Mathematical Ideas Expanded Edition

by Miller, Charles D.; Heeren, Vern E.; Hornsby, John

• ISBN13: 9780201793918
• ISBN10: 0201793911
• Edition: 11th
• Format: Hardcover
• Copyright: 2008-01-01
• Publisher: Addison Wesley

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