Mathematical Ideas, 15th edition
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Overview
Hallmark features of this title
 Numerous examples with annotations illustrate concepts and skills, providing stepbystep directions for solving similar problems.
 When Will I Ever Use This? in each chapter aims to answer that ageold 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 noteworthy interesting sources.
Published by Pearson (September 1st 2023)  Copyright © 2024
ISBN13: 9780137969036
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
 Summary
 Test
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
 Summary
 Test
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
 Summary
 Test
4. Numeration Systems
 4.1 Historical Numeration Systems
 4.2 More Historical Numeration Systems
 4.3 Arithmetic in the HinduArabic System
 4.4 Conversion Between Number Bases
 4.5 Arithmetic in Other Bases
 Summary
 Test
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)*
 Summary
 Test
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
 Summary
 Test
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
 Summary
 Test
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
 Summary
 Test
9. Geometry
 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 NonEuclidian Geometry and Topology
 9.8 Chaos and Fractal Geometry
 Summary
 Test
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”
 Summary
 Test
11. Probability
 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
 Summary
 Test
12. Statistics
 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
 Summary
 Test
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
 Summary
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
 Summary
 Test
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
 Summary
 Test
Answers to Selected Exercises
Credits
Index of Applications
Index
Your questions answered
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