Discrete-Mathematics syllabus sample.docx

Discrete Mathematics sample syllabus and course outline

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COURSE SYLLABUS
In
DISCRETE MATHEMATICS
2
nd
Semester S/Y 2020 – 2021

I. COURSE INFORMATION

A. COURSE CODE : IT 212
B. COURSE NAME : Discrete Mathematics
C. DEGREE PROGRAM/LEVEL : Bachelor of Science in Information Technology / 1
D. COURSE CREDIT : Three (3) units
E. CONTACT HOURS PER WEEK : Three (3) hours lecture / week
F. PREREQUISITE : NONE
G. COURSE DESCRIPTION : This course introduces the foundations of discrete mathematics that
are widely used in Information Technology. Topics include Functions,
Relations and Set Theory, Basic Logic, Proof Techniques, Discrete
Probability and Introduction to Graphs, and Trees. This key topics
will include techniques in how to think logically and mathematically
and apply these techniques in solving problems.

II. PROGRAM EDUCATION AL OBJECTIVES : The graduates of Bachelor of Science in Information Technology should
be able to:
1. Apply and demonstrate computing skills in developing, implementing and maintaining computer-based systems
evident in their profession;
2. Demonstrate effective communication skills with team members and the public;
3. Exhibit exemplary behavior conscious of social and environmental responsibility through active professional
engagement; and
4. Engage in lifelong learning for personal and professional development

III. PROGRAM OUTCOMES (PO) AND COURSE OUTCOMES (CO): Upon completion of the program and the course, the students must be able to do the following:
PROGRAM OUTCOMES (PO) CODE COURSE OUTCOMES (CO) CODE DESIRED LEARNING OUTCOMES (LO)

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PO1

Understand best practices and standards
and their applications
CO1






Show formal methods of proving arguments
through symbolic prepositional and predicate
logic, which are the building blocks of basic
programming skills.



DLO1

DLO2


DLO3
Identify propositional statements

Prove propositional statements using
symbolic logic

Write a formal proof of validity
PO2 Analyze complex problems, and identify and
define the computing requirements
appropriate to its solution
CO2 Understand the basic terminology of functions,
relations, and sets.
DLO4 Identify the basic concepts of set theory,
function and relation including its properties

CO3 Analyze complex problems then perform the
standard operations associated with sets,
functions, and relations.
DLO5



DLO6


DLO7
Solve given problems pertaining to set
operations

Construct a directed and undirected graph
given a problem in graph theory

Apply the basic concepts of counting and
discrete probability
PO3 Apply knowledge through the use of current
techniques, skills, tools and practices
necessary for the IT profession
CO4 Apply knowledge through practical examples to
the appropriate set, functions, or relation
model, and interpret the
associated operations and terminology in
context necessary for the IT profession.


DLO8

Solve real-world problems using the
concepts of discrete mathematics


IV. LEARNING OUTCOMES (LO): As evidence of attaining the above learning outcomes, the student has to do and submit the following:

Learning Output Description and other Details
Course Outcomes it
represents
LO1 Learning Portfolio A digital or paper-based compilation of learning tasks accomplished by the students
Prelim: week 1 to 6;
Midterm: week 7 to 12;
Final: week 13 to 18.
CO1, CO2, CO3, CO4


V. ASSESSMENTS (A): Aside from the final output, the student will be assessed at other times during the term by the following:

Assessment
Methods
Description and other Details Course Outcomes it
represents
A1 Quizzes High Level Technology - This is a quick check short assessment, which may be conducted after the discussion of CO1, CO2, CO3,

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every topic. This shall be given in a form of Real-Time Quiz via CSPC LeOnS or a game using other live interactive
applications e.g. mentimeter.com, quizizz.com, kahoot.com

Medium Level Technology - This is a quick check short assessment, which may be conducted after the discussion of
every topic. This shall be given in a form of either Real-Time Quiz via CSPC LeOnS, or a game using other live
interactive applications e.g. mentimeter.com, quizizz.com, kahoot.com OR traditional paper-pen as integrated in the
given printed module.

