Mathematical Ideas, 14th Edition Miller
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, Table of Contents are Given Below
Here is the table of contents for "Mathematical Ideas," 14th Edition by Charles D. Miller, Vern E. Heeren, John
Hornsby, and Christopher Heeren:
1. The Art of Problem Solving
o 1.1 Solving Problems by Inductive Reasoning
o 1.2 An Application of Inductive Reasoning: Number Patterns
o 1.3 Strategies for Problem Solving
o 1.4 Numeracy in Today’s World
2. The Basic Concepts of Set Theory
o 2.1 Symbols and Terminology
o 2.2 Venn Diagrams and Subsets
o 2.3 Set Operations
o 2.4 Surveys and Cardinal Numbers
3. Introduction to Logic
o 3.1 Statements and Quantifiers
o 3.2 Truth Tables and Equivalent Statements
o 3.3 The Conditional and Circuits
o 3.4 The Conditional and Related Statements
o 3.5 Analyzing Arguments with Euler Diagrams
o 3.6 Analyzing Arguments with Truth Tables
4. Numeration Systems
o 4.1 Historical Numeration Systems
o 4.2 More Historical Numeration Systems
o 4.3 Arithmetic in the Hindu-Arabic System
o 4.4 Conversion Between Number Bases
5. Number Theory
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, o 5.1 Prime and Composite Numbers
o 5.2 Large Prime Numbers
o 5.3 Selected Topics from Number Theory
o 5.4 Greatest Common Factor and Least Common Multiple
o 5.5 The Fibonacci Sequence and the Golden Ratio
o 5.6 Magic Squares (online)*
6. The Real Numbers and Their Representations
o 6.1 Real Numbers, Order, and Absolute Value
o 6.2 Operations, Properties, and Applications of Real Numbers
o 6.3 Rational Numbers and Decimal Representation
o 6.4 Irrational Numbers and Decimal Representation
o 6.5 Applications of Decimals and Percents
7. The Basic Concepts of Algebra
o 7.1 Linear Equations
o 7.2 Applications of Linear Equations
o 7.3 Ratio, Proportion, and Variation
o 7.4 Linear Inequalities
o 7.5 Properties of Exponents and Scientific Notation
o 7.6 Polynomials and Factoring
o 7.7 Quadratic Equations and Applications
8. Graphs, Functions, and Systems of Equations and Inequalities
o 8.1 The Rectangular Coordinate Systems and Circles
o 8.2 Lines, Slope, and Average Rate of Change
o 8.3 Equations of Lines
o 8.4 Linear Functions, Graphs, and Models
o 8.5 Quadratic Functions, Graphs, and Models
o 8.6 Exponential and Logarithmic Functions, Graphs, and Models
o 8.7 Systems of Linear Equations
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, o 8.8 Applications of Linear Systems
o 8.9 Linear Inequalities, Systems, and Linear Programming
9. Geometry
o 9.1 Points, Lines, Planes, and Angles
o 9.2 Curves, Polygons, Circles, and Geometric Constructions
o 9.3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
o 9.4 Perimeter, Area, and Circumference
o 9.5 Volume and Surface Area
o 9.6 Transformational Geometry
o 9.7 Non-Euclidean Geometry and Topology
o 9.8 Chaos and Fractal Geometry
10. Counting Methods
o 10.1 Counting by Systematic Listing
o 10.2 Using the Fundamental Counting Principle
o 10.3 Using Permutations and Combinations
o 10.4 Using Pascal’s Triangle
o 10.5 Counting Problems Involving “Not” and “Or”
11. Probability
o 11.1 Basic Concepts
o 11.2 Events Involving “Not” and “Or”
o 11.3 Conditional Probability and Events Involving “And”
o 11.4 Binomial Probability
o 11.5 Expected Value and Simulation
12. Statistics
o 12.1 Visual Displays of Data
o 12.2 Measures of Central Tendency
o 12.3 Measures of Dispersion
o 12.4 Measures of Position
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