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Mathematical Ideas Expanded Edition,9780201793918
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Mathematical Ideas Expanded Edition

by ; ;
Edition:
11th
ISBN13:

9780201793918

ISBN10:
0201793911
Format:
Hardcover
Pub. Date:
1/1/2008
Publisher(s):
Addison Wesley

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Summary

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 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, chapter summaries are made more intuitive to aid review, and chapter tests now include specific section references, making it easier for students to refer back to topics that need more attention. With great care and effort, the authors have crafted this new edition to serve the needs of today's students and instructors.

Table of Contents

Preface ix
The Art of Problem Solving
1(48)
Solving Problems by Inductive Reasoning
2(8)
An Application of Inductive Reasoning: Number Patterns
10(10)
Strategies for Problem Solving
20(11)
Calculating, Estimating, and Reading Graphs
31(18)
Extension: Using Writing to Learn About Mathematics
40(6)
Collaborative Investigation: Discovering Mathematics in Pascal's Triangle
46(1)
Chapter 1 Test
47(2)
The Basic Concepts of Set Theory
49(45)
Symbols and Terminology
50(6)
Venn Diagrams and Subsets
56(7)
Set Operations and Cartesian Products
63(13)
Cardinal Numbers and Surveys
76(7)
Infinite Sets and Their Cardinalities
83(11)
Collaborative Investigation: A Survey of Your Class
90(1)
Chapter 2 Test
91(3)
Introduction to Logic
94(57)
Statements and Quantifiers
95(7)
Truth Tables and Equivalent Statements
102(11)
The Conditional and Circuits
113(10)
More on the Conditional
123(6)
Analyzing Arguments with Euler Diagrams
129(7)
Extension: Logic Puzzles
133(3)
Analyzing Arguments with Truth Tables
136(15)
Collaborative Investigation: Logic Puzzles Revisited
148(1)
Chapter 3 Test
149(2)
Numeration and Mathematical Systems
151(44)
Historical Numeration Systems
152(8)
Arithmetic in the Hindu-Arabic System
160(9)
Conversion Between Number Bases
169(10)
Finite Mathematical Systems
179(7)
Groups
186(9)
Collaborative Investigation: A Perpetual Calendar Algorithm
193(1)
Chapter 4 Test
194(1)
Number Theory
195(52)
Prime and Composite Numbers
196(10)
Selected Topics from Number Theory
206(6)
Greatest Common Factor and Least Common Multiple
212(8)
Clock Arithmetic and Modular Systems
220(12)
The Fibonacci Sequence and the Golden Ratio
232(15)
Extension: Magic Squares
240(4)
Collaborative Investigation: Investigating an Interesting Property of Number Squares
244(1)
Chapter 5 Test
245(2)
The Real Numbers and Their Representations
247(67)
Real Numbers, Order, and Absolute Value
248(9)
Operations, Properties, and Applications of Real Numbers
257(13)
Rational Numbers and Decimal Representation
270(13)
Irrational Numbers and Decimal Representation
283(10)
Applications of Decimals and Percents
293(21)
Extension: Complex Numbers
306(4)
Collaborative Investigation: Budgeting to Buy a Car
310(1)
Chapter 6 Test
311(3)
The Basic Concepts of Algebra
314(79)
Linear Equations
315(10)
Applications of Linear Equations
325(14)
Ratio, Proportion, and Variation
339(13)
Linear Inequalities
352(8)
Properties of Exponents and Scientific Notation
360(12)
Polynomials and Factoring
372(9)
Quadratic Equations and Applications
381(12)
Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?
390(1)
Chapter 7 Test
391(2)
Graphs, Functions, and Systems of Equations and Inequalities
393(98)
The Rectangular Coordinate System and Circles
394(8)
Lines and Their Slopes
402(10)
Equations of Lines and Linear Models
412(10)
An Introduction to Functions: Linear Functions, Applications, and Models
422(12)
Quadratic Functions, Applications, and Models
434(10)
Exponential and Logarithmic Functions, Applications, and Models
444(12)
Systems of Equations and Applications
456(25)
Extension: Using Matrix Row Operations to Solve Systems
476(5)
Linear Inequalities, Systems, and Linear Programming
481(10)
Collaborative Investigation: Living with AIDS
488(1)
Chapter 8 Test
489(2)
Geometry
491(85)
Points, Lines, Planes, and Angles
492(10)
Curves, Polygons, and Circles
502(10)
Extension: Geometric Constructions
509(3)
Perimeter, Area, and Circumference
512(11)
The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
523(13)
Space Figures, Volume, and Surface Area
536(9)
Transformational Geometry
545(11)
Non-Euclidean Geometry, Topology, and Networks
556(11)
Chaos and Fractal Geometry
567(9)
Collaborative Investigation: Generalizing the Angle Sum Concept
573(1)
Chapter 9 Test
574(2)
Trigonometry
576(53)
Angles and Their Measures
577(5)
Trigonometric Functions of Angles
582(4)
Trigonometric Identities
586(5)
Right Triangles and Function Values
591(9)
Applications of Right Triangles
600(8)
The Laws of Sines and Cosines; Area Formulas
608(12)
The Unit Circle and Graphs
620(9)
Collaborative Investigation: Making a Point About Trigonometric Function Values
626(1)
Chapter 10 Test
627(2)
Counting Methods
629(44)
Counting by Systematic Listing
630(7)
Using the Fundamental Counting Principle
637(9)
Using Permutations and Combinations
646(12)
Using Pascal's Triangle and the Binomial Theorem
658(6)
Counting Problems Involving ``Not'' and ``Or''
664(9)
Collaborative Investigation: Approximating Factorials Using Stirling's Formula
671(1)
Chapter 11 Test
672(1)
Probability
673(50)
Basic Concepts
674(10)
Events Involving ``Not'' and ``Or''
684(7)
Events Involving ``And''
691(10)
Binomial Probability
701(6)
Expected Value
707(9)
Estimating Probabilities by Simulation
716(7)
Collaborative Investigation: Finding Empirical Values of π
720(1)
Chapter 12 Test
721(2)
Statistics
723(65)
Frequency Distributions and Graphs
725(10)
Measures of Central Tendency
735(13)
Measures of Dispersion
748(8)
Measures of Position
756(7)
The Normal Distribution
763(15)
Extension: How to Lie with Statistics
771(7)
Regression and Correlation
778(10)
Collaborative Investigation: Combining Sets of Data
784(1)
Chapter 13 Test
785(3)
Consumer Mathematics
788(62)
The Time Value of Money
789(17)
Extension: Annuities
802(4)
Consumer Credit
806(7)
Truth in Lending
813(9)
Purchasing a House
822(10)
Investing
832(18)
Collaborative Investigation: To Buy or to Rent?
848(1)
Chapter 14 Test
849(1)
Graph Theory (available only in the expanded tenth edition)
850(61)
Basic Concepts
851(14)
Euler Circuits
865(15)
Hamilton Circuits
880(14)
Trees and Minimum Spanning Trees
894(17)
Collaborative Investigation: Finding the Number of Edges in a Complete Graph
906(2)
Chapter 15 Test
908(3)
Voting and Apportionment (available only in the expanded tenth edition)
911(1)
The Possibilities of Voting
912(18)
The Impossibilities of Voting
930(17)
The Possibilities of Apportionment
947(15)
The Impossibilities of Apportionment
962(13)
Collaborative Investigation: Class Favorites, an Election Exploration
975(2)
Chapter 16 Test
977
Appendix The Metric System 1(8)
Answers to Selected Exercises 9(56)
Credits 65
Index 1(18)
Index of Applications 19


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