Mathematical Ideas, 15th edition
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Hallmark features of this title
- Numerous examples with annotations illustrate concepts and skills, providing step-by-step directions for solving similar problems.
- When Will I Ever Use This? in each chapter aims to answer that age-old question by connecting topics to career or workplace situations.
- For Further Thought encourages students to share their reasoning processes among themselves to gain a deeper understanding of key concepts.
- Optional Graphing Technology: Graphing calculator screens show how technology can help support results found analytically, but students do not need a graphing calculator to use the text.
- Margin Notes interspersed throughout the text touch on the lives of mathematicians, research in math, newspaper and magazine articles, and other note-worthy interesting sources.
Published by Pearson (September 1st 2023) - Copyright © 2024
Subject: Advanced Statistics
Category: Mathematical Statistics
Table of contents
1. The Art of Problem Solving
- 1.1 Solving Problems by Inductive Reasoning
- 1.2 An Application of Inductive Reasoning: Number Patterns
- 1.3 Strategies for Problem Solving
- 1.4 Numeracy in Today’s World
2. The Basic Concepts of Set Theory
- 2.1 Symbols and Terminology
- 2.2 Venn Diagrams and Subsets
- 2.3 Set Operations
- 2.4 Surveys and Cardinal Numbers
3. Introduction to Logic
- 3.1 Statements and Quantifiers
- 3.2 Truth Tables and Equivalent Statements
- 3.3 The Conditional and Circuits
- 3.4 The Conditional and Related Statements
- 3.5 Analyzing Arguments with Euler Diagrams
- 3.6 Analyzing Arguments with Truth Tables
4. Numeration Systems
- 4.1 Historical Numeration Systems
- 4.2 More Historical Numeration Systems
- 4.3 Arithmetic in the Hindu-Arabic System
- 4.4 Conversion Between Number Bases
- 4.5 Arithmetic in Other Bases
5. Number Theory
- 5.1 Prime and Composite Numbers
- 5.2 Large Prime Numbers
- 5.3 Selected Topics from Number Theory
- 5.4 Greatest Common Factor and Least Common Multiple
- 5.5 The Fibonacci Sequence and the Golden Ratio
- 5.6 Magic Squares (online)*
6. The Real Numbers and Their Representations
- 6.1 Real Numbers, Order, and Absolute Value
- 6.2 Operations, Properties, and Applications of Real Numbers
- 6.3 Rational Numbers and Decimal Representation
- 6.4 Irrational Numbers and Decimal Representation
- 6.5 Applications of Decimals and Percents
7. The Basic Concepts of Algebra
- 7.1 Linear Equations
- 7.2 Applications of Linear Equations
- 7.3 Ratio, Proportion, and Variation
- 7.4 Linear Inequalities
- 7.5 Properties of Exponents and Scientific Notation
- 7.6 Polynomials and Factoring
- 7.7 Quadratic Equations and Applications
8. Graphs, Functions, and Systems of Equations and Inequalities
- 8.1 The Rectangular Coordinate Systems and Circles
- 8.2 Lines, Slope, and Average Rate of Change
- 8.3 Equations of Lines
- 8.4 Linear Functions, Graphs, and Models
- 8.5 Quadratic Functions, Graphs, and Models
- 8.6 Exponential and Logarithmic Functions, Graphs, and Models
- 8.7 Systems of Linear Equations
- 8.8 Applications of Linear Systems
- 8.9 Linear Inequalities, Systems, and Linear Programming
- 9.1 Points, Lines, Planes, and Angles
- 9.2 Curves, Polygons, Circles, and Geometric Constructions
- 9.3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
- 9.4 Perimeter, Area, and Circumference
- 9.5 Volume and Surface Area
- 9.6 Transformational Geometry
- 9.7 Non-Euclidian Geometry and Topology
- 9.8 Chaos and Fractal Geometry
10. Counting Methods
- 10.1 Counting by Systematic Listing
- 10.2 Using the Fundamental Counting Principle
- 10.3 Using Permutations and Combinations
- 10.4 Using Pascal’s Triangle
- 10.5 Counting Problems Involving “Not” and “Or”
- 11.1 Basic Concepts
- 11.2 Events Involving “Not” and “Or”
- 11.3 Conditional Probability and Events Involving “And”
- 11.4 Binomial Probability
- 11.5 Expected Value and Simulation
- 12.1 Visual Displays of Data
- 12.2 Measures of Central Tendency
- 12.3 Measures of Dispersion
- 12.4 Measures of Position
- 12.5 The Normal Distribution
13. Personal Financial Management
- 13.1 The Time Value of Money
- 13.2 Consumer Credit
- 13.3 Truth in Lending
- 13.4 The Costs and Advantages of Home Ownership
- 13.5 Financial Investments
- 13.6 Income Tax Liability
14. Graph Theory
- 14.1 Basic Concepts
- 14.2 Euler Circuits and Route Planning
- 14.3 Hamilton Circuits and Algorithms
- 14.4 Trees and Minimum Spanning Trees
15. Voting and Apportionment
- 15.1 The Possibilities of Voting
- 15.2 The Impossibilities of Voting
- 15.3 The Possibilities of Apportionment
- 15.4 The Impossibilities of Apportionment
Answers to Selected Exercises
Index of Applications
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