holy angel university

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HOLY ANGEL UNIVERSITY College of Engineering & Architecture

Department of Computer Engineering

University Vision, Mission, Goals and Objectives:

Mission Statement (VMG)

We, the academic community of Holy Angel University, declare ourselves to be a Catholic University. We dedicate ourselves to our core purpose, which is to provide accessible quality education that transforms students into persons of conscience, competence, and compassion. We commit ourselves to our vision of the University as a role-model catalyst for countryside development and one of the most influential, best managed Catholic universities in the Asia-Pacific region. We will be guided by our core values of Christ-centeredness, integrity, excellence, community, and societal responsibility. All these we shall do for the greater glory of God. LAUS DEO SEMPER!

College Vision, Goals and Objectives:

Vision

A center of excellence in engineering and architecture education imbued with Catholic mission and identity serving as a role-model catalyst for countryside development

Mission

To provide accessible quality engineering and architecture education leading to the development of conscientious, competent and

compassionate professionals who continually contribute to the advancement of technology, preserve the environment, and improve life for countryside development.

Goals

The College of Engineering and Architecture is known for its curricular programs and services, research undertakings, and community involvement that are geared to produce competitive graduates:

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- who are equipped with high impact educational practices for global employability and technopreneurial opportunities;

- whose performance in national licensure examinations and certifications is consistently above national passing rates and that falls within the 75^th to 90^th percentile ranks; and,

- who qualify for international licensure examinations, certifications, and professional recognitions;

Objectives

In its pursuit for academic excellence and to become an authentic instrument for countryside development, the College of Engineering and Architecture aims to achieve the following objectives:

1. To provide students with fundamental knowledge and skills in the technical and social disciplines so that they may develop a sound perspective for competent engineering and architecture practice;

2. To inculcate in the students the values and discipline necessary in developing them into socially responsible and globally competitive professionals;

3. To instill in the students a sense of social commitment through involvement in meaningful community projects and services;

4. To promote the development of a sustainable environment and the improvement of the quality of life by designing technology solutions beneficial to a dynamic world;

5. To adopt a faculty development program that is responsive to the continuing development and engagement of faculty in research, technopreneurship, community service and professional development activities both in the local and international context;

6. To implement a facility development program that promotes a continuing acquisition of state of the art facilities that are at par with leading engineering and architecture schools in the Asia Pacific region; and,

7. To sustain a strong partnership and linkage with institutions, industries, and professional organizations in both national and international levels.

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Relationship of the Program Educational Objectives to the Vision-Mission of the University and the College of Engineering & Architecture:

Computer Engineering Program Educational Outcomes (PEOs):

Within a few years after graduation, our graduates of the Computer Engineering program are expected to have:

Vision-Mission

Christ-

Centeredness Integrity Excellence Community Societal

Responsibility

1. Practiced their profession     

2. Shown a commitment to life-long learning     

3. Manifested faithful stewardship     

Relationship of the Computer Engineering Program Outcomes to the Program Educational Objectives:

Computer Engineering Student Outcomes (SOs):

At the time of graduation, BS Computer Engineering program graduates should be able to:

PEOs

1 2 3

a) Apply knowledge of mathematics, physical sciences, and engineering sciences to the practice of Computer

Engineering.   

b) Design and conduct experiments, as well as to analyze and interpret data   

c) Design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability, in accordance with standards

  

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d) Function on multidisciplinary teams   

e) Identify, formulate and solve engineering problems   

f) Have an understanding of professional and ethical responsibility   

g) Demonstrate and master the ability to listen, comprehend, speak, write and convey ideas clearly and effectively, in

person and through electronic media to all audiences.   

h) Have broad education necessary to understand the impact of engineering solutions in a global, economic,

environmental, and societal context   

i) Recognition of the need for, and an ability to engage in life-long learning and to keep current of the development

in the field   

j) Have knowledge of contemporary issues   

k) Use the techniques, skills, and modern engineering tools necessary for engineering practice.    l) Have knowledge and understanding of engineering and management principles as a member and leader in a

team, to manage projects and in multidisciplinary environments.   

