石家庄经济学院本科生毕业论文I摘要数学作为一门应用性很强的学科，如何将理论与现实问题有效结合起来是一大难题。而语言学作为一门重要的社会科学，与自然科学的精确性存在很大区别。研究现实表明数学将可以在语言学等社会学科上得到极大应用。本文首先介绍数学、语言学和数理语言学之间的关系及其内在联系，然后再从概率论和统计学两个角度分别简述其在语言学上应用。概率论方面主要介绍语言文字的熵，讨论其信息量，并以汉字为例兼论常见语言的字母熵，从而窥探每个文字背后蕴含的信息量度。统计学方面主要通过统计方法介绍语言单位的出现频率，计算作家的语言风格，以及计算语言存在的绝对年代和亲属语言分化的年代，并简要介绍齐普夫定律。关键词：数理语言学；概率论；统计学；熵；齐普夫定律；马尔可夫链；语言年代学ABSTRACTAppliedMathematics,asanapplicationofastrongdiscipline,hasamajorproblemthathowtocombinethetheoryandpracticalproblemseffectively.Linguisticsasanimportantsocialsciences,,hasabigdifferencewithnaturalsciencesaccuracy.Therealityshowsthatmathematicshasbeengreatlyusedinlinguisticsandsocialsciences.Thispaperfirstintroducestherelationshipbetweentheirinternalrelationsofmathematics,linguistics,andmathematicallinguistics,andthenfromtwoanglesoftheprobabilitytheoryandstatistics,respectively,outlineditsapplicationinlinguistics.Probabilitytheorydescribestheentropyofthelanguagetodiscusstheirinformationcontent,andontheentropyofthelettersofthecommonlanguageofChinesecharacters,forexample,inordertospyonthemeasureoftheinformationcontainedineachtextbehind.Instatisticswediscussonthefrequencyofoccurrenceofthelinguisticunitbystatisticalmethods,thecomputinglanguageofthewriter'sstyle,aswellascomputinglanguageofabsoluteageandageofrelativesoflanguagedifferentiation,andthenabriefintroductiontoZipf'sLaw.Keywords:MathematicalLinguistics;ProbabilityTheory;Statistics;Entropy;Zipf'sLaw;MarkovChain;Glottochronology石家庄经济学院本科生毕业论文II目录摘要???????????????????????????????Ⅰ目录???????????????????????????????Ⅱ1数学、语言学和数理语言学?????????????????????11.1数学在语言学上的渗透及其意义??????????????????11.2数理语言学及其分支???????????????????????21.2.1统计语言学?????????????????????????21.2.2代数语言学?????????????????????????32概率及其在语言学中应用???????????????????32.1熵、语言的熵????????????????????????32.2汉字的熵?????????????????????????52.3汉字的极限熵???????????????????????63统计及其在语言学中应用??????????????????83.1齐普夫定律?????????????