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Chapter Openers and Section Openers introduce each chapter and section with interesting and motivational applications, illustrating the real-world nature of the
Problem Solving begins in Chapter 1 where students are introduced to problem solving and critical thinking. The problem-solving theme is then continued throughout the text, and special problem-solving exercises are presented in the exercise sets.
Critical Thinking Skills are featured in sections on inductive reasoning and the important skills of estimation and dimensional analysis.
Profiles in Mathematics present the stories of people who have advanced the discipline of mathematics in brief historical sketches and vignettes.
Mathematics Today relates mathematics to everyday life, helping students to recognize the need for math and gain an appreciation for math in their lives.
Did You Know? features highlights the connections between mathematics and a variety of other disciplines, including history, the arts and sciences, and technology in colorful and engaging boxed features.
Timely Tips, added to assist students, help with concept comprehension or relate the material to other sections of the book.
Technology Tips appear as notes that have been added in selected sections to explain how a graphing calculator and/or Microsoft Excel may be used to work certain problems.
Exercise Sets include diverse and numerous exercise types such as Concept/Writing, Practice the Skills, Problem Solving, Challenge Problem/Group Activity, Recreational Mathematics, and Internet/Research Activities.
Chapter Summaries, Review Exercises, and Chapter Tests comprise end-of-chapter sections that help students review material and prepare for tests.
Group Projects appear at the end of each chapter and are suggested projects that can be used to have students work together. These projects can also be assigned to individual students if desired.
In this edition, certain topics have been revised or expanded in order to introduce new material and increase understanding:
Chapter 14: Graph Theory includes new creative exercises, and a revised method of representing buildings as graphs.
Chapter 15: Voting and Apportionment includes more real-life examples and exercises.
In addition, several important improvements have been made to the presentation of the material:
Chapter 1 Critical Thinking Skills
1.1 Inductive Reasoning
1.3 Problem Solving
Chapter 2 Sets
2.1 Set Concepts
2.3 Venn Diagrams and Set Operations
2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets
2.5 Application of Sets
2.6 Infinite Sets
Chapter 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
Chapter 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
Chapter 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
Chapter 6 Algebra, Graphs, and Functions
6.1 Order of Operations
6.2 Linear Equations In One Variable
6.4 Applications of Linear Equations In One Variable
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
Chapter 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
7.4 Solving Systems of Linear Equations by Using Matrices
7.5 Systems of Linear Inequalities
7.6 Linear Programming
Chapter 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
Chapter 9 Geometry
9.1 Points, Lines, Planes, and Angles
9.3 Perimeter and Area
9.4 Volume and Surface Area
9.5 Transformational Geometry, Symmetry, and Tessellations
9.7 Non-Euclidean Geometry and Fractal Geometry
Chapter 10 Mathematical Systems
10.2 Finite Mathematical Systems
10.3 Modular Arithmetic
Chapter 11 Consumer Mathematics
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
Chapter 12 Probability
12.1 The Nature of Probability
12.2 Theoretical Probability
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
12.10 Solving Probability Problems By Using Combinations
12.11 Binomial Probability
Chapter 13 Statistics
13.1 Sampling Techniques
13.2 The Misuses of Statistics
13.3 Frequency Distributions
13.4 Statistical Graphs
13.5 Measures of Central Tendency
13.6 Measures of Dispersion
13.7 The Normal Curve
13.8 Linear Correlation and Regression
Chapter 14 Graph Theory
14.1 Graphs, Paths, and Circuits
14.2 Euler Paths and Euler Circuits
14.3 Hamilton Paths and Hamilton Circuits
Chapter 15 Voting and Apportionment
15.1 Voting Methods
15.2 Flaws of Voting
15.3 Apportionment Methods
15.4 Flaws of the Apportionment Methods
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<>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 over fifteen years at Manatee Community College in Florida and for almost ten 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.
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