MATH 327 Discrete Structures

Spring2016 Syllabus

Instructor: Dr.Ana Vasilic

Instructor Email:

Office: GE 114

Office Hours: MW 2:00-3:15pm(GE 114),TR 11:30-12:45pm(SERPA 103) Course Time andLocation:TR10:00-11:15AM,SERPA 103

Course Length:3credithours

Prerequisite: Math 163

Textbook: Please consultNNMCBookstoreforlatestbookandedition

S.Epp:DiscreteMathematics:AnIntroductiontoMathematicalReasoning,BriefEdition, Brooks/Cole, 2011.

Supplementaryrequirements:Computer andinternetaccess.

CourseDescription:Thecoursewillemphasize principlesofdiscretemath,including mathematicallogic,inductive anddeductivereasoning, recursivemethods,aswellas conceptsof discretestructuresand theirconnectionsto problems inscience, technology,andengineering.

MATH 327meets the followingCollege WideGoals.

A. Communication:

Studentswillsolve problems andpresent theirsolutionstothe class.

Studentswillworktogetherinsmallgroupsoncompletinganappliedmathproject.

Theywillsubmittheirfinalreportinwriting,andalsopresenttheirresultstothe classmates.

B. Criticalthought:

Studentswillpractice distinctionbetween valid andinvalid arguments.

Studentswillanalyze and solve realworld problems.

C. CulturalCompetence:

Studentswillparticipate inclass discussionsandwork togetheronahands-on mathematical project,creating anenvironment that promotes professional

behavior, understanding andrespectforindividualdifferences.

D. InformationCompetency and Research:

Studentswilluse online resources tocompletetheirproject.

StudentswilluseBlackboardtoaccess lecture notesand extramaterial.

StudentLearning Outcomes: Atthe end of thiscourse thestudentwill be able to:

1. Apply theprinciplesofmathematical logicand valid argumentsto solve real-world problems.

2. Read and write different typesofmathematical proofs:directproof, proof by contradiction, proof bycases, or bymathematicalinduction.

3. Performoperationson discrete mathematical structures, such assetsand relations.

4. Understand theconceptof recursionanditsrelationshipto the principle of mathematical induction.

5. Solve problemsinvolving recurrencerelations andgeneratingfunctions.

6. Solve real-world problemsusingcounting techniquesandCombinatorics.

7. Applygraph theory to solve real world problems.

Course Requirements:

1. Attendance,In-ClassParticipationQuizzes: Studentsareexpectedtoattendall classsessionsandare responsiblefor materialmissedduringanyabsence. Occasionally, shortquizzeswillbegivenattheendofclass. Theobjectiveofthe quizzesisto teststudents’understandingof thenewmaterial coveredinclass.

2. E-mailBlackboard:StudentsareexpectedtochecktheirNNMCe-mailandthe courseBlackboardpageregularly.Lecturenotes,aswellas someextra materialand all the importantannouncementswill be postedonthe Blackboard.

3. Practiceproblems: Practiceproblemsand readingassignmentswillbeassigned nearlyeveryclasssession. Completing theassignmentsisessential to understanding the coursematerialand succeeding in class. Studentsareencouragedtodiscussthe practice problemswith theirpeers.

4. Gradedhomeworkproblems:Severalsetsofgradedhomeworkassignmentswill begiven.Ifyoucannotattenda class,arrangetoturn in yourassignmentson time. Latehomeworkwillnotbeacceptedunlessitiscausedbyextenuatingcircumstances asdetermined by theinstructor.

5. GroupProject: Studentswillworkinsmallgroups(2-3students)onaproject.The goaloftheprojectistoextendtheknowledgeoftheclassmaterialandapplyittoa

‘real-world’problem.Studentswillsubmittheirfinalreportinwriting,andalso

present theirresultsto the classmates.

6. Exams:Therewillbethreein-classexams.Theexamsareclosed-book,closed-notes.

Shouldtherebeanyformulasneeded,theywillbeprovidedbytheinstructor.The examdatesand topicswill be announced atleastoneweekinadvance.

