由Thomas L.Pirnot编著的Mathematics All Around一书是为从事社会科学、教育学、商业、艺术和其他非理工类专业的学生而写的教学教科书。本书可以使从事这些专业的学生理解并欣赏到数学在各个领域的许多精彩应用。

全书贯穿着强烈的应用意识，使数学理论紧密联系政治、经济、体育、艺术、医学、生物、科技、环境等方面的实际问题，这在国内外数学教科书中是不多见的。本书还从教育学的角度对叙述方式和版面作了精心安排，使得所有概念和理论都由浅入深，因此本书在阅读时易读好懂。

本书是为从事社会科学、教育学、商业、艺术和其他非理工类专业的学生而写的数学教科书，可以使从事这些专业的学生理解并欣赏到数学在各个领域的许多精彩应用。内容包括集合论、数理逻辑、图论、数论、统计、概率、代数、几何等。全书以数学的应用作为动机，每一章的开始提出实际问题，然后发展必要的数学工具，再解决这些实际问题，在应用中进一步加强对数学的理解。全书贯穿着强烈的应用意识，这在国内外数学教科书中是不多见的。

出版说明

序

SET THEORY: Using Mathematics to Classify Objects

1.1 Problem Solving

1.2 Estimafion

1.3 The Language of Sets

1.4 Comparing Sets

1.5 Set Operafions

1.6 Survey Problems

Chapter Summary

Chapter Test

Of FurtherInterest: Infinite Sets

LOGIC: The Study of What's True or False or Somewhere in Between

2.1 Inductive and Deductive Reasoning

2.2 Statements, Connectives, and Quantifiers

2.3 Thumb Tables

2.4 The Conditional and Biconditional

2.5 Veilfying Arguments

2.6 Using Euler Diagrams to Verify Syllogisms

Chapter Summary

Chapter Test

Of Further Interest: Fuzzy Logic

GRAPH THEORY: The Mathematics of Relationships

3.1 Graphs, Puzzles, and Map Coloring

3.2 The Traveling Salesperson Problem

3.3 Directed Graphs

Chapter Summary

Chapter Test

Of Further Interest: Scheduling Projects Using PERT

NUMERATION SYSTEMS: Does It Matter How We Name Numbers?

4.1 The Evolution of Numeration Systems

4.2 Place Volume Systems

4.3 Calculating in Other Bases

Chapter Summary

Chapter Test

Of Further Interest: Modular Systems

NUMBER THEORY AND THE REAL NUMBER SYSTEM: Understanding the Numbers All Around Us

5.1 Number Theory

5.2 The Integers

5.3 The Rational Numbers

5.4 The Real Number System

5.5 Exponents and Scientific Notation

Chapter Summary

Chapter Test

Of Further Interest: Sequences

ALGEBRAIC MODELS: How Do We Approximate Reality?

6.1 Linear Equations

6.2 Modeling with Linear Equations

6.3 Modeling with Quadratic Equations

6.4 Exponential Equations and Growth

6.5 Proportions and Variation

Chapter Summary

Chapter Test

Of Further Interest: Dynamical Systems

MODELING WITH SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES: What's the Best Way to Do It?

7.1 Systems of Linear Equations

7.2 Systems of Linear Inequalities

Chapter Summary

Chapter Test

Of Further Interest: Linear Programming

GEOMETRY: Ancient and Modern Mathematics Embrace

8.1 Lines, Angles, and Circles

8.2 Polygons

8.3 Perimeter and Area

8.4 Volume and Surface Area

8.5 The Metric System and Dimensional Analysis

8.6 Geometric Symmetry and Tessellations

Chapter Summary

Chapter Test

Of Further Interest: Fractals

APPORTIONMENT How Do We Measure Fairness?

9.1 Understanding Apportionment

9.2 The Huntington—Hill Apportionment Principle

9.3 Applications of the Apportionment Principle

9.4 Other Paradoxes and Apportionment Methods

Chapter Summary

Chapter Test

Of Further Interest: Fair Division

VOTING: Using Mathematics to Make Choices

10.1 Voting Methods

10.2 Defects in Voting Methods

10.3 Weighted Voting Systems

Chapter Summary

Chapter Test

Of Further Interest: The Shapley-Shubik Index

CONSUMER MATHEMATICS: The Mathematics of Everyday Life

11.1 Percent

11.2 Interest

11.3 ConsumerLoans

11.4 Annuities

11.5 Amortization

Chapter Summary

Chapter Test

Of Further Interest: The Annual Percentage Rate

COUNTING: Just How Many Are There?

12.1 Introduction to Counting Methods

12.2 The Fundamental Counting Principle

12.3 Permutations and Combinations

Chapter Summary

Chapter Test

Of Further Interest: Counting and Gambling

PROBABI LITY: What Are the Chances?

13.1 The Basics of Probability Theory

13.2 Complements and Unions of Events

13.3 Conditional Probability and Intersections of Events

13.4 Expected Value

Chapter Summary

Chapter Test

Of Further Interest: Binomial Experiments

DESCRIPTIVE STATISTICS: What a Data Set Tells Us

14.1 Organizing and Visualizing Data

14.2 Measures of Central Tendency

14.3 Measures of Dispersion

14.4 The Normal Distfibution

Chapter Summary

Chapter Test

Of Further Interest: Linear Correlation

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