Mathematical Ideas
United States Edition
11th Edition
Published on 6. February 2007
Book
Hardback
952 pages
978-0-321-36148-6 (ISBN)
Description
One of the biggest issues college math instructors face is capturing and keeping student interest. Over the years, John Hornsby has refined a creative solution--bringing the best of Hollywood into his mathematics classroom. Mathematical Ideas applies this same strategy of engaging students through descriptions of video clips from popular cinema and television to the textbook. Alongside fresh data and tools, this Eleventh Edition uses up-to-the-minute images as well as old favorites of math being done in Hollywood. In addition, examples are clarified with additional annotations, the margin notes have been freshened, and Chapter 14: Personal Financial Management has been updated to meet the needs of today's students. With great care and effort, Vern Heeren and John Hornsby have crafted this new edition to serve the needs of today's students and instructors.
More details
Edition
11th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 209 mm
Width: 259 mm
Thickness: 38 mm
Weight
1976 gr
ISBN-13
978-0-321-36148-6 (9780321361486)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Charles Miller | Vern Heeren | John Hornsby
Mathematical Ideas Expanded Edition
Book
05/2007
11th Edition
Pearson
€186.92
Article exhausted; check for reprint
Persons
Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.
John Hornsby When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country.
John Hornsby When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country.
Content
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 Calculating, Estimating, and Reading Graphs
Extension: Using Writing to Learn About Mathematics
Collaborative Investigation: Discovering Patterns in Pascal's Triangle
Chapter 1 Test
2 The Basic Concepts of Set Theory
2.1 Symbols and Terminology
2.2 Venn Diagrams and Subsets
2.3 Set Operations and Cartesian Products
2.4 Surveys and Cardinal Numbers
2.5 Infinite Sets and Their Cardinalities
Collaborative Investigation: Surveying the Members of your Class
Chapter 2 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 More on the Conditional
3.5 Analyzing Arguments with Euler Diagrams
Extension: Logic Problems and Sodoku
3.6 Analyzing Arguments with Truth Tables
Collaborative Investigation: Logic Problems and Sodoku Revisited
Chapter 3 Test
4 Numeration and Mathematical Systems
4.1 Historical Numeration Systems
4.2 Arithmetic in the Hindu-Arabic System
4.3 Conversion between Number Bases
4.4 Clock Arithmetic and Modular Systems
4.5 Properties of Mathematical Systems
4.6 Groups
Collaborative Investigation: A Perpetual Calendar Algorithm
Chapter 4 Test
5 Number Theory
5.1 Prime and Composite Numbers
5.2 Selected Topics from Number Theory
5.3 Greatest Common Factor and Least Common Multiple
Extension: Modern Cryptography
5.4 The Fibonacci Sequence and the Golden Ratio
Extension: Magic Squares
Collaborative Investigation: Investigating an Interesting Property of Number Squares
Chapter 5 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
Extension: Complex Numbers
Collaborative Investigation: Budgeting to Buy a Car
Chapter 6 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
Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?
Chapter 7 Test
8 Graphs, Functions, and Systems of Equations and Inequalities
8.1 The Rectangular Coordinate System and Circles
8.2 Lines and Their Slopes
8.3 Equations of Lines and Linear Models
8.4 An Introduction to Functions: Linear Functions, Applications, and Models
8.5 Quadratic Functions, Applications, and Models
8.6 Exponential and Logarithmic Functions, Applications, and Models
8.7 Systems of Equations and Applications
Extension: Using Matrix Row Operations to Solve Systems
8.8 Linear Inequalities, Systems, and Linear Programming
Collaborative Investigation: Living with AIDS
Chapter 8 Test
9 Geometry
9.1 Points, Lines, Planes, and Angles
9.2 Curves, Polygons, and Circles
Extension: Geometric Constructions
9.3 Perimeter, Area, and Circumference
9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
9.5 Space Figures, Volume, and Surface Area
9.6 Transformational Geometry
9.7 Non-Euclidean Geometry, Topology, and Networks
9.8 Chaos and Fractal Geometry
Collaborative Investigation: Generalizing the Angle Sum Concept
Chapter 9 Test
10 Trigonometry
10.1 Angles and Their Measures
10.2 Trigonometric Functions of Angles
10.3 Trigonometric Identities
10.4 Right Triangles and Function Values
10.5 Applications of Right Triangles
10.6 The Laws of Sines and Cosines: Area Formulas
Collaborative Investigation: Making a Point about Trigonometric Function Values
Chapter 10 Test
11 Counting Methods 11.1 Counting by Systematic Listing
11.2 Using the Fundamental Counting Principle
11.3 Using Permutations and Combinations
11.4 Using Pascal's Triangle
11.5 Counting Problems Involving "Not" and "Or"
Collaborative Investigation: Solving a Traveling Salesman Problem
Chapter 11 Test
12 Probability
12.1 Basic Concepts
12.2 Events Involving "Not" and "Or"
12.3 Conditional Probability; Events Involving "And"
12.4 Binomial Probability
12.5 Expected Value
Extension: Estimating Probabilities by Simulation
Collaborative Investigation: Finding Empirical Values of p
Chapter 12 Test
13 Statistics
13.1 Frequency Distributions and Graphs
13.2 Measures of Central Tendency
13.3 Measures of Dispersion
13.4 Measures of Position
13.5 The Normal Distribution
Extension: How to Lie with Statistics
13.6 Regression and Correlation
Collaborative Investigation: Combining Sets of Data
Chapter 13 Test
14 Personal Financial Management
14.1 The Time Value of Money
Extension: Annuities
14.2 Installment Buying
14.3 Truth in Lending
14.4 The Costs and Advantages of Home Ownership
14.5 Investing
Collaborative Investigation: To Buy or to Rent?
