SCHEME OF WORK MAT 1093

DISCRETE
MATHEMATICS

MAT 1093

SCHEME OF WORK

i

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Contents Page

SCHEME OF WORK i - iv
1 - 28
Topic 1
SET 29 - 57

1.1.Set theoretic, Notations and Terminology 58 - 93
1.2.Operations on Sets
1.3.The Addition Principle
1.4.Computer Representation Of Sets
Tutorial 1
Review Questions 1
Compilation of Quiz 1 Questions

Topic 2
LOGIC

2.1 Propositions and Logical Operations

2.2 Conditional and Biconditional Statements

2.3 Methods of Proof

2.3.1 Argument

2.3.2 Tautology and Contradiction

2.3.3 Rules of Inference

Tutorial 2
Review Questions 2
Compilation of Quiz 2 Questions

Topic 3
COUNTING

3.1 Permutations

3.2 Combinations

3.2 Probability

Tutorial 3
Review Questions 3
Compilation of Test 1 Questions

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Contents Page
94 - 128
Topic 4
RELATIONS 129 - 142
143 - 171
4.1 Introduction to relations

4.2 Cartesian Product

4.3 Matrix Of relations

4.4.Properties Of Relations

4.4.1 Reflexive Relations

4.4.2 Symmetric Relations

4.4.3 Antisymmetric Relation

4.4.4 Transitive Relations

Tutorial 4
Review Questions 4
Compilation of Test 2 Questions

Topic 5
FUNCTIONS

5.1 Introduction to functions

5.2 Floor and Ceiling functions

5.3 Permutation functions

5.3.1 Cyclic permutation functions

5.3.2 Even and odd permutation functions

Tutorial 5
Review Questions 5

Topic 6
TREE

6.1 Introduction to Trees
6.2 Rooted Tree
6.2.1 Properties of Trees
6.3 Binary Trees
6.3.1 Binary Search Trees

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6.3.2 Expression Trees
Tutorial 6
Review Questions 6

Topic 7 172 – 202

LOGIC GATES AND BOOLEAN ALGEBRA

7.1 Basic Gates and Boolean Algebra
7.2 Truth Table
7.3 Boolean Expression and Theorems
7.4 Minimization of Boolean Expression
7.5. Sum of Product
7.5.1 Converting SOP Expression to Truth Table
7.5.2 Converting Truth Table to SOP Expression
7.5.3 Karnaugh Maps and Minimization of SOP Boolean Expression
7.6 Product of Sum
7.6.1 Converting POS Expression to Truth Table
7.6.2 Converting Truth Table to POS Expression

Tutorial 7

Review Questions 7

COMPILATION OF FINAL 203 - 216
EXAM QUESTIONS

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KOLEJ PROFESIONAL MARA BERANANG

SCHEME OF WORK

1. Name of Course DISCRETE MATHEMATICS

2. Course Code MAT 1093

3. Name(s) of Aniza binti Alias: MBA (UKM), BSc.Hons (Mathematics)(UPM),DipEdu
academic staff (Matemathics)(KOPEDA)

Atty Azanira binti Abd. Rashid: MEdu (UPM), BSc.Hons (Statistics)(UPM),DipEdu
(Matemathics)(MPKTBR)

Eliza Yusreen binti Abd. Razak :BApp.Sc.Hons (Statistics)(USM),DipEdu
(Matemathics)(MPKTBR)

Murniwati binti Wan Ahmad: MBA (UKM), BSc.Hons (Mathematics)(UPM),DipEdu
(Matemathics)(UKM)

Norhaiza binti Mohd Yusof Senusi: BSc. Hons (Mathematics), Univ. Of Auckland, New
Zealand. DipEdu (UPSI)

4. Synopsis The purpose of this course is to understand and use (abstract) discrete structures that
are backbones of computer science. This course is meant to introduce logic, proofs,
sets, relations, functions,counting, and probability, with an emphasis on applications in
computer science.

5. Semester and 1/1
Year offered

6. Credit Value 3

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7. Prerequisite None
(if any)

8. Course Learning Upon successful completion of the course students will be able to:
Outcomes
CLO1 - Explain the fundamental concepts associated with sets, notation and logic.
(C2,PLO1)

CLO2 - Apply counting principles and relations using their properties (C3,PLO6)

CLO3 - Demonstrate various properties of functions. (A3,PLO5)

CLO4 - Illustrate characteristic of binary tree and logic gates and Boolean Algebra.
(C4,PLO6)

9. Transferable This course will help the students to acquire knowledge, logical thinking and
Skills: problem solving skills in the field of computer science.