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COURSE SYLLABUS

Course Title: DISCRETE MATHEMATICS Course Code: DISMATH

Course Credit: 3 Units Year Level: 4^th Year

Pre-requisites: ALGEBRA 2 Course Calendar:

1^st Semester Course Description:

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. It concerns counting,

probability, addition, and limit process over discrete sets. It is an essential part of the foundations of computer science, statistics, probability theory, and algebra.

Course Outcomes (COs):

After completing this course, the students should be able to:

Relationship to the Program Outcomes:

a b c d e f g h i j k l

1) Prove theorems and using logic

E E

2) Demonstrate knowledge of the basic concepts and exhibit awareness of issues related to the computer engineering applications of discrete

mathematics. E E E

3) Apply counting techniques in calculation of discrete probabilities and use trees and graph theory in dealing with discrete mathematics

problems E E

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COURSE ORGANIZATION

Time

Frame Hours Course

Outcomes Course Outline

Teaching &

Learning Activities

Assessment

Tools Resources

Week 1

3 CO2 A. INTRODUCTION TO DISCRETE MATHEMATICS

 What is Discrete Mathematics

 Importance of Discrete Mathematics

 Uses of Discrete Mathematics Library Activity

 Set Theory

 Lecture

 Multimedia instruction

 Small group discussion on real-life

applications of Discrete Mathematics

 Class discussion

 Questioning

 Library work:

Set Theory

Recitation Classroom assignment Direct observation Group work

A[1], B[1], B[2], B[4]

Week 2

3 CO1

CO2

B. SET THEORY

 Introduction to Sets

 Venn Diagram

 Set Operations

 Mathematical Induction

 Small group discussion on Set Theory

 Questioning

Seatwork Recitation Direct observation Board Work Group work Quiz

A[1], B[1], B[2], B[3], B[4], B[5],

B[6]

Week 3

3 CO1

CO2

C. RELATIONS

 Relations

 Pictorial Representation of

 Small group discussion on applications of

Recitation Direct observation

B[1], B[2], B[4], B[5], B[6]

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Relations

 Composition of Relations

 Types of Relations

 Partial Ordering Relations Library Activity:

 Functions and Algorithms

relations

 Questioning

 Library work:

Functions and Algorithms

Classroom assignment Board Work Group work

Week 4

3 CO1

CO2

D. FUNCTIONS AND ALGORITHMS

 Introduction to Functions

 One-to-One, Onto, and Invertible Functions

 Mathematical Functions, Exponential and Logarithmic Functions

 Small group discussion on the design of Functions and Algorithms

 Questioning

Seatwork Recitation Direct observation Group work Quiz

B[1], B[2], B[4], B[5], B[6]

Week 5

3 CO1

CO2

E. FUNCTIONS AND ALGORITHMS II

 Recursively Defined Functions

 Cardinality

 Algorithms and Functions

 Complexity of Functions Library Activity:

 Logic and Propositions

 Questioning

 Library work:

Logic and Propositions

Recitation Direct observation Classroom assignment Board Work Group work

B[1], B[2], B[4], B[5], B[6]

PRELIM EXAMINATION Week

6-7

6 CO1

CO2

F. LOGIC AND PROPOSITIONAL CALCULUS

 Propositions and Compound Propositions

 Basic Logical Operations

 Propositions and Truth Table

 Lecture

 Small group

Seatwork Recitation Direct observation

A[1], B[1], B[2], B[3], B[5], B[6]

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 Logical Equivalence discussion on real-life application in

 Questioning

Board Work Group work Written examination

Week 8

3 CO1

CO2

G. LOGIC AND PROPOSITIONAL CALCULUS II

 Algebra of Propositions

 Logical Implication

 Propositional Functions, Quantifiers Library Activity

 Vectors and Matrices

 Lecture

 Questioning

 Small group activities on real-life

applications of Logic and Propositions

Classroom assignment Recitation Direct observation Board Work Group work Quiz

A[1], B[1], B[2], B[3], B[5], B[6]

