discrete math in computer science - bogart , stein

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1、DiscreteMathinComputerScienceKenBogartCliffSteinDept.ofMathematicsDept.ofComputerScienceDartmouthCollegeDartmouthCollegeJune23,20022Thisisaworkingdraftofatextbookforadiscretemathematicscourse.Thiscourseisdesignedtobetakenbycomputersciencestudents.Theprerequisit

2、esarefirstsemestercalculus(Math3)andtheintroductorycomputersciencecourse(CS5).Theclassismeanttobetakenconcurrentlywithorafterthesecondcomputersciencecourse,DataStructuresandComputerProgramming(CS15).ThisclassisaprerequitetoAlgorithms(CS25)anditisrecommendedthat

3、itbetakenbeforeallCScoursesotherthan5and15.
cCopyrightKennethP.BogartandCliffStein2002Chapter1Counting1.1BasicCountingAboutthecourseInthesenotes,studentactivitiesalternatewithexplanationsandextensionsofthepointoftheactivities.Thebestwaytousethesenotesistotrytom

4、asterthestudentactivitybeforebeginningtheexplanationthatfollows.Theactivitiesarelargelymeanttobedoneingroupsinclass;thusforactivitiesdoneoutofclasswerecommendtryingtoformagroupofstudentstoworktogether.Thereasonthattheclassandthesenotesaredesignedinthiswayistoh

5、elpstudentsdeveloptheirownhabitsofmathematicalthought.Thereisconsiderableevidencethatstudentswhoareactivelydiscoveringwhattheyarelearningrememberitfarlongerandaremorelikelytobeabletouseitoutofthecontextinwhichitwaslearned.Studentsaremuchmorelikelytoaskquestion

6、suntiltheyunderstandasubjectwhentheyareworkinginasmallgroupwithpeersratherthaninalargerclasswithaninstructor.Thereisalsoevidencethatexplainingideastosomeoneelsehelpsusorganizetheseideasinourownminds.However,differentpeoplelearndifferently.Alsotheamountofmaterial

7、indiscretemathematicsthatisdesirableforcomputersciencestudentstolearnismuchmorethancanbecoveredinanacademictermifalllearningistobedonethroughsmallgroupinteraction.Forthesereasonsabouthalfofeachsectionofthesenotesisdevotedtostudentactivities,andhalftoexplanatio

8、nandextensionofthelessonsoftheseactivities.Analyzingloops1.1-1Theloopbelowispartofanimplementationofselectionsorttosortalistofitemschosenfromanorderedset(numbers,alphabetcharacters