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