Week 9-10

6 CO1

CO2

H. VECTORS AND MATRICES

 Vectors and Matrices

 Vector Operations

 Matrix Operations

 Square Matrices

 Determinants

 Gaussian Elimination and Boolean Matrices

 Lecture

 Small group activities on Vectors and Matrices

 Questioning

A[1], B[6]

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Week 11-12

6 CO1

CO2 CO3

I. COUNTING

 Basic Counting Principles

 Factorial Notation

 Binomial Coefficients

 Permutations

 The Pigeonhole Principle Library Activity:

 Graph Theory

 Lecture

 Small group activities on Counting

 Questioning

 Jeopardy game

 Library work:

Graph Theory

Classroom assignment Recitation Direct observation Board Work Group work Written examination

B[1], B[2], B[3], B[4], B[5], B[6]

MIDTERM EXAMINATION Week

13

3 CO1

CO2 CO3

J. GRAPH THEORY

 Data Structures

 Graphs and Multigraphs

 Tree Graphs

 Representing Graphs in Computer Memory

 Lecture

 Small group activities on real-life

applications of Graph Theory

 Questioning

Seatwork Recitation Direct observation Board Work Group work

A[1], B[1], B[2], B[4], B[6]

Week 14

3 CO1

CO2 CO3

K. DIRECTED GRAPHS

 Directed Graphs

 Rooted Trees

 Warshall’s Algorithm: Shortest Path

 Graph Algorithms:

 Depth-First and Breadth-First Searches

 Small group activities on Directed Graphs

Classroom assignment Recitation Direct observation Board Work

A[1], B[1], B[2], B[4], B[6]

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Library Activity

 Binary Trees

 Questioning

 Library work:

Binary Trees

Group work Quiz

Week 15

3 CO1

CO2 CO3

L. BINARY TRESS

 Binary Trees

 Representing Binary Trees in Memory

 Binary Search Trees

 Lecture

 Small group discussion on applications of Binary Trees

 Questioning

 Small group discussion on

Seatwork Recitation Direct observation Board Work Group work

[B1], B[2], B[4]

Week 16

3 CO1

CO2

M. PROPERTIES OF THE INTEGERS

 Order and Inequalities, Absolute Value

 Mathematical Induction

 Division Algorithm

 Congruence Relation

 Lecture

 Questioning

Recitation Board Work

[B1], B[2], B[4], B[5]

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Week 17

3 CO1

CO2 CO3

N. MODELING COMPUTATIONS: LANGUAGE, GRAMMARS, MACHINES

Languages and Grammars

 Phrase Structure Grammars

 Types of Phrase Structure Grammars

 Derivation Trees

 Backus-Naur Form

Finite State Machines with Output

 Finite State Machines with Outputs Finite State Machines with no Output

 Set of Strings

 Finite-State Automata

 Language Recognition by Finite-State Machines

 Non-Deterministic Finite-State Automata

 Small group discussion on Modeling Computations

 Small group activities on Finite State Machines

 Questioning

B[1], B[2], B[5]

Week 18

3 CO1

CO2 CO3

Language Recognition

 Regular Sets

 Kleene’s Theorem

 Regular Sets and Regular Grammars

 More Powerful Types of Machines Turing Machines

 Definition of Turing Machines

 Using Turing Machines to Recognize Sets

 Lecture

 Questioning

 Jeopardy game

Recitation Written examination

B[1], B[2], B[5]

FINAL EXAMINATION

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Course References:

A. Basic Readings

1) Brown, J.I. (2013). Discrete structures and their interactions. Taylor & Francis Group B. Online References