Chapter 14 Test
1.1 Solving Problems by Inductive Reasoning
1.2 An Application of Inductive Reasoning: Number Patterns
1.3 Strategies for Problem Solving
1.4 Calculating, Estimating, and Reading Graphs
Extension: Using Writing to Learn About Mathematics
Collaborative Investigation: Discovering Patterns in Pascal's Triangle
Chapter 1 Test
2 The Basic Concepts of Set Theory
2.1 Symbols and Terminology
2.2 Venn Diagrams and Subsets
2.3 Set Operations and Cartesian Products
2.4 Surveys and Cardinal Numbers
2.5 Infinite Sets and Their Cardinalities
Collaborative Investigation: Surveying the Members of your Class
Chapter 2 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 More on the Conditional
3.5 Analyzing Arguments with Euler Diagrams
Extension: Logic Problems and Sodoku
3.6 Analyzing Arguments with Truth Tables
Collaborative Investigation: Logic Problems and Sodoku Revisited
Chapter 3 Test
4 Numeration and Mathematical Systems
4.1 Historical Numeration Systems
4.2 Arithmetic in the Hindu-Arabic System
4.3 Conversion between Number Bases
4.4 Clock Arithmetic and Modular Systems
4.5 Properties of Mathematical Systems
4.6 Groups
Collaborative Investigation: A Perpetual Calendar Algorithm
Chapter 4 Test
5 Number Theory
5.1 Prime and Composite Numbers
5.2 Selected Topics from Number Theory
5.3 Greatest Common Factor and Least Common Multiple
Extension: Modern Cryptography
5.4 The Fibonacci Sequence and the Golden Ratio
Extension: Magic Squares
Collaborative Investigation: Investigating an Interesting Property of Number Squares
Chapter 5 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
Extension: Complex Numbers
Collaborative Investigation: Budgeting to Buy a Car
Chapter 6 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
Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?
Chapter 7 Test
8 Graphs, Functions, and Systems of Equations and Inequalities
8.1 The Rectangular Coordinate System and Circles
8.2 Lines and Their Slopes
8.3 Equations of Lines and Linear Models
8.4 An Introduction to Functions: Linear Functions, Applications, and Models
8.5 Quadratic Functions, Applications, and Models
8.6 Exponential and Logarithmic Functions, Applications, and Models
8.7 Systems of Equations and Applications
Extension: Using Matrix Row Operations to Solve Systems
8.8 Linear Inequalities, Systems, and Linear Programming
Collaborative Investigation: Living with AIDS
Chapter 8 Test
9 Geometry
9.1 Points, Lines, Planes, and Angles
9.2 Curves, Polygons, and Circles
Extension: Geometric Constructions
9.3 Perimeter, Area, and Circumference
9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
9.5 Space Figures, Volume, and Surface Area
9.6 Transformational Geometry
9.7 Non-Euclidean Geometry, Topology, and Networks
9.8 Chaos and Fractal Geometry
Collaborative Investigation: Generalizing the Angle Sum Concept
Chapter 9 Test
10 Trigonometry
10.1 Angles and Their Measures
10.2 Trigonometric Functions of Angles
10.3 Trigonometric Identities
10.4 Right Triangles and Function Values
10.5 Applications of Right Triangles
10.6 The Laws of Sines and Cosines: Area Formulas
Collaborative Investigation: Making a Point about Trigonometric Function Values
Chapter 10 Test
11 Counting Methods 11.1 Counting by Systematic Listing
11.2 Using the Fundamental Counting Principle
11.3 Using Permutations and Combinations
11.4 Using Pascal's Triangle
11.5 Counting Problems Involving "Not" and "Or"
Collaborative Investigation: Solving a Traveling Salesman Problem
Chapter 11 Test
12 Probability
12.1 Basic Concepts
12.2 Events Involving "Not" and "Or"
12.3 Conditional Probability; Events Involving "And"
12.4 Binomial Probability
12.5 Expected Value
Extension: Estimating Probabilities by Simulation
Collaborative Investigation: Finding Empirical Values of p
Chapter 12 Test
13 Statistics
13.1 Frequency Distributions and Graphs
13.2 Measures of Central Tendency
13.3 Measures of Dispersion
13.4 Measures of Position
13.5 The Normal Distribution
Extension: How to Lie with Statistics
13.6 Regression and Correlation
Collaborative Investigation: Combining Sets of Data
Chapter 13 Test
14 Personal Financial Management
14.1 The Time Value of Money
Extension: Annuities
14.2 Installment Buying
14.3 Truth in Lending
14.4 The Costs and Advantages of Home Ownership
14.5 Investing
Collaborative Investigation: To Buy or to Rent?
Chapter 14 Test