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Head Department Approval:

Date:

UNIVERSITI PENDIDIKAN SULTAN IDRIS

COURSE CURRICULAR DESIGN AND INSTRUCTIONAL PLAN

Faculty : Faculty of Art, Computing and Creative IndustryDepartment : ComputingSemester : 1Session : 2011/2012Course Name : Discrete StructuresCourse Code : MTK 2023/ MTK3013Credit Hour : 3 hours (2 hours lecture + 1 hour tutorial)Pre-requisition : None

LECTURERS INFORMATION

Name : Dr. Ramlah Binti Mailok (Coordinator)E-mail : [email protected] Number : 05-4505014 (013-6076645)Room Number : 2B-, Malim Sarjana Complex, UPSI

Name : Mrs. Noriza Binti NayanE-mail : [email protected] Number : 05-4505023
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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2. To understand and use the notation associated with fundamental concepts of discretestructures / mathematics such as formal proof techniques, including mathematical inductionand proof by contradiction, logical deduction, sets, functions, permutations and combinations,discrete probability and also basic graph theory especially in solving and the formulation ofmathematical problems.

3. To understand algorithmic complexity and will be able to use it to compare different programdesigns for a problem.

4. To give an exposure to finite or discontinuous quantities in order to master the process oftheorem proving, problem-solving, communication, reasoning, and modeling that commonlyused in daily activities.

LEARNING OUTCOMES:

Students should be able to:

1. Acquire and practise various strategies in discrete structures especially in teaching andlearning process.

2. Select, use and apply appropriate techniques in daily basis especially in problem solvingand computer program learning.

3. Plan and manage information well and able to manipulate, practise and impart all the

techniques in tailoring the problems.4. Analyze discretely the impotencies of discrete structures in real world environment

applications.5. Present ideas clearly with good command of languages and confidently.

MAIN REFERENCE (TEXT BOOK):

1. Rosen, K. H. (2005). Discrete Mathematics And Its Applications (Fifth Edition).Boston : Mc Graw Hill.

ADDITIONAL REFERENCES:

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SOFT SKILLS EMBEDDED:

ACTIVITIES / SOFT SKILLS KOM KBPM PBPM PSK PIM ETIK KUIndividual Assignment

Group Project

Quiz

Examination

Legend :

KOM Communication SkillKBPM Thinking and Problem Solving SkillPBPM Continous / Advance Learning and Information Management SkillPSK Teamwork SkillPIM Leadership SkillETIK Prefessional EthicsKU Entrepreneurship Skill

COURSE EVALUATION:

Courseworks 60%Tutorial 10%Quizzes (3) 15%Group Project (Journal Review) 10%Mid Semester Examination 25%

Final Examination 40%

Total 100%

Notes:

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B 65 69 3.00 Distinction

B- 60 64 2.70 Distinction

C+ 55 59 2.40 Pass

C 50 54 2.00 Pass

C- 45 49 1.70 Weekly Pass

D+ 40 44 1.40 Weekly Pass

D 35 39 1.00 Weekly Pass

F 0 34 0 Fail

SOFT SKILLS GRADING SCALE

GRADING SCALE CRITERIA FOR SOFT SKILLS

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14 WEEKS TEACHING SCHEDULE

WeekTopic Learning Outcome(s) Teaching and

Learning

Activities

Soft SkillsIncorporated Reference(s)

1 Introduction To RI- Instructional plan briefing.- Discussion of course

implementation.- Discussion of course evaluation.

Listen attentively.

Identify course contentand evaluation taken.

Lecture anddiscussion.

KOM.

2 Logic Proposition- False, True, Statements.- Propositions.

Compound propositions.

Logical connectives.- Bit string

Outline the basic terms inlogic proposition andcompound propositionssuch as negation,conjunction, disjunction,exclusive-or, conditionaland bi-conditional.

Illustrate thedifferentiation of compound propositionsand its use ness.


KBPM.

KOM.

Rosen, K. H. (2005).Discrete MathematicsAnd Its Applications,Fifth Edition. Mc GrawHill.

JohnsonBaugh, R. 2006).Discrete Mathematics.Prentice Hall.

3 Propositional Equivalences- Tautologies.

Tautologies.

Contradictions.

Contingencies.- Logical Equivalences.

Conditional.

Contrapositive.

Converse.- Use of logic to illustrate connectives- Normal forms (conjunctive and

disjunctive)

Outline the basicpropositionalequivalences.