1) Conradie, W. & Goranko, V. (2015). Logic and Discrete Mathematics: A Concise Introduction. Wiley. Retrieved from http://site.ebrary.com/lib/haulib/detail.action?docID=11048164&p00=discrete+mathematics&

token=1dad4626-6e53-41d6-a197-293c919d23ea

2) Conradie, W., Goranko, V., Robinson, C. (2015). Logic and Discrete Mathematics: A Concise Introduction, Solutions Manual. Wiley. Retrieved from http://site.ebrary.com/lib/haulib/detail.action?docID=11052380&p00=discrete+mathematics

3) CourseHack (2012). Dicrete Math Tutorial. Retrieved from https://www.youtube.com/watch?v=aM1fuQzWWuQ&list=PL32BBBE7E5C80439B 4) Epp, S. (2014). Discrete Mathematics: An Introduction to Mathematical Reasoning. Cengage Learning. Retrieved from

https://books.google.com.ph/books?id=HzPvg03I_xkC&printsec=frontcover&dq=discrete+mathematics&hl=

en&sa=X&ved=0ahUKEwj47sCk8aLOAhVJNpQKHaJ0BIM4ChDoAQg7MAY#v=onepage&q=discrete%20mathematics&f=false

5) TheTrevTutor (2014). Discrete Math Tutorials. Retrieved from https://www.youtube.com/watch?v=5plFb4jrzd4&list=PLDDGPdw7e6Ag1EIznZ-m- qXu4XX3A0cIz

6) Wallis, W.D. (2012). A Beginner’s Guid to Discrete Mathematics. Springer Science Business Media, LLC. Retrieved from https://books.google.com.ph/books?id=18W4_LJ5bL0C&printsec=frontcover&dq=discrete+mathematics

&hl=en&sa=X&ved=0ahUKEwjhtMjO7KLOAhUHF5QKHYRzAE4Q6AEIKDAC#v=onepage&q=discrete%20mathematics&f=false

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Course Requirements 1) 3 Major Exams (Prelims, Midterms, and Finals) 2) 6 Quizzes

3) Assignments &Seatworks

Grading System CAMPUS++ COLLEGE ONLINE GRADING SYSTEM

Legend: (All Items in Percent)

CSA Class Standing Average for All Performance Items (Cumulative) P Prelim Examination Score

M Midterm Examination Score F Final Examination Score MEA Major Exam Average PCA Prelim Computed Average MCA Midterm Computed Average FCA Final Computed Average

Computation of Prelim Computed Average (PCA) CSA =

MEA = P

PCA = (60%)(CSA) + (40%)(MEA)

Computation of Midterm Computed Average (MCA) CSA =

MEA =

MCA = (60%)(CSA) + (40%)(MEA)

Computation of Final Computed Average (FCA)

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CSA =

MEA =

FCA = (60%)(CSA) + (40%)(MEA) Passing Percent Average: 50

Transmutation Table

Range of Computed Averages Range of Transmuted Values Grade General Classification 94.0000 – 100.0000 97 – 100 1.00 Outstanding

88.0000 – 93.9999 94 – 96 1.25 Excellent 82.0000 – 87.9999 91 – 93 1.50 Superior 76.0000 – 81.9999 88 – 90 1.75 Very Good 70.0000 – 75.9999 85 – 87 2.00 Good 64.0000 – 69.9999 82 – 84 2.25 Satisfactory 58.0000 – 63.9999 79 – 81 2.50 Fairly Satisfactory 52.0000 – 57.9999 76 – 78 2.75 Fair

50.0000 – 51.9999 75 3.00 Passed

Below Passing Average 5.00 Failed

6.00 Failure due to absences 8.00 Unauthorized or unreported withdrawal

Note: A student's Computed Average is a consolidation of Class Standing Percent Average and Major Exam Percent Average.

Course Policies Maximum Allowable Absences: 10 (held 3 times a week); 7 (held 2 times a week)

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Date Revised: Date Effectivity: Prepared By: Checked By: Approved By:

May 30, 2016 June, 2016 Engr. Gerard C. Cortez CpE Faculty

Engr. Gerard C. Cortez Chairperson, CpE Department

Dr. Doris Bacamante

Dean, College of Engineering and Architecture