by Ignacio Bello, Jack R. Britton and Anton Kaul
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Topics in Contemporary Mathematics is uniquely designed to help students see math at work in the contemporary world by presenting problem solving in purposeful and meaningful contexts.
1. Problem Solving
1.1 Inductive reasoning
1.2 Estimation: A Problem Solving tool
1.3 Graph Interpretation: A Problem Solving Tool
2. Sets
2.1 Sets: A Problem-Solving Tool
2.2 Set Operations
2.3 Venn Diagrams
2.4 The Number of Elements in a Set: A Problem-Solving Tool
2.5 Infinite Sets
3. Logic
3.1 Statements
3.2 Truth Tables: A Problem-Solving Tool
3.3 The Conditional and the Biconditional
3.4 Variations of the Conditional and Implications
3.5 Euler Diagrams: A Problem-Solving Tool
3.6 Truth Tables and Validity Arguments
Online Only: 3.7 Switching Networks: A Problem-Solving Tool
4. Numeration Systems
4.1 Egyptian, Babylonian, and Roman Numeration Systems
4.2 The Hindu-Arabic (Decimal) System
4.3 Number Systems with Bases Other Than 10
4.4 Binary Arithmetic
4.5 Octal and Hexadecimal Arithmetic
5. Number Theory and the Real Numbers
5.1 Number Theory: Primes and Composites
5.2 Whole Numbers, Integers, and Order or Operations
5.3 The Rational Numbers
5.4 Decimals, Scientific Notation, and Significant Digits
5.5 Rationals as Decimals: Percents
5.6 Real Numbers, Square Roots, and Decimal Representation
5.7 Radicals
5.8 Number Sequences
6. Equations, Inequalities, and Problem Solving
6.1 Solutions of First-Degree Sentences
6.2 Graphs of Algebraic Sentences
6.3 Sentences Involving Absolute Values
6.4 Quadratic Equations
6.5 Modeling and Problem Solving
6.6 Ratio Proportion, and Variation
7. Functions and Graphs
7.1 Graphing Relations and Functions
7.2 Linear Functions, Relations, and Applications
7.3 Slopes and Equations of A Line
7.4 Quadratic Functions and Their Graphs
7.5 Exponential and Logarithmic Functions
7.6 Two Linear Equations in Two Variables
7.7 Linear Inequalities
Online Only: 7.8 Linear Programming
8. Geometry
8.1 Points, lines, planes, and angles
8.2 Triangles and Other Polygons
8.3 Perimeter and Circumfrence
8.4 Area Measure and the Pythagorean Theorem
8.5 Volume and Surface Area
Online Only: 8.6 Right Triangle Trigonometry
8.7 Networks, Non-Euclidean Geometry, and Topology
Online Only: 8.8 Chaos and Fractals
9. Mathematical Systems and Matrices
9.1 Matrix Operations
9.2 Solving of Linear Equations with Matrices
9.3 Clock and Modular Arithmetic
9.4 Abstract Mathematical Systems: Groups and Fields
9.4 Game Theory
10. Counting Techniques
10.1 The Sequential Counting Principle (SCP): A Problem-Solving Tool
10.2 Permutations
10.3 Combinations
10.4 Miscellaneous Counting Methods
11. Probability
11.1 Sample Spaces and Probability
11.2 Poker Improbabilities
11.3 Computation and Probability
11.4 Conditional Probability
11.5 Independent Events
11.6 Odds and Mathematical Expectation
12. Statictics
12.1 Sampling and Frequency Distribution
12.2 The Measures Central Tendency: The Mean, the Median, and the Mode
12.3 Measures of Depression: The Range and Standard Deviation
12.4 The Normal Dsitribution: A Problem Solving Tool
12.5 Statistical Graphics: A Problem-Solving Tool
12.6 Making Predictions: Linear Regression
12.7 Scattergrams and Correlation
13. Your Money and Your Math
13.1 Interest, Taxes, and Discounts
13.2 Credit Cards and Comsumer Credit
13.3 Annual Percentage Rate (APR) and the Rules of 78
13.4 Buying a House
13.5 Investing in Stocks, Bonds, and Mutual Funds
Online Only: 14. Voting and Apportionment
14.1 Voting Systems
14.2 Voting Objections
14.3 Apportionment Methods
14.4 Apportionment Objections
Online Only: 15. Graph Theory
15.1 Introduction to Graph Theory
15.2 Euler Paths and Euler Circuits
15.3 Hamilton Paths and Hamilton Circuits
15.4 Trees
Ignacio Bello, Jack R. Britton and Anton Kaul
ISBN13: 978-0618775248Topics in Contemporary Mathematics is uniquely designed to help students see math at work in the contemporary world by presenting problem solving in purposeful and meaningful contexts.
