Mathematics All Around

by Pirnot, Tom

• ISBN13: 9780321356864
• ISBN10: 0321356861
• Edition: 3rd
• Format: Hardcover
• Copyright: 2007-01-01
• Publisher: Addison Wesley

Summary

Tom Pirnotbelieves 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

Preface	ix
Set Theory: Using Mathematics to Classify Objects	1	(73)
Problem Solving	2	(16)
Estimation	18	(8)
The Language of Sets	26	(8)
Comparing Sets	34	(8)
Set Operations	42	(12)
Survey Problems	54	(20)
Chapter Summary	64	(2)
Chapter Review Exercises	66	(2)
Chapter Test	68	(1)
Of Further Interest: Infinite Sets	69	(5)
Logic: The Study of What's True or False or Somewhere in Between	74	(71)
Inductive and Deductive Reasoning	75	(8)
Statements, Connectives, and Quantifiers	83	(10)
Truth Tables	93	(12)
The Conditional and Biconditional	105	(9)
Verifying Arguments	114	(9)
Using Euler Diagrams to Verify Syllogisms	123	(22)
Chapter Summary	131	(3)
Chapter Review Exercises	134	(1)
Chapter Test	135	(2)
Of Further Interest: Fuzzy Logic	137	(8)
Graph Theory (Networks): The Mathematics of Relationships	145	(50)
Graphs, Puzzles, and Map Coloring	146	(15)
The Traveling Salesperson Problem	161	(11)
Directed Graphs	172	(23)
Chapter Summary	181	(2)
Chapter Review Exercises	183	(1)
Chapter Test	184	(2)
Of Further Interest: Scheduling Projects Using PERT	186	(9)
Numeration Systems: Does It Matter How We Name Numbers?	195	(47)
The Evolution of Numeration Systems	196	(9)
Place Value Systems	205	(10)
Calculating in Other Bases	215	(27)
Chapter Summary	229	(1)
Chapter Review Exercises	230	(1)
Chapter Test	231	(1)
Of Further Interest: Modular Systems	232	(10)
Number Theory and the Real Number System: Understanding the Numbers All Around Us	242	(72)
Number Theory	243	(11)
The Integers	254	(8)
The Rational Numbers	262	(13)
The Real Number System	275	(12)
Exponents and Scientific Notation	287	(27)
Chapter Summary	298	(2)
Chapter Review Exercises	300	(1)
Chapter Test	301	(2)
Of Further Interest: Sequences	303	(11)
Algebraic Models: How Do We Approximate Reality?	314	(78)
Linear Equations	315	(13)
Modeling with Linear Equations	328	(10)
Modeling with Quadratic Equations	338	(9)
Exponential Equations and Growth	347	(12)
Proportions and Variation	359	(8)
Functions	367	(25)
Chapter Summary	378	(2)
Chapter Review Exercises	380	(2)
Chapter Test	382	(2)
Of Further Interest: Dynamical System	384	(8)
Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?	392	(34)
Systems of Linear Equations	393	(13)
Systems of Linear Inequalities	406	(20)
Chapter Summary	416	(1)
Chapter Review Exercises	417	(1)
Chapter Test	417	(1)
Of Further Interest: Linear Programming	418	(8)
Geometry. Ancient and Modern Mathematics Embrace	426	(87)
Lines, Angles, and Circles	427	(10)
Polygons	437	(11)
Perimeter and Area	448	(13)
Volume and Surface Area	461	(9)
The Metric System and Dimensional Analysis	470	(12)
Geometric Symmetry and Tessellations	482	(31)
Chapter Summary	497	(3)
Chapter Review Exercises	500	(2)
Chapter Test	502	(2)
Of Further Interest: Fractals	504	(9)
Apportionment: How Do We Measure Fairness?	513	(57)
Understanding Apportionment	514	(11)
The Huntington-Hill Apportionment Principle	525	(7)
Applications of the Apportionment Principle	532	(8)
Other Paradoxes and Apportionment Methods	540	(30)
Chapter Summary	556	(2)
Chapter Review Exercises	558	(1)
Chapter Test	559	(2)
Of Further Interest: Fair Division	561	(9)
Voting: Using Mathematics to Make Choices	570	(48)
Voting Methods	571	(11)
Defects in Voting Methods	582	(13)
Weighted Voting Systems	595	(23)
Chapter Summary	605	(1)
Chapter Review Exercises	606	(2)
Chapter Test	608	(2)
Of Further Interest: The Shapley-Shubik Index	610	(8)
Consumer Mathematics: The Mathematics of Everyday Life	618	(62)
Percent	619	(8)
Interest	627	(13)
Consumer Loans	640	(9)
Annuities	649	(8)
Amortization	657	(23)
Chapter Summary	668	(3)
Chapter Review Exercises	671	(1)
Chapter Test	671	(2)
Of Further Interest: The Annual Percentage Rate	673	(7)
Counting: Just How Many Are There?	680	(40)
Introduction to Counting Methods	681	(9)
The Fundamental Counting Principle	690	(8)
Permutations and Combinations	698	(22)
Chapter Summary	712	(1)
Chapter Review Exercises	713	(1)
Chapter Test	713	(2)
Of Further Interest: Counting and Gambling	715	(5)
Probability: What Are the Chances?	720	(60)
The Basics of Probability Theory	721	(16)
Complements and Unions of Events	737	(8)
Conditional Probability and Intersections of Events	745	(16)
Expected Value	761	(19)
Chapter Summary	770	(1)
Chapter Review Exercises	771	(1)
Chapter Test	772	(1)
Of Further Interest: Binomial Experiments	773	(7)
Descriptive Statistics: What a Data Set Tells Us	780	(67)
Organizing and Visualizing Data	781	(13)
Measures of Central Tendency	794	(13)
Measures of Dispersion	807	(12)
The Normal Distribution	819	(28)
Chapter Summary	834	(2)
Chapter Review Exercises	836	(1)
Chapter Test	837	(1)
Of Further Interest: Linear Correlation	838	(9)
Appendix A	847	(4)
Answers to Quiz Yourself Problems	851	(8)
Answers to Exercises	859
Photo Credits	1	(1)
Index	1