Illustrate the

differentiation of tautologies,contradict ions andcontingencies and relateit with logicalequivalences.


KBPM.

KOM.

Rosen, K. H. (2005).Discrete MathematicsAnd Its Applications,Fifth Edition. Mc Graw

Hill. JohnsonBaugh,R. 2006).

Discrete Mathematics.Prentice Hall.

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4 Predicates and Quantifiers- Predicates.- Quantifiers.

Existential quantifier

Universal quantifier.- Propositional function.- Multivariable predicates.- Multivariable propositional functions.- Multivariate quantification.

Illustrate thedifferentiation of predicates andquantifiers.


KBPM.

KOM.


JohnsonBaugh,R. 2006).Discrete Mathematics.Prentice Hall.

5 Logic and Proof- Addition.- Simplication.- Combination / Conjunction.- Hypothetical syllogism.

- Modes ponens.- Modes tollens.- Resolution.

Outline basic notions oflogic.

Solve problems bydifferent methods oflogic.


KBPM.

KOM.



6 Logic and Proof- Direct proof.- Indirect proof (by contradiction).- Proof by cases.- Proving equivalences.

Outline the structure offormal proofs for theorems using thetechniques of proofs.

Solve problems bydifferent methods ofproof.


KBPM.

KOM.



7 Logic and Proof- Proof.- Proof by Induction

Mathematical Induction.

Outline basic proofs fortheorems using thetechniques of proofs.

Solve problems by usingmathematical induction.


KBPM. KOM.



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8 Sets- Element.- Subset.- Empty set.- Cardinality.- Power set.- Ordered n-tuples.- Cartesian product.- Universe of discourse.- Set builder notation.- Set theoretic operation.

Union.

Intersection.

Difference.

Complement. Symmetric difference.

Set identities.- Venn diagrams.

Outline by examples thebasic terminology of sets.

Illustrate thedifferentiation of settheoretic operation.

Interpret the associatedoperations andterminology in context.


KOM.

KBPM.



9 Functions and Sequences- Functions.

Domain, co-domain,range.

Image, pre-image.

One-to-one, onto,bijective, inverse.

Functionalcompositionand exponentiation.

Ceiling and floor.

Sequences

Outline by examples thebasic terminology offunctions.



KOM.

KBPM.


JohnsonBaugh,R. 2006).Discrete Mathematics.

Prentice Hall.

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10 Basic Number Theory- Basic number theory.

Divisors.

Primality.

Fundamental theorem ofarithmetic.

Division algorithm.

Greatest common divisors(GCD) / least commonmultiples (LCM).

Relative primality.

Modular arithmetic.- Euclidean algorithm for GCD.

Outline by examples thebasic terminology ofbasic number theory.



KOM.

KBPM.


Hill.


11 Relations

- Relational databases.- Relations as subsets.- Properties of binary relations- Digraph representation.

Outline by examples the

basic terminology ofrelations.


Relate practicalexamples to theappropriate relationmodel.

Lecture and

discussion.

KOM.

KBPM.

Rosen, K. H. (2005).

Discrete MathematicsAnd Its Applications,Fifth Edition. Mc GrawHill.


12 Relations- Reflexitivity.

- Symmetry.- Transitivity.- Equivalence relations.- Matrices of relations.

Outline by examples thebasic terminology of

functions. Interpret the associated

operations andterminology in context.

Relate practicalexamples to theappropriate relationmodel.


KOM.

KBPM.

Rosen, K. H. (2005).Discrete Mathematics

And Its Applications,Fifth Edition. Mc GrawHill.


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13 Recurrence Relations- Recursive mathematical definitions.- Developing recursive equations.- Solving recursive equations.

Solve a variety of basicrecursive equations.

Analyze a problem tocreate relevantrecurrence equations orto identify importantcounting questions.

Relate the ideas ofmathematical induction torecursion and recursivelydefined structures.


KBPM.

KOM.


Hill. JohnsonBaugh,R. 2006).

Discrete Mathematics.Prentice Hall.

14 Counting Methods- Probability.- Permutations and combinations.- Counting arguments rule of products,

rule of sums.- The pigeonhole principle.

Graph Theory and Trees- Undirected graphs.- Directed graphs.- Spanning trees.- Traversal strategies.

Calculate probabilities ofevents and expectationsof random variables forproblems arising fromgames of chance.

Compute permutationsand combinations of aset and interpret themeaning in the context ofthe particular application.

