Mathematical Ideas

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

• ISBN13: 9780321043245
• ISBN10: 0321043243
• Edition: 9th
• Format: Hardcover
• Copyright: 2001-01-01
• 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	xi
The Art of Problem Solving	1	(51)
Solving Problems by Inductive Reasoning	2	(9)
An Application of Inductive Reasoning: Number Patterns	11	(10)
Strategies for Problem Solving	21	(12)
Calculating, Estimating, and Reading Graphs	33	(19)
Extension: Using Writing to Learn About Mathematics	42	(7)
Collaborative Investigation: Discovering Mathematics in Pascal's Triangle	49	(1)
Test	50	(2)
The Basic Concepts of Set Theory	52	(48)
Symbols and Terminology	53	(7)
Venn Diagrams and Subsets	60	(8)
Set Operations and Cartesian Products	68	(14)
Cardinal Numbers and Surveys	82	(7)
Infinite Sets and Their Cardinalities	89	(11)
Collaborative Investigation: A Survey of Your Class	96	(1)
Test	97	(3)
Introduction to Logic	100	(59)
Statements and Quantifiers	101	(7)
Truth Tables and Equivalent Statements	108	(12)
The Conditional and Circuits	120	(10)
More on the Conditional	130	(6)
Analyzing Arguments with Euler Diagrams	136	(10)
Extension: Logic Puzzles	141	(5)
Analyzing Arguments with Truth Tables	146	(13)
Collaborative Investigation: Logic Puzzles Revisited	157	(1)
Test	158	(1)
Numeration and Mathematical Systems	159	(49)
Historical Numeration Systems	160	(10)
Arithmetic in the Hindu-Arabic System	170	(9)
Conversion Between Number Bases	179	(11)
Finite Mathematical Systems	190	(8)
Groups	198	(10)
Collaborative Investigation: A Perpetual Calendar Algorithm	205	(1)
Test	206	(2)
Number Theory	208	(51)
Prime and Composite Numbers	209	(11)
Selected Topics from Number Theory	220	(7)
Greatest Common Factor and Least Common Multiple	227	(7)
Modular Systems	234	(10)
The Fibonacci Sequence and the Golden Ratio	244	(15)
Extension: Magic Squares	252	(5)
Collaborative Investigation: Investigating an Interesting Property of Number Squares	257	(1)
Test	258	(1)
The Real Numbers and Their Representations	259	(72)
Real Numbers, Order, and Absolute Value	260	(10)
Operations, Properties, and Applications of Real Numbers	270	(13)
Rational Numbers and Decimal Representation	283	(16)
Irrational Numbers and Decimal Representation	299	(10)
Applications of Decimals and Percents	309	(22)
Extension: Complex Numbers	322	(4)
Collaborative Investigation: Budgeting to Buy a Car	326	(1)
Test	327	(4)
The Basic Concepts of Algebra	331	(84)
Linear Equations	332	(10)
Applications of Linear Equations	342	(14)
Ratio, Proportion, and Variation	356	(14)
Linear Inequalities	370	(9)
Properties of Exponents and Scientific Notation	379	(14)
Polynomials and Factoring	393	(9)
Quadratic Equations and Applications	402	(13)
Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-Walkers?	412	(1)
Test	413	(2)
Graphs, Functions, and Systems of Equations and Inequalities	415	(105)
The Rectangular Coordinate System and Circles	416	(10)
Lines and Their Slopes	426	(11)
Equations of Lines and Linear Models	437	(10)
An Introduction to Functions: Linear Functions, Applications, and Models	447	(14)
Quadratic Functions, Applications, and Models	461	(10)
Exponential and Logarithmic Functions, Applications, and Models	471	(12)
Systems of Equations and Applications	483	(26)
Extension: Using Matrix Row Operations to Solve Systems	504	(5)
Linear Inequalities, Systems, and Linear Programming	509	(11)
Collaborative Investigation: Olympic Track and Field Results	517	(1)
Test	518	(2)
Geometry	520	(88)
Points, Lines, Planes, and Angles	522	(10)
Curves, Polygons, and Circles	532	(10)
Perimeter, Area, and Circumference	542	(14)
The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem	556	(19)
Extension: Right Triangle Trigonometry	570	(5)
Space Figures, Volume, and Surface Area	575	(10)
Non-Euclidean Geometry, Topology, and Networks	585	(12)
Chaos and Fractal Geometry	597	(11)
Collaborative Investigation: Generalizing the Angle Sum Concept	604	(1)
Test	604	(4)
Counting Methods	608	(49)
Counting by Systematic Listing	609	(10)
Using the Fundamental Counting Principle	619	(9)
Using Permutations and Combinations	628	(12)
Using Pascal's Triangle and the Binomial Theorem	640	(8)
Counting Problems Involving ``Not'' and ``Or''	648	(9)
Collaborative Investigation: Approximating Factorials Using Stirling's Formula	655	(1)
Test	656	(1)
Probability	657	(53)
Basic Concepts	658	(11)
Events Involving ``Not'' and ``Or''	669	(8)
Events Involving ``And''	677	(11)
Binomial Probability	688	(6)
Expected Value	694	(9)
Estimating Probabilities by Simulation	703	(7)
Collaborative Investigation: Finding Empirical Values of π	707	(1)
Test	708	(2)
Statistics	710	(76)
Frequency Distributions and Graphs	712	(12)
Measures of Central Tendency	724	(15)
Measures of Dispersion	739	(9)
Measures of Position	748	(8)
The Normal Distribution	756	(17)
Extension: How to Lie with Statistics	766	(7)
Regression and Correlation	773	(13)
Collaborative Investigation: Combining Sets of Data	782	(1)
Test	783	(3)
Consumer Mathematics	786	(60)
Interest and Inflation	787	(18)
Extension: Annuities	801	(4)
Consumer Credit	805	(8)
Truth in Lending	813	(9)
Buying a House	822	(12)
Investing in the Stock Market	834	(12)
Collaborative Investigation: To Buy or to Rent?	844	(1)
Test	845	(1)
Graph Theory	846	(71)
Basic Concepts	847	(16)
Euler Circuits	863	(18)
Hamilton Circuits	881	(16)
Trees and Minimum Spanning Trees	897	(20)
Collaborative Investigation: Finding the Number of Edges in a Complete Graph	911	(1)
Test	912	(5)
Voting and Apportionment	917
The Possibilities of Voting	918	(21)
The Impossibilities of Voting	939	(21)
The Possibilities of Apportionment	960	(17)
The Impossibilities of Apportionment	977
Collaborative Investigation: Class Favorites, An Election Exploration	990	(2)
Test	992
Appendix The Metric System	A-1
Answers to Selected Exercises	A-9
Credits	A-59
Index	I-1
Index of Applications	I-18