身邊的數(shù)學(xué)

前言

由Thomas L.Pirnot編著的Mathematics Au Around一書是為從事社會科學(xué)、教育學(xué)、商業(yè)、藝術(shù)和其他非理工類專業(yè)的學(xué)生而寫的教學(xué)教科書。本書可以使從事這些專業(yè)的學(xué)生理解并欣賞到數(shù)學(xué)在各個領(lǐng)域的許多精彩應(yīng)用。本書共14章，內(nèi)容包括集合論、數(shù)理邏輯、圖論、數(shù)論、統(tǒng)計、概率、代數(shù)、幾何等。全書以數(shù)學(xué)的應(yīng)用作為動機，每一章的開始提出實際問題，然后發(fā)展必要的數(shù)學(xué)工具，再解決這些實際問題，在應(yīng)用中進一步加強對數(shù)學(xué)的理解。因此提出問題和解決問題占本書很大篇幅。眾多應(yīng)用問題中有些聯(lián)系日常生活：如信用卡購物問題，分期付款與抵押貸款問題，年利率的計算，運動隊成績的評價，彩票獲獎的幾率，股票市場中的決策問題，疾病的傳播問題，席位的公平分配問題，唱片銷售的回歸模型等；有些是著名的數(shù)學(xué)問題：如四色問題，TSP問題（Traveling Salesman Problem）；也有些是數(shù)學(xué)在高新技術(shù)中的應(yīng)用問題：如模糊邏輯用于空調(diào)系統(tǒng)，矩陣用于醫(yī)學(xué)計算機成像、圖形加速和計算機圖形學(xué)，分形用于人體中血管、氣管的研究，用于創(chuàng)作逼真的自然景觀。總之它們使本書變得越味橫生。全書貫穿著強烈的應(yīng)用意識，使數(shù)學(xué)理論緊密聯(lián)系政治、經(jīng)濟、體育、藝術(shù)、醫(yī)學(xué)、生物、科技、環(huán)境等方面的實際問題，這在國內(nèi)外數(shù)學(xué)教科書中是不多見的。本書還從教育學(xué)的角度對敘述方式和版面作了精心安排，使得所有概念和理論都由淺人深，因此本書在閱讀時易讀好懂。為了引導(dǎo)學(xué)生掌握正確的學(xué)習(xí)方法，作者還在第一章的第一節(jié)討論了解決實際數(shù)學(xué)應(yīng)用問題的策略和原則，并提供用以下方式來解決數(shù)學(xué)問題：1.畫圖；2.用自己的語言敘述問題；3.理清問題的條理；4.找規(guī)律；5.簡化問題；6.猜想；7.將新問題變?yōu)槔蠁栴}。本書除了可作為社會科學(xué)、教育學(xué)、商業(yè)、藝術(shù)等文科專業(yè)的教材以外，還可以作為理工類學(xué)生、教師、工程技術(shù)人員和管理工作者的參考書或工具書。

內(nèi)容概要

本書是為從事社會科學(xué)、教育學(xué)、商業(yè)、藝術(shù)和其他非理工類專業(yè)的學(xué)生而寫的數(shù)學(xué)教科書，可以使從事這些專業(yè)的學(xué)生理解并欣賞到數(shù)學(xué)在各個領(lǐng)域的許多精彩應(yīng)用。內(nèi)容包括集合論、數(shù)理邏輯、圖論、數(shù)論、統(tǒng)計、概率、代數(shù)、幾何等。全書以數(shù)學(xué)的應(yīng)用作為動機，每一章的開始提出實際問題，然后發(fā)展必要的數(shù)學(xué)工具，再解決這些實際問題，在應(yīng)用中進一步加強對數(shù)學(xué)的理解。全書貫穿著強烈的應(yīng)用意識，這在國內(nèi)外數(shù)學(xué)教科書中是不多見的。

作者簡介

作者：(美國)皮納德

書籍目錄

出版說明序1 SET THEORY: Using Mathematics to Classify Objects   1.1 Problem Solving   1.2 Estimation   1.3 The Language of Sets   1.4 Comparing Sets   1.5 Set Operations   1.6 Survey Problems 　Chapter Summary 　Chapter Test 　Of Further Interest: Infinite Sets 2 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 Truth Tables   2.4 The Conditional and Biconditional   2.5 Verifying Arguments   2.6 Using Euler Diagrams to Verify Syllogisms 　Chapter Summary 　Chapter Test 　Of Further Interest: Fuzzy Logic 3 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 PERT4 NUMERATION SYSTEMS: Does it Matter How We Name Numbers?   4.1 The Evolution of Numeration Systems   4.2 Place Value Systems   4.3 Calculating in Other Bases 　Chapter Summary 　Chapter Test 　Of Further Interest:Modular Systems 5  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 6 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 7 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   ……8 GEOMETRY:Ancient and Modern Mathematics Embrace9 APPORTIONMENT:How Do We Measure Fairness?10 VOTING:Using Mathematics to Make Choices11 CONSUMER MATHEMATICS:The Mathematics of Everyday Life12 COUNTING:Just How Many Are There?13 PROBABILITY:What Are the Chances?14 DESCRIPTIVE STATISTICS:What a Data Set Tells Us

章節(jié)摘錄

插圖：Little was done to develop the theory of counting until the sixteenth century, when mathematicians began to analyze games of chance. While answering questions about throwing dice and drawing cards, a group of Eu- ropean mathematicians began to organize their results into a formal theory of counting. One of the most prominent figures in this development was the French- man Blaise Pascal, who wrote a paper in 1654 dealing with the theory of combinations.Pascal was a child prodigy who became inter- ested in Euclid's Elements at age twelve. Within four years he was doing original research and wrote a paper of such quality that some of the leading mathemati- cians of the time refused to believe that it had been written by a sixteen-year-old boy.Pascal later abandoned mathematics to devote himself completely to philosophy and religion. In 1658, however, while unable to sleep because of a toothache, he decided to think about geometry to take his mind off the pain and, surprisingly, the pain stopped. Pascal took this as a sign from heaven that he should return to mathematics. For a short while he re- turned to his research, but soon became seriously ill with dyspepsia, a digestive disorder. Pascal spent the remaining years of his life in excruciating pain, doing little work until his death at age 39 in 1662.

編輯推薦

《身邊的數(shù)學(xué)(英文版)(原書第2版)》是皮納德編寫的，由機械工業(yè)出版社出版。

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