7. Evaluation:Gradeswillbedeterminedaccordingtothefollowingweightingscheme:

Exams: / 60 %
Quizzesand Participation: / 10 %
Homeworkand Projects: / 30 %

Course Grading Scale:Thefollowinggradingscalewill be used to determine yourfinal letter grade:

A+ = 99 –100% A = 93 –98%

A-= 90 – 92%

B+= 88 – 89% B= 83 – 87% B-= 80 – 82% C+ = 78 – 79% C = 70 – 77% C-= 68 – 69% D+ = 66 – 67% D = 63 – 65% D-= 60 – 62% F= 0 – 59%

Importantnote:GradesofC-andbelowdonotcounttowardgraduationanddonot meetthe criteriafor satisfying prerequisites.

Stu dents with Disabilities:

NorthernNewMexicoCollegerecognizesitsresponsibility forcreating aninstitutional climateinwhichstudentswithdisabilitiescansucceed.InaccordancewithSection504ofthe RehabilitationAct andtheAmericanswithDisabilitiesAct;ifyouhaveadocumented disability, youmayrequest

accommodationstoobtainequalaccessandtopromoteyourlearninginthisclass.Please contacttheVernaTrujillo,CoordinatorofAccessibilityandResourceCenterat505-747-2152 or ryoureligibility isdetermined,youwillbegivenaletter,whichwhenpresentedto instructors,willhelpus know besthowto assist you.

StudentCode of Conductand AcademicDishonestyPolicy:

Studentsinthiscourseandinall collegeclassesare expectedtocompletetheircoursework inaccordancetoourCollegepolicies.Academicdishonestyonthepartofastudentincluding cheatingona test, plagiarismorfalsificationwillbesubjecttoacademicsanctions.Formore informationaboutacademicdishonestyandhow suchincidentswillbehandledbyyour instructor and by theCollege, please refer to Northern’sstudenthandbook.

Tentativetimetable

Week / Week
start / S ect ions
covered / Topics
1 / 01/19* / 1.1, 1.2
2.1 / Variables,TheLanguage of Sets
Logical Formand LogicalEquivalence
2 / 01/25 / 2.2, 2.3
Extra material
3.1,3.2 / ConditionalStatements, Valid and Invalid Arguments
Applicationsto Digital LogicCircuitsetc. Predicatesand QuantifiedStatements
3 / 02/01 / 4.1-4.5 / ElementaryNumberTheoryand Methodsof Proof
(selectedtopicsonly)
4 / 02/08 / Review
ExamI / Reviewfor ExamI
EXAM I
5 / 02/15 / 5.1
5.2, 5.3
5.4 / Sequences
Mathematical Induction I, Mathematical InductionII
StrongMathematical Inductionand theWell-Ordering Principle for Integers(time permitting)
6 / 02/22 / 5.5
5.6
Extra material / DefiningSequencesRecursively
SolvingRecurrence Relations byIteration
Second-Order Linear HomogeneousRecurrence Relations
7 / 02/29 / 6.1
6.2
8.1, 8.2 / Set Theory: Definitionsand the Element Proof Method
Propertiesof Sets
RelationsonSets, Reflexivity, Symmetry, and Transitivity
8 / 03/07 / Review
ExamII / Reviewfor ExamII
EXAM II
03/14 / Spring Break
9 / 03/21 / 8.3
8.4 / EquivalenceRelations
Modular Arithmetic
10 / 03/28 / 9.1, 9.2
9.3 / Introductionto Countingand Probability, TheMultiplicationRule
TheAdditionRule, TheInclusion/ExclusionRule
11 / 04/04 / 9.5
9.6
10.1 / Combinations and Permutations
Binomial Formula(time permitting) Graphs: Definitionsand BasicProperties
12 / 04/11 / Review
ExamIII / Reviewfor ExamIII
EXAM III
13 / 04/18 / 10.2
10.3, 10.4 / Trails, Paths, and Circuits
Trees, Rooted trees
14 / 04/25 / Extra material / Applications(e.g. networks, schedulingetc.)
15 / 05/02 / Projectpresentations

* 01/18Martin LutherKingJr. Holiday– College closed