Survey of Mathematics with Applications, A, 12th edition

Each chapter concludes with Chapter Summary, Chapter Review Exercises, and Chapter Test.

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, Set Operations, and Data Representation
• 2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets
• 2.5 Set Applications and Survey Data Analysis
• 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 The Fibonacci Sequence and The Golden Ratio

6: Algebra, Graphs, and Functions

• 6.1 Order of Operations and Solving Linear Equations
• 6.2 Formulas and Modeling
• 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
• 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

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

Index of Applications

Index