Table of Contents
1. Problem Solving
1.1 Inductive reasoning
1.2 Estimation: A Problem Solving tool
1.3 Graph Interpretation: A Problem Solving Tool
2. Sets
2.1 Sets: A Problem-Solving Tool
2.2 Set Operations
2.3 Venn Diagrams
2.4 The Number of Elements in a Set: A Problem-Solving Tool
2.5 Infinite Sets
3. Logic
3.1 Statements
3.2 Truth Tables: A Problem-Solving Tool
3.3 The Conditional and the Biconditional
3.4 Variations of the Conditional and Implications
3.5 Euler Diagrams: A Problem-Solving Tool
3.6 Truth Tables and Validity Arguments
Online Only: 3.7 Switching Networks: A Problem-Solving Tool
4. Numeration Systems
4.1 Egyptian, Babylonian, and Roman Numeration Systems
4.2 The Hindu-Arabic (Decimal) System
4.3 Number Systems with Bases Other Than 10
4.4 Binary Arithmetic
4.5 Octal and Hexadecimal Arithmetic
5. Number Theory and the Real Numbers
5.1 Number Theory: Primes and Composites
5.2 Whole Numbers, Integers, and Order or Operations
5.3 The Rational Numbers
5.4 Decimals, Scientific Notation, and Significant Digits
5.5 Rationals as Decimals: Percents
5.6 Real Numbers, Square Roots, and Decimal Representation
5.7 Radicals
5.8 Number Sequences
6. Equations, Inequalities, and Problem Solving
6.1 Solutions of First-Degree Sentences
6.2 Graphs of Algebraic Sentences
6.3 Sentences Involving Absolute Values
6.4 Quadratic Equations
6.5 Modeling and Problem Solving
6.6 Ratio Proportion, and Variation
7. Functions and Graphs
7.1 Graphing Relations and Functions
7.2 Linear Functions, Relations, and Applications
7.3 Slopes and Equations of A Line
7.4 Quadratic Functions and Their Graphs
7.5 Exponential and Logarithmic Functions
7.6 Two Linear Equations in Two Variables
7.7 Linear Inequalities
Online Only: 7.8 Linear Programming
8. Geometry
8.1 Points, lines, planes, and angles
8.2 Triangles and Other Polygons
8.3 Perimeter and Circumfrence
8.4 Area Measure and the Pythagorean Theorem
8.5 Volume and Surface Area
Online Only: 8.6 Right Triangle Trigonometry
8.7 Networks, Non-Euclidean Geometry, and Topology
Online Only: 8.8 Chaos and Fractals
9. Mathematical Systems and Matrices
9.1 Matrix Operations
9.2 Solving of Linear Equations with Matrices
9.3 Clock and Modular Arithmetic
9.4 Abstract Mathematical Systems: Groups and Fields
9.4 Game Theory
10. Counting Techniques
10.1 The Sequential Counting Principle (SCP): A Problem-Solving Tool
10.2 Permutations
10.3 Combinations
10.4 Miscellaneous Counting Methods
11. Probability
11.1 Sample Spaces and Probability
11.2 Poker Improbabilities
11.3 Computation and Probability
11.4 Conditional Probability
11.5 Independent Events
11.6 Odds and Mathematical Expectation
12. Statictics
12.1 Sampling and Frequency Distribution
12.2 The Measures Central Tendency: The Mean, the Median, and the Mode
12.3 Measures of Depression: The Range and Standard Deviation
12.4 The Normal Dsitribution: A Problem Solving Tool
12.5 Statistical Graphics: A Problem-Solving Tool
12.6 Making Predictions: Linear Regression
12.7 Scattergrams and Correlation
13. Your Money and Your Math
13.1 Interest, Taxes, and Discounts
13.2 Credit Cards and Comsumer Credit
13.3 Annual Percentage Rate (APR) and the Rules of 78
13.4 Buying a House
13.5 Investing in Stocks, Bonds, and Mutual Funds
Online Only: 14. Voting and Apportionment
14.1 Voting Systems
14.2 Voting Objections
14.3 Apportionment Methods
14.4 Apportionment Objections
Online Only: 15. Graph Theory
15.1 Introduction to Graph Theory
15.2 Euler Paths and Euler Circuits
15.3 Hamilton Paths and Hamilton Circuits
15.4 Trees