Low Level Technology - This is a quick check short assessment, after every topic, which is given in the printed
module.
CO4
A2 Learning Task High/Medium Level Technology – This will be provided after the discussion of each topic to apply the learning
through a hands-on activity. This shall be given via CSPC LeOnS and for the laboratory related activities students
are provided a Freeware installer which can be utilized on Android Phone and/or Personal Computer.

Low Level Technology - This is a hands-on activity which may be given after the discussion of every topic. This shall
be given in a form of traditional paper-pen as integrated in the given printed module.
CO1, CO2, CO3,
CO4
A3 Prelim
Examination
This is a written summative test to assess the knowledge accumulated from weeks 1–6.
High Level Technology - This is to be accomplished synchronous- or asynchronously through online exam via CSPC
LeOnS.
Medium Level Technology - This is to be accomplished asynchronously through online exam via CSPC LeOnS.
Low Level Technology - This is to be accomplished offline through paper-and-pen exam and should be submitted on
scheduled pick-up day and time.
CO1, CO2, CO3,
CO4
A4 Midterm
Examination
This is a written summative test to assess the knowledge accumulated from weeks 7–12.
High Level Technology - This is to be accomplished synchronous- or asynchronously through online exam via CSPC
LeOnS.
Medium Level Technology - This is to be accomplished asynchronously through online exam via CSPC LeOnS.
Low Level Technology - This is to be accomplished offline through paper-and-pen exam and should be submitted on
scheduled pick-up day and time.
CO1, CO2, CO3,
CO4
A5 Final Examination This is a written summative test to assess the knowledge accumulated from weeks 7–12.
High Level Technology - This is to be accomplished synchronous- or asynchronously through online exam via CSPC
LeOnS.
Medium Level Technology - This is to be accomplished asynchronously through online exam via CSPC LeOnS.
Low Level Technology - This is to be accomplished offline through paper-and-pen exam and should be submitted on
scheduled pick-up day and time.
CO1, CO2, CO3,
CO4

VI. RUBRIC TO ASSESS LEARN ING OUTPUTS (R): Please see attached sample table of specification and rubric of assessment.

VII. GRADING SYSTEM: At the end of the course, the students will be graded based on the given College Grading System:

Criteria Codes Grade Source Percentage of
Final Grade
COMPUTATION FOR PRELIM GRADE
Prelim Grade (PG) = Class Standing (50%) + Examination (50%) = 100%
COMPUTATION FOR MIDTERM GRADE
Final Midterm Grade (FMG) =
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2

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A. Class Standing A1, A2,
LO1
Quizzes Score, Learning
Task Score/Rubric Score,
Project Rubric Score
(Learning Portfolio)
50

B. Examination A3, A4, A5 Prelim Exam
Score/Midterm Exam
Score/Final Exam Score
50
TOTAL 100


VIII. LEARNING PLAN:

WEEK DESIRED
LEARNING
OUTCOMES
(DLO)
TOPICS TEACHING AND
LEARNING
ACTIVITIES (TLAs)
TEACHING MODALITIES RESOURCES ASSESSMENT
METHODS
COURSE
OUTCOMES
(CO)
1 ORIENTATION
• Grading system as per
student’s handbook
• Subject Requirements
• School policies as per
student’s handbook
• Classroom policies
• Course Overview
• Rationale of the Course
Interactive
Discussion
High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.

Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.
Student
Handbook
Course
Syllabus

AA1
AA2


2-4 DLO1
DLO2
DLO8
 Overview of Discrete
Mathematical
Structures
 Propositional Logic
 Propositional
Equivalence
Online Discussion,
Self-Paced Learning

High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

1, 2, 3, 4, 5,
6, 7, 8, 9, 10
AA1
AA2

CO1, CO4

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Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.

Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.
5-6 DLO3
DLO8
Proof Methods and
Strategy
Online Discussion,
Self-Paced
Learning,

High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.

Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.
1, 2, 3, 4, 5,
6, 7, 8, 9, 10
AA1
AA2
AA3
LO1
CO1, CO4
7-9 DLO4
DLO5
DLO8
The Fundamentals
• Set Theory
• Properties of Sets
• Set Operations


Online Discussion,
Self-Paced
Learning,

High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.

Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.
1, 2, 3, 4, 5,
6, 7, 8, 9, 10
AA1
AA2

CO2, CO3,
CO4

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10-12 DLO4
DLO5
DLO8
FUNCTIONS &
RELATIONS
• Functions defined on
General Sets
• Relations and Their
Properties
• Representing Relations
• Equivalence Relations
Online Discussion,
Self-Paced
Learning,

High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.

Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.
1, 2, 3, 4, 5,
6, 7, 8, 9, 10
AA1
AA2
AA4
LO1

CO2,CO3,
CO4
13-15 DLO6
DLO8
GRAPHS & TREES
• Trees
• Undirected & Directed
Graphs
Online Discussion,
Self-Paced Learning
High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.

Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.
1, 2, 3, 4, 5,
6, 7, 8, 9, 10
AA1
AA2

CO3, CO4
16-18 DLO7
DLO8
BASIC of COUNTING
and DISCRETE
PROBABILITY
• The Basics of Counting
(Sum & Product Rules)
• An Introduction to
Discrete Probability

Online Discussion,
Self-Paced
Learning,

High Level Technology:
Online Discussion with oral recitation and
brainstorming, problem solving.
Online Quizzes and Activities

Middle Level Technology:
Combined online discussion and self-paced
learning via LMS
Online quizzes and/or activities.
1, 2, 3, 4, 5,
6, 7, 8, 9, 10
AA1
AA2
AA5
LO1
CO3, CO4

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Low Level Technology: Self-paced learning
(Modular).
Module includes short quizzes and
activities.

IX. REFERENCES:

Books/E-Book/ Internet sources:

1. Susana S. Epp. 2019. Discrete mathematics with applications [Ebook]. Boston, MA: Cengage Learning. Retrieved from
http://dl.booktolearn.com/ebooks2/science/mathematics/9781337694193_Discrete_Mathematics_with_Applications_5th_3f15.pdf
2. Jean Gallier. 2019. Discrete Mathematics [Ebook] (2nd ed.). Philadelphia: Springer. Retrieved from http://www.cis.upenn.edu/~jean/discmath-root-b.pdf
3. Oscar Levin. 2019. Discrete Mathematics An Open Introduction [Ebook] (3rd ed.). Colorado. Retrieved from http://discrete.openmathbooks.org/pdfs/dmoi-
4. Rafael Pass and Wei-Lung Dustin Tseng. 2019. A Course in Discrete Structures [Ebook] Retrieved from https://www.cs.cornell.edu/~rafael/discmath.pdf
5. Kenneth Rosen. 2019. Discrete mathematics and its applications [Ebook]. New York, NY: McGraw-Hill. Retrieved from
http://dl.booktolearn.com/ebooks2/science/mathematics/9781259676512_Discrete_Mathematics_and_Its_Applications_8th_Edition_6a1e.pdf
6. Desmond Ballard. 2017. Discrete Mathematics. Larsen and Keller Education.
7. Willem Conradie and Valentin Goranko. 2015. Logic and Discrete Mathematics : a concise introduction. Hoboken: Wiley.
8. Richard Johnsonbaugh. 1993. Discrete Mathematics. 3rd Edition. Pearson
9. James Aspnes. 2020. Notes on Discrete Mathematics. Retrieved from http://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf
10. Lecture Notes on Discrete Mathematics. 2019. Retrieved from http://home.iitk.ac.in/~arlal/book/mth202.pdf



X. CLASSROOM POLICIES:

Student of this course are expected to:
1. Take and pass all short/long quizzes, laboratory exercises, prelim, midterm examinations and projects.
2. The students are required to submit the laboratory exercises, quizzes, projects, within the date specified.
3. Students are expected to attend regularly and punctually all scheduled classes.
4. Observe honesty and independence during recitation, examinations, and quizzes. Any student caught to be dishonest will be dealt with accordingly based on the
College policies.
5. Students are subject to the academic integrity and behavioral expectations of the school.
6. If a student’s absence causes them to miss a scheduled exam, the exam will be made up at the earliest possible time together with their medical certificate. It is
the student’s responsibility to coordinate with the instructor to have a make-up exam available.
7. Students are expected to ask questions and not just agree; for any difficulties encountered in the subject do not hesitate to talk to the instructor.
8. Keep your microphone on mute or raise your hand in case you want to speak or participate.

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