Illustrate by example thebasic terminology ofgraph theory, and someof the properties andspecial cases of each.

Models problems incomputing using graphsand trees.

Relate graphs and treesto data structures,algorithms, and counting.


KBPM.

KOM.



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14 WEEKS TUTORIAL SCHEDULE

WeekTopic

Learning Outcome(s) Teaching andLearning Activities

Soft SkillsIncorporated

Reference (s)

1 Tutorial 1- False, True, Statements.- Propositions.

Compound propositions.

Logical connectives.- Bit string.

Portray verbal and non-verbal communications

Do independent learning.

Manage information well.

Present ideas clearly withconfident.

Discussion in aform of group.

KOM.

KBPM.

Rosen, K. H. (2005).Discrete Mathematics AndIts Applications, FifthEdition. Mc Graw Hill.


2

Tutorial 2- Tautologies.

Tautologies

Contradictions.

Contingencies.- Logical Equivalences.

Conditional.

Contrapositive.

Converse.- Use of logic to illustrate

connectives.- Normal forms (conjunctive

and disjunctive).

Journal Titles Submission






KOM.

KBPM.



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3 Tutorial 3- Predicates.- Quantifiers.

Existential quantifier.

Universal quantifier.- Propositional function.- Multivariable predicates.- Multivariable propositional

functions.- Multivariate quantification.






KOM.

KBPM.



4 Quiz 1 Present ideas clearly withconfident.


KOM.

KBPM.



5 Tutorial 4- Addition.- Simplication.- Combination / Conjunction.

- Hypothetical syllogism.- Modes ponens.- Modes tollens.- Resolution.




KOM.

KBPM.



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6 Tutorial 5- Direct proof.- Indirect proof (by

contradiction).

- Proof by cases.- Proving equivalences.- Proof.

- Proof by Induction Mathematical Induction






KOM.

KBPM.





KOM.

KBPM.



8 Tutorial 6- Element.- Subset.- Empty set.- Cardinality.- Power set.- Ordered n-tuples.- Cartesian product.- Universe of discourse.

- Set builder notation.

- Set theoretic operation.

Union.

Intersection.

Difference.

Complement.

Symmetric difference

Set identities.






KOM.

KBPM.



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- Venn diagrams.- Functions.

Domain, co-domain,range.

Image, pre-image.

One-to-one, onto,bijective, inverse.

Functionalcompositionand exponentiation.

Ceiling and floor.- Sequences

9 Mid Semester Examination Present ideas clearly withconfident.


KOM.

KBPM.

Rosen, K. H. (2005).Discrete Mathematics And

Its Applications, FifthEdition. Mc Graw Hill.


10 Tutorial 7- Basic number theory.

Divisors.

Primality.

Fundamental theorem ofarithmetic.

Division algorithm. Greatest common divisors

(GCD) / least commonmultiples (LCM).

Relative primality.

Modular arithmetic.- Euclidean algorithm for GCD





Complete task on time.


KOM.

KBPM.

ETIK.


JohnsonBaugh,R. 2006).Discrete Mathematics.

Prentice Hall.

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Journal Submission

11 Tutorial 8 and 9

- Relational databases.- Relations as subsets.- Properties of binary relations- Digraph representation.- Reflexitivity.- Symmetry.- Transitivity.- Equivalence relations.- Matrices of relations..- Recursive mathematical

definitions.- Developing recursive

equations.- Solving recursive equations.

Portray verbal and non-

verbal communications Do independent learning.



Discussion in a

form of group.

KOM.

KBPM.

Rosen, K. H. (2005).

Discrete Mathematics AndIts Applications, FifthEdition. Mc Graw Hill.




KOM.

KBPM.



13 Tutorial 10

- Probability.- Permutations and

combinations.- Counting arguments rule of

products, rule of sums.- The pigeonhole principle.- Undirected graphs.- Directed graphs.- Spanning trees.

Portray verbal and non-

verbal communications Do independent learning.



Discussion in a

form of group.

KOM.

KBPM.

Rosen, K. H. (2005).

Discrete Mathematics AndIts Applications, FifthEdition. Mc Graw Hill.


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- Traversal strategies.

14 Discussion Portray verbal and non-verbal communications



Present ideas clearly withconfident..


KOM.

KBPM.

Rosen, K. H. (2005).Discrete Mathematics And

Its Applications, FifthEdition. Mc Graw Hill.


20110913140929_MTK 2013 (RI) SEM 1 1011-1

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