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[美] 罗森 著 / 机械工业出版社 / 2012-09 / 平装
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离散数学及其应用(英文版)(第7版)
《离散数学及其应用(英文版)(第7版)》是介绍离散数学理论和方法的经典教材,已经成为采用率最高的离散数学教材,被美国众多名校用作教材,获得了极大的成功。《离散数学及其应用(英文版)(第7版)》中文版也已被国内大学广泛采用为教材。作者参考用书教师和学生的反馈,并结合自身对教育的洞察,在第7版中做了大量的改进,使其成为更有效的教学工具。《离散数学及其应用(英文版)(第7版)》可作为1~2个学期的离散数学课程教材,适用于数学、计算机科学、计算机工程、信息技术等专业的学生。
refaceivabouttheauthorxiiithecompanionwebsitexivtothestudentxvilistofsymbolsxix1thefoundations:logicandproofs1.1propositionallogic1.2applicationsofpropositionallogic1.3propositionalequivalences1.4predicatesandquantifiers1.5nestedquantifiers1.6rulesofinference1.7introductiontoproofs1.8proofmethodsandstrategyend-of-chaptermaterial-2basicstructures:sets,functions,sequences,sums,andmatrices2.1sets2.2setoperations2.3functions.2.4sequencesandsummations2.5cardinalityofsets2.6matricesend-of-chaptermaterial3algorithms3.1algorithms3.2thegrowthoffunctions3.3complexityofalgofithmsend-of-chaptermaterial4numbertheoryandcryptography4.1divisibilitvandmodulararithmetic4.2integerrepresentationsandalgorithms4.3primesandgreatestcommondivisors4.4solvingcongruences4.5applicationsofcongruences4.6cryptographyend-of-chaptermaterial5inductionandrecursion5.1mathematicalinduction5.2stronginductionandwell-ordering5.3recursivedefinitionsandstructuralinduction5.4recursivealgorithms5.5programcorrectnessend-of-chaptermaterial6counting6.1tllebasicsofcounting6.2thepigeonholeprinciple6.3permutationsandcombinations6.4binomialcoefficientsandidentities6.5generalizedpermutationsandcombinations6.6generatingpermutationsandcombinationsend-of-chaptermaterial7discreteprobability7.1anintroductiontodiscreteprobability7.2probabilitytheory7.3bayes'theorem7.4expectedvalueandvarianceend-of-chaptermaterial8advancedcounringtechnigues8.1applicationsofrecurrencerelations8.2solvinglinearrecurrencerelations8.3divide-and-conqueralgorithmsandrecurrencerelations8.4generatingfunctions8.5inclusion-exclusion8.6applicationsofinclusion-exclusionend-of-chaptermaterial9relations9.1relationsandtheirproperties9.2n-aryrelationsandtheirapplications9.3representingrelations9.4closuresofrelations9.5equivalencerelations9.6partialorderingsend-of-chaptermaterial10graphs10.1graphsandgraphmodels10.2graphterminologyandspecialtypesofgraphs10.3representinggraphsandgraphisomorphism10.4connectivity10.5eulerandhamiltonpaths10.6shortest.pathproblems10.7planargraphs10.8graphcoloringend-of-chaptermaterial11trees11.1introductiontotrees11.2applicationsoftrees11.3treetravcrsal11.4spanningtrees11.5minimumspanningtreesend-of-chaptermaterial12booleanalgebra12.1booleanfunctions12.2representingbooleanfunctions12.3logicgates12.4minimizationofcircuitsend-of-chaptermaterial13modelingcornputation13.1languagesandgrammars13.2finite-statemachineswithoutput13.3finite-statemachineswithnooutput13.4languagerecognition13.5turingmachinesend-of-chaptermaterialappendixes1axiomsfortherealnumbersandthepositiveintegers2exponentialandlogarithmicfunctions3pseudocodesuggestedreadingsb-1answerstoodd-numberedexercisess-1photocreditsc-1indexofbiographiesi-1indexi-2
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