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

1. Critical Thinking Skills

1.1 Inductive and Deductive 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

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 and Solving Equations

6.2 Formulas

6.3 Applications of Algebra

6.4 Variation

6.5 Linear Inequalities

6.6 Graphing Linear Equations

6.7 Solving Systems of Linear Equations

6.8 Linear Inequalities and Systems of Linear Inequalities

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

6.10 Functions and Their Graphs

7. The Metric System

7.1 Basic Terms and Conversions Within the Metric System

7.2 Length, Area, and Volume

7.3 Mass and Temperature

7.4 Dimensional Analysis and Conversions to and from the Metric System

8. Geometry

8.1 Points, Lines, Planes, and Angles

8.2 Polygons

8.3 Perimeter and Area

8.4 Volume and Surface Area

8.5 Transformational Geometry, Symmetry, and Tessellations

8.6 Topology

8.7 Non-Euclidean Geometry and Fractal Geometry

9. Mathematical Systems

9.1 Groups

9.2 Finite Mathematical Systems

9.3 Modular Arithmetic

9.4 Matrices

10. Consumer Mathematics

10.1 Percent

10.2 Personal Loans and Simple Interest

10.3 Compound Interest

10.4 Installment Buying

10.5 Buying a House with a Mortgage

10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments

11. Probability

11.1 Empirical and Theoretical Probabilities

11.2 Odds

11.3 Expected Value (Expectation)

11.4 Tree Diagrams

11.5 OR and AND Problems

11.6 Conditional Probability

11.7 The Counting Principle and Permutations

11.8 Combinations

11.9 Solving Probability Problems by Using Combinations

11.10 Binomial Probability Formula

12. Statistics

12.1 Sampling Techniques and Misuses of Statistics

12.2 Frequency Distributions and Statistical Graphs

12.3 Measures of Central Tendency

12.4 Measures of Dispersion

12.5 The Normal Curve

12.6 Linear Correlation and Regression

13. Graph Theory

13.1 Graphs, Paths, and Circuits

13.2 Euler Paths and Euler Circuits

13.3 Hamilton Paths and Hamilton Circuits

13.4 Trees

14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of the Voting Methods

14.3 Apportionment Methods

14.4 Flaws of the Apportionment Methods

ANSWERS

Credits

Index of Applications

Index

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