monroe Community College and has recently chaired the department. In her spare time she enjoys watching sporting events, particularly baseball, college basketball, college football, and the NFL. She also enjoys spending time with her family, traveling, and reading

Dennis Runde has a BS degree and an MS degree in Mathematics from the University of Wisconsin--Platteville and Milwaukee respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for more than fifteen years at State College of Florida–Manatee-Sarasota and for almost ten years at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with their three sons--Alex, Nick, and Max.

1. Critical Thinking Skills

1.1 Inductive Reasoning

1.2 Estimation

1.3 Problem Solving

2. Sets

2.1 Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets

2.5 Applications of Sets

2.6 Infinite Sets

3. Logic

3.1 Statements and Logical Connectives

3.2 Truth Tables for Negation, Conjunction, and Disjunction

3.3 Truth Tables for the Conditional and Biconditional

3.4 Equivalent Statements

3.5 Symbolic Arguments

3.6 Euler Diagrams and Syllogistic Arguments

3.7 Switching Circuits

4. Systems of Numeration

4.1 Additive, Multiplicative, and Ciphered Systems of Numeration

4.2 Place-Value or Positional-Value Numeration Systems

4.3 Other Bases

4.4 Computation In Other Bases

4.5 Early Computational Methods

5. Number Theory and the Real Number System

5.1 Number Theory

5.2 The Integers

5.3 The Rational Numbers

5.4 The Irrational Numbers and the Real Number System

5.5 Real Numbers and Their Properties

5.6 Rules of Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

5.8 Fibonacci Sequence

6. Algebra, Graphs, and Functions

6.1 Order of Operations

6.2 Linear Equations in One Variable

6.3 Formulas

6.4 Applications of Linear Equations In One Variable

6.5 Variation

6.6 Linear Inequalities

6.7 Graphing Linear Equations

6.8 Linear Inequalities In Two Variables

6.9 Solving Quadratic Equations By Using Factoring and By Using the Quadratic Formula

6.10 Functions and Their Graphs

7. Systems of Linear Equations and Inequalities

7.1 Systems of Linear Equations

7.2 Solving Systems of Linear Equations by the Substitution and Addition Methods

7.3 Matrices

7.4 Solving Systems of Linear Equations by Using Matrices

7.5 Systems of Linear Inequalities

7.6 Linear Programming

8. The Metric System

8.1 Basic Terms and Conversions Within the Metric System

8.2 Length, Area, and Volume

8.3 Mass and Temperature

8.4 Dimensional Analysis and Conversions To and From the Metric System

9. Geometry

9.1 Points, Lines, Planes, and Angles

9.2 Polygons

9.3 Perimeter and Area

9.4 Volume and Surface Area

9.5 Transformational Geometry, Symmetry, and Tessellations

9.6 Topology

9.7 Non-Euclidean Geometry and Fractal Geometry

10. Mathematical Systems

10.1 Groups

10.2 Finite Mathematical Systems

10.3 Modular Arithmetic

11. Consumer Mathematics

11.1 Percent

11.2 Personal Loans and Simple Interest

11.3 Compound Interest

11.4 Installment Buying

11.5 Buying A House With A Mortgage

11.6 Ordinary Annuities, Sinking Funds, and Retirement Investments

12. Probability

12.1 The Nature of Probability

12.2 Theoretical Probability

12.3 Odds

12.4 Expected Value (Expectation)

12.5 Tree Diagrams

12.6 OR and AND Problems

12.7 Conditional Probability

12.8 The Counting Principle and Permutations

12.9 Combinations

12.10 Solving Probability Problems By Using Combinations

12.11 Binomial Probability Formula

13. Statistics

13.1 Sampling Techniques

13.2 The Misuses of Statistics

13.3 Frequency Distributions and Statistical Graphs

13.4 Measures of Central Tendency

13.5 Measures of Dispersion

13.6 The Normal Curve

13.7 Linear Correlation and Regression

14. Graph Theory

14.1 Graphs, Paths, and Circuits

14.2 Euler Paths and Euler Circuits

14.3 Hamilton Paths and Hamilton Circuits

14.4 Trees

15. Voting and Apportionment

15.1 Voting Methods

15.2 Flaws of Voting

15.3 Apportionment Methods

15.4 Flaws of the Apportionment Methods

Answers

Credits

Index of Applications

Index

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