10. Assessment Course Learning Duration
Methods and Outcome
Types

Assessment Topic Percentage

CLO 1 1
2
Quiz 1 3 40 minutes
4
CLO2 Quiz 2 5 40 minutes 10%
Test 1 6&7 1 hour 10%
CLO3 Test 2 1 hour 15%
CLO4 Assignment 2 weeks 15%
20%
Final Exam 1 hour 30
minutes 30%

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11. Mapping of the PEO PEO PEO PEO
course/module to 1 2 3 4
the Programme
Educational CLO 1 √ √ √
Objectives CLO 2
CLO 3 √
CLO4

12. Mapping of the PLO PLO PLO PLO PLO PLO PLO PLO
course/module to 1 2 3 4 5 6 7 8
the Programme
Learning CLO 1 √ √ √
Outcomes 1
√
CLO 2 2

CLO 3

CLO4

TOTAL 1

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13. Course/ Module Content Outline F2F NF2F Total
WEEK Topic and Sub-Topic C SLT
1-2
L L TP O L T PO
2-3 O

Topic 1: Set

1.5. Set theoretic, Notations and C

Terminology L 41 81 14
1.6. Operations on Sets

1.7. The Addition Principle O
1.8. Computer Representation Of Sets

1

QUIZ 1 (WEEK 3)-TOPIC 1

Topic 2: Logic C

2.1 Propositions and Logical Operations L

2.2 Conditional and Biconditional O

Statements 1

2.3 Methods of Proof 41 81 14
2.3.1 Argument

2.3.2 Tautology and Contradiction

2.3.3 Rules of Inference

• Direct Proof
• Indirect Proof

QUIZ 2 (WEEK5)-TOPIC 2

3-4 C 10 1 17
Topic 3: Counting L 51
O
3.1 Permutations 2

3.2 Combinations

3.2 Probability

TEST 1 (WEEK7)-TOPIC 3

5-6 Topic 4: Relations

4.1 Introduction to relations C

4.2 Cartesian Product L

4.3 Matrix and digraph of a relations O 51 10 1 17

4.4.Properties Of Relations 2

4.4.1 Reflexive Relations

4.4.2 Symmetric Relations

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4.4.3 Antisymmetric Relation
4.4.4 Transitive Relations

TEST 2 (WEEK9)-TOPIC 4

7-9 Topic 5: Functions

WEEK 5.1 Introduction to functions C
9-11
11-14 5.2 Floor and Ceiling functions L 2 12 20
5.3 Permutation functions O6

5.3.1 Cyclic permutation functions 3

5.3.2 Even and odd permutation
functions

ASSIGNMENT (TOPIC 5)

WEEK 9- OUT

WEEK 11 - IN

Course/ Module Content Outline F2F NF2F Total
L TP SLT
C 51

Topic and Sub-Topic L 51 L TPLT P
O

Topic 6: Tree

6.1 Introduction to Trees

6.2 Properties of Trees C

6.3 Rooted Trees L 10 1 17

6.4 Binary Trees O

6.4.1 Binary Search Trees 4
6.4.2 Huffman Code Trees
6.4.3 Expression Trees
Topic 7: Logic Gates and Boolean

Algebra

7.1 Basic Gates and Boolean Algebra C 10 1 17
7.2 Truth Table L
7.3 Boolean Expression and Theorems O
7.4 Minimization of Boolean Expression 4
7.5. Sum of Product
7.5.1 Converting SOP Expression to

Truth Table
7.5.2 Converting Truth Table to SOP

x

Expression
7.5.3 Karnaugh Maps and Minimization

of SOP Boolean Expression.
7.6 Product of Sum
7.6.1 Converting POS Expression to

Truth Table
7.6.2 Converting Truth Table to POS

Expression

FINAL EXAMINATION ( TOPIC 6 & 7)

Main Reference
19 • Internal Circulation Module: Discrete Mathematics (MAT 1093)
. • Kolman, Busby, Ross (2014), Discrete Mathematical Structures 6th Ed., Pearson New International Edition.

Additional References:
1. Asma,Ahmad Shariff ,Ibrahim Mohamed, Fadzilah Abd Manaf (2018), Comprehensive College Mathematics 3rd

Ed. SAP Publication
2. Jamalludin Talib (2006), Struktur Matematik Diskret. Universiti Teknologi Malaysia (UTM)
3. D.S. MALIK, M.K.SEN (2004), Discrete Mathematical Structures: Theory And Application 7th Ed. Thomson

Course Technology.
4. O Level Classified Mathematics (2005), Singapore Asian Publication (SAP)

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