Mathematics All Around

by Pirnot, Tom

• ISBN13: 9780201795110
• ISBN10: 0201795116
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Addison Wesley

Summary

"Tom Pirnot" believes that conceptual understanding is the key to a student' s success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that they encounter daily, transforming them into mathematically aware citizens.

Table of Contents

Set Theory: Using Mathematics to Classify Objects	1	(67)
Problem Solving	2	(14)
Estimation	16	(7)
The Language of Sets	23	(7)
Comparing Sets	30	(8)
Set Operations	38	(12)
Survey Problems	50	(18)
Chapter Summary	58	(3)
Chapter Test	61	(2)
Of Further Interest: Infinite Sets	63	(5)
Logic: The Study of What's True or False or Somewhere in Between	68	(72)
Inductive and Deductive Reasoning	69	(9)
Statements, Connectives, and Quantifiers	78	(10)
Truth Tables	88	(12)
The Conditional and Biconditional	100	(10)
Verifying Arguments	110	(9)
Using Euler Diagrams to Verify Syllogisms	119	(21)
Chapter Summary	127	(2)
Chapter Test	129	(3)
Of Further Interest: Fuzzy Logic	132	(8)
Graph Theory: The Mathematics of Relationships	140	(54)
Graphs, Puzzles, and Map Coloring	141	(18)
The Traveling Salesperson Problem	159	(12)
Directed Graphs	171	(23)
Chapter Summary	180	(2)
Chapter Test	182	(2)
Of Further Interest: Scheduling Projects Using PERT	184	(10)
Numeration Systems: Does It Matter How We Name Numbers?	194	(50)
The Evolution of Numeration Systems	195	(11)
Place Value Systems	206	(11)
Calculating in Other Bases	217	(27)
Chapter Summary	230	(2)
Chapter Test	232	(1)
Of Further Interest: Modular Systems	233	(11)
Number Theory and the Real Number System: Understanding the Numbers All Around Us	244	(75)
Number Theory	245	(12)
The Integers	257	(9)
The Rational Numbers	266	(14)
The Real Number System	280	(12)
Exponents and Scientific Notation	292	(27)
Chapter Summary	303	(3)
Chapter Test	306	(1)
Of Further Interest: Sequences	307	(12)
Algebraic Models: How Do We Approximate Reality?	319	(65)
Linear Equations	320	(13)
Modeling with Linear Equations	333	(9)
Modeling with Quadratic Equations	342	(9)
Exponential Equations and Growth	351	(12)
Proportions and Variation	363	(21)
Chapter Summary	371	(3)
Chapter Test	374	(2)
Of Further Interest: Dynamical Systems	376	(8)
Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?	384	(36)
Systems of Linear Equations	385	(14)
Systems of Linear Inequalities	399	(21)
Chapter Summary	409	(1)
Chapter Test	410	(1)
Of Further Interest: Linear Programming	411	(9)
Geometry: Ancient and Modern Mathematics Embrace	420	(87)
Lines, Angles, and Circles	421	(10)
Polygons	431	(11)
Perimeter and Area	442	(13)
Volume and Surface Area	455	(9)
The Metric System and Dimensional Analysis	464	(12)
Geometric Symmetry and Tessellations	476	(31)
Chapter Summary	491	(4)
Chapter Test	495	(2)
Of Further Interest: Fractals	497	(10)
Apportionment: How Do We Measure Fairness?	507	(59)
Understanding Apportionment	508	(11)
The Huntington--Hill Apportionment Principle	519	(7)
Applications of the Apportionment Principle	526	(9)
Other Paradoxes and Apportionment Methods	535	(31)
Chapter Summary	551	(3)
Chapter Test	554	(2)
Of Further Interest: Fair Division	556	(10)
Voting: Using Mathematics to Make Choices	566	(48)
Voting Methods	567	(12)
Defects in Voting Methods	579	(14)
Weighted Voting Systems	593	(21)
Chapter Summary	602	(2)
Chapter Test	604	(2)
Of Further Interest: The Shapley-Shubik Index	606	(8)
Consumer Mathematics: The Mathematics of Everyday Life	614	(63)
Percent	615	(8)
Interest	623	(14)
Consumer Loans	637	(8)
Annuities	645	(9)
Amortization	654	(23)
Chapter Summary	665	(3)
Chapter Test	668	(2)
Of Further Interest: The Annual Percentage Rate	670	(7)
Counting: Just How Many Are There?	677	(39)
Introduction to Counting Methods	678	(9)
The Fundamental Counting Principle	687	(8)
Permutations and Combinations	695	(21)
Chapter Summary	709	(1)
Chapter Test	710	(1)
Of Further Interest: Counting and Gambling	711	(5)
Probability: What Are the Chances?	716	(59)
The Basics of Probability Theory	717	(18)
Complements and Unions of Events	735	(8)
Conditional Probability and Intersections of Events	743	(14)
Expected Value	757	(18)
Chapter Summary	765	(2)
Chapter Test	767	(1)
Of Further Interest: Binomial Experiments	768	(7)
Descriptive Statistics: What a Data Set Tells Us	775	(74)
Organizing and Visualizing Data	776	(15)
Measures of Central Tendency	791	(15)
Measures of Dispersion	806	(13)
The Normal Distribution	819	(30)
Chapter Summary	834	(2)
Chapter Test	836	(2)
Of Further Interest: Linear Correlation	838	(11)
Answers to Quiz Yourself Problems	849	(10)
Answers to Exercises	859	(46)
Photo Credits	905
Index	1