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 twenty-five years at State College of Florida–Manatee-Sarasota. His interests include reading, history, 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 and Deductive Reasoning 

1.2 Estimation Techniques

1.3 Problem-Solving Procedures 

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 Perform Computations 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 Linear Equations 

6.2 Formulas

6.3 Applications of Algebra

6.4 Variation

6.5 Solving Linear Inequalities 

6.6 Graphing Linear Equations

6.7 Solving Systems of Linear Equations 

6.8 Linear Inequalities in Two Variables 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 678 

11.5 OR and AND Problems 

11.6 Conditional Probability 

11.7 The Fundamental 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 and Position 

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 864 14 Voting and Apportionment 

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 

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