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内容简介
本书最为难能可贵的是始终贯穿着强烈的应用意识，即把数学理论紧密地与政治、经济、体育、艺术、医学、生物、科技、环境等实际问题相结合，这在国内外数学教科书中是不多见的。本书内容包括集合论、数理逻辑、图论、运筹、统计、概率、排列组合、代数、几何和矩阵等。书中每一章的开始提出实际问题，然后发展必要的数学工具，解决问题，从而在应用中进一步加强对数学的理解。讨论的问题涉及日常生活，如信用卡购物、年利率计算、运动队成绩的评价等；也有著名的数学问题，如四色问题等；还有数学在高新技术中的应用。众多的应用问题使本书变得趣味横生。
本书主要可作为非理工类专业师生的教科书，也可作为理工类师生、工程技术人员、管理人员的参考书。
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顾客评论
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目录
目 录 1 SET THEORY: Using Mathematics to Classify Objects 1 l.l Problem Solving 2 l.2 The Language of Sets 16 1.3 Comparing Sets 23 l.4 Set Operations 30 l.5 Survey Problems 42 Chapter Sununary 51 ChaPterTest 53 Of Further Interest: Fuzzy Sets 55 2 LOGIC: The Study of What''''S TFue or False or Somewhere in Between 62 2.l Statements, Connectives, and Quanhfiers 63 2.2 TruthTables 75 2.3 The Conditional and Biconditional 88 2.4 VerifyingArguments 97 2.5 Using Euler Diagrams to Verify Syllogisms 108 ChaPter Summary 116 ChaPterTest 119 Of Further Interest: Fuzzy Logic I21 3 GRAPH THEORY: The Mathematics of Relationships 130 3.l Graphs, Puzzles, and Map Coloring 131 3.2 The Traveling Salesperson Problem 152 3.3 Directed Graphs 166 3.4 Scheduling Projects Using PERT 177 Chapter Summary 189 ChapterTest 192 Of Further Interest: Finite State Machines 196 4 LEGISLATIVE APPORTIONMENT: How Do We Measure Fairness 202 4.1 Understandin g Apportionment 203 4.2 Inequalities 212 4.3 The Huntington-Hill Apportionment Principle 216 4.4 Apponioning a Representative Board 224 4.5 Other Applicahons of Apponionment 232 Chapter Sununary 239 ChapterTest 240 Of Further Interest: Fair Division 242 5 VOTING: Using Mathematics to Make Choices 2S3 5.l Voting Methods 254 5.2 Defects in Voting Methods 267 5.3 WeightedVoting Systems 283 Chapter Sununary 293 Chapter Test 295 Of Further Interest: The Shapley-Shubik Index 298 6 CONSUMER MATHEMATlCS: The Mathematic: of Everyday Life 306 6.1 Interest 307 6.2 ConsumerLoans 321 6.3 Annuities 331 6.4 Amortization 340 Chapter Summary 351 ChapterTest 353 Of Further Interest: The Annual Percentage Rate 355 7 DATA: How Do We Know What Is TFue 362 7.l Surveys and Survey Biases 363 7.2 Detendning the Accuracy of Surveys 373 Chapter Sununary 388 ChapterTest 389 Of Further Interest: Experiments 391 8 DESCRIPTIVE STATISTICS: What a Data Set Tells Us 8.l Organizing and Visualizing Data 399 8.2 Measures of Central Tendency 412 8.3 Measures of Dispersion 427 8.4 The Normal Distribution 441 Chapter Sununary 455 Chapter Test 4S7 Of Further Interest: Linear Correlation 459 9 COUNTING: Just How Many Are There 9.1 Introduction to Counting Methods 468 9.2 The Fundamental Counting Principle 477 9.3 Permutations and Combinations 485 9.4 Pascal''''s Triangle 495 Chapter Sununary 502 Chapter Test 503 Of Further Interest: Counting and Gambling 504 10 PROBABILITY: What Are the Chances l0.l The Basics of Probability Theory 510 l0.2 Complements and Unions of Events 527 10.3 Conditional Probability and Intersechons of Events 535 10.4 ExpectedValue 547 Chapter Surnmary S55 ChapterTest 556 Of Further Interest. Binomial Experiments 558 11 ALGEBRAIC MODELS: How Do we Approximate Reality ll.1 Linear Equations 566 l1.2 Modeling with Linear Equations 579 1l.3 Modeling with Quadratic Equations 590 11.4 Exponential Equations and Growth 599 Chapter Summary 613 Chapter Test 6I4 Of Further Interest: Dynamical Systems 6I6 12 GEOMETRY Ancient and Modern Mathematics Embrace 12.l Lines, Angles, and Circles 625 l2.2 Polygons 636 l2.3 Perimeter and Area 648 l2.4 Volume and Sdse Area 664 l2.5 Geometric Synunetry and Tessellations 675 Chapter Summary 694 Chapter Test co7 Of Further Interet: Fractals 701 13 MATRICES: Calculating with Tables of Numerical Information l3.l Matrix Terminology and Operations 712 13.2 MatrixMultiPlication 722 13.3 Transformational Geometry 732 l3.4 More Transformahons and Homogeneous Coordinates Chapter Sunnnmp 755 Chapter Test 757 Of Fuhaer Interest. Matrices and Directed Graphs Answers to QuizYourself 769 Answers to Exercises 779 Index I-1
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