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1、2.1数学、方程与比例1－AWhatismathematics1－BEquation2.2几何与三角2－AWhystudygeometry?2－BSomegeometricalterms2.3集合论的基本概念3－ANotationsfordenotingsets3－BSubsets子集2.4整数、有理数与实数Integers,RationalNumbersandRealNumbers4－AIntegersandrationalnumbers整数和有理数4－BGeometricinterpretationofrealnumbers
2、aspointsonaline在直线上描点的方式表示实数的几何意义2.5basicconceptsofCartesiangeometry解析几何的基本概念5-AthecoordinatesystemofCartesiangeometry解析几何的坐标系5-BGeometricfigure几何图形2.6functionconceptandfunctionidea函数的概念与函数思想6-CTheconceptoffunction2.7SequencesandTheirLimits序列及其极限7-AThedefinitionofseq
3、uences7-BThelimitofasequence8-A函数的导数2.9微分方程简介differentialequations2.10线性空间中的相关与无关集DependentandIndependentSetsinaLinearSpace2.11数理逻辑入门ElementaryMathematicalLogic11-APredicates11-BQuantifiers2.12概率论与数理统计ProbabilityTheoryandMathematicalStatisticsNewWords&Expressions:alg
4、ebra代数学geometrical几何的algebraic代数的identity恒等式arithmetic算术,算术的measure测量，测度axiom公理numerical数值的,数字的conception概念，观点operation运算constant常数postulate公设logicaldeduction逻辑推理proposition命题division除，除法subtraction减，减法formula公式term项，术语trigonometry三角学variable变化的，变量2.1数学、方程与比例Mathemat
5、ics,EquationandRatio1－AWhatismathematics4Mathematicscomesfromman’ssocialpractice,forexample,industrialandagriculturalproduction,commercialactivities,militaryoperationsandscientificandtechnologicalresearches.数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。Andinturn,mathematicss
6、ervesthepracticeandplaysagreatroleinallfields.Nomodernscientificandtechnologicalbranchescouldberegularlydevelopedwithouttheapplicationofmathematics.反过来，数学服务于实践，并在各个领域中起着非常重要的作用。没有应用数学，任何一个现在的科技的分支都不能正常发展。5Fromtheearlyneedofmancametheconceptsofnumbersandforms.Then,geo
7、metrydevelopedoutofproblemsofmeasuringland,andtrigonometrycamefromproblemsofsurveying.Todealwithsomemorecomplexpracticalproblems,manestablishedandthensolvedequationwithunknownnumbers,thusalgebraoccurred.很早的时候，人类的需要产生了数和形的概念。接着，测量土地问题形成了几何学，测量问题产生了三角学。为了处理更复杂的实际问题，人类建
8、立和解决了带未知数的方程，从而产生了代数学。Before17thcentury,manconfinedhimselftotheelementarymathematics,i.e.,geometry,trigonometryandalgebra,inwhichon
