9780201308150

Mathematics All Around

by
  • ISBN13:

    9780201308150

  • ISBN10:

    0201308150

  • Format: Hardcover
  • Copyright: 1/1/2001
  • Publisher: Addison Wesley
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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(61)
Problem Solving
2(14)
The Language of Sets
16(7)
Comparing Sets
23(7)
Set Operations
30(12)
Survey Problems
42(20)
Chapter Summary
51(2)
Chapter Test
53(2)
Of Further Interest: Fuzzy Sets
55(7)
Logic: The Study of What's True or False or Somewhere in Between
62(68)
Statements, Connectives, and Quantifiers
63(12)
Truth Tables
75(13)
The Conditional and Biconditional
88(9)
Verifying Arguments
97(11)
Using Euler Diagrams to Verify Syllogisms
108(22)
Chapter Summary
116(3)
Chapter Test
119(2)
Of Further Interest: Fuzzy Logic
121(9)
Graph Theory: The Mathematics of Relationships
130(72)
Graphs, Puzzles, and Map Coloring
131(21)
The Traveling Salesperson Problem
152(14)
Directed Graphs
166(11)
Scheduling Projects Using PERT
177(25)
Chapter Summary
189(3)
Chapter Test
192(4)
Of Further Interest: Finite State Machines
196(6)
Legislative Apportionment: How Do We Measure Fairness?
202(51)
Understanding Apportionment
203(9)
Inequalities
212(4)
The Huntington-Hill Apportionment Principle
216(8)
Apportioning a Representative Board
224(8)
Other Applications of Apportionment
232(21)
Chapter Summary
239(1)
Chapter Test
240(2)
Of Further Interest: Fair Division
242(11)
Voting: Using Mathematics to Make Choices
253(53)
Voting Methods
254(13)
Defects in Voting Methods
267(16)
Weighted Voting Systems
283(23)
Chapter Summary
293(2)
Chapter Test
295(3)
Of Further Interest: The Shapley-Shubik Index
298(8)
Consumer Mathematics: The Mathematics of Everyday Life
306(56)
Interest
307(14)
Consumer Loans
321(10)
Annuities
331(9)
Amortization
340(22)
Chapter Summary
351(2)
Chapter Test
353(2)
Of Further Interest: The Annual Percentage Rate
355(7)
Data: How Do We Know What Is True?
362(407)
Surveys and Survey Biases
363(10)
Determining the Accuracy of Surveys
373(26)
Chapter Summary
388(1)
Chapter Test
389(2)
Of Further Interest: Experiments
391(8)
Descriptive Statistics: What a Data Set Tells Us
Organizing and Visualizing Data
399(13)
Measures of Central Tendency
412(15)
Measures of Dispersion
427(14)
The Normal Distribution
441(27)
Chapter Summary
455(2)
Chapter Test
457(2)
Of Further Interest: Linear Correlation
459(9)
Counting: Just How Many Are There?
Introduction to Counting Methods
468(9)
The Fundamental Counting Principle
477(8)
Permutations and Combinations
485(10)
Pascal's Triangle
495(15)
Chapter Summary
502(1)
Chapter Test
503(1)
Of Further Interest: Counting and Gambling
504(6)
Probability: What Are the Chances?
The Basics of Probability Theory
510(17)
Complements and Unions of Events
527(8)
Conditional Probability and Intersections of Events
535(12)
Expected Value
547(19)
Chapter Summary
555(1)
Chapter Test
556(2)
Of Further Interest: Binomial Experiments
558(8)
Algebraic Models: How Do We Approximate Reality?
Linear Equations
566(13)
Modeling with Linear Equations
579(11)
Modeling with Quadratic Equations
590(9)
Exponential Equations and Growth
599(26)
Chapter Summary
613(1)
Chapter Test
614(2)
Of Further Interest: Dynamical Systems
616(9)
Geometry: Ancient and Modern Mathematics Embrace
Lines, Angles, and Circles
625(11)
Polygons
636(12)
Perimeter and Area
648(16)
Volume and Surface Area
664(11)
Geometric Symmetry and Tessellations
675(37)
Chapter Summary
694(3)
Chapter Test
697(4)
Of Further Interest: Fractals
701(11)
Matrices: Calculating with Tables of Numerical Information
Matrix Terminology and Operations
712(10)
Matrix Multiplication
722(10)
Transformational Geometry
732(12)
More Transformations and Homogeneous Coordinates
744(25)
Chapter Summary
755(2)
Chapter Test
757(2)
Of Further Interest: Matrices and Directed Graphs
759(10)
Answers to Quiz Yourself 769(10)
Answers to Exercises 779
Index I-1

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