College of Science

University of the Philippines Cebu

UP Leading Regional and Global University in an Environment that Sustains 21st Century
Vision Learning, Knowledge Creation and Public Service for Society and Humanity
UP • Academic excellence and operational excellence;
Mission • Strong research and creative capability, supported by an expanded graduate program
and geared to addressing the country’s problems;
• Excellent faculty and staff working in an environment conducive to outstanding
performance and high productivity;
• The best and brightest students from across the country prepared for successful careers
and responsive citizenship;
• Strong support from the alumni and other stakeholders;
• High visibility and effective public service;
• Modernized physical facilities and technological infrastructure for teaching, research,
and administration; and
• Financial sustainability achieved by resource generation and administrative efficiency,
while preserving its public character.
UP Core Values Honor and Excellence
UP A lead university in pioneering research, creative design, ICT-driven innovation,
Cebu responsible governance, and community service in Central Visayas and the global society
Vision
UP UP Cebu promotes scientific, socio-economic, cultural, and environmental progress in
Cebu Central Visayas, in the nation and the world through creative and innovative instruction,
Mission research, intellectual productivity, and public service. UP Cebu:
• offers accessible quality graduate, undergraduate, and continuing education that will
produce innovative, critical, nationalist, ethical, gender-sensitive and socially
responsible graduates who demonstrate high levels of academic pursuit;
• conducts pioneering research and develops novel and creative technologies through
transdisciplinary collaboration.
• applies products of knowledge generation, dissemination, and intellectual
productivity to improve social welfare; and
• ensures administrative efficiency in the delivery of excellent, responsible service in
support of learning, research, intellectual productivity, and public service.
College Vision A dynamic institution recognized as a regional, national, and international leader in
excellent instruction, innovative research, and relevant extension in science and
technology
College Mission • To conduct pioneering research and develop novel technologies through
transdisciplinary collaboration
• To produce graduates with the highest level of academic pursuit and personal
growth through a conducive learning environment
• To share the scientific and technological expertise to address societal challenges

COURSE NUMBER : Stat 117

COURSE TITLE : Mathematics for Statistics
COURSE DESCRIPTION : The Real number system; Principles of logic; Methods of proof;
Fields; Sigma fields; Sequences of sets; Sequences and Series;
Combinatorial analysis
COURSE CREDIT : 3 units
EXPECTED LEARNING OUTCOMES AND RELATIONSHIP TO PROGRAM LEARNING OUTCOMES

Course Outcomes Program Outcomes*

At the end of the course, the students should be able to: a b c d e f g h i j k l m n o p q r s

Determine the logical equivalence involving quantifiers; x x x x x x x x x

Prove using direct proof, indirect or proof by contradiction,
proof by counterexample and mathematical induction; x x x x x x x x x

Prove existence and uniqueness; x x x x x x x x x

Define and illustrate terminologies on set theory; x x x x x x x x x

Perform operations on sets; x x x x x x x x x x

Define and illustrate classes of sets; x x x x x x x x x
Identify the difference among one-to-one, onto and one-to-
x x x x x x x x x
one correspondence;
Prove that a function is one-to-one, onto and one-to-one
x x x x x x x x x
correspondence;
Find the inverse of a function; x x x x x x x x x x
Determine if a sequence is increasing, decreasing and
x x x x x x x x x
monotonic;
Show that a sequence has a greatest lower bound (glb) and
x x x x x x x x x
lowest upper bound (lub);
Generate power series and generate using Taylor series; x x x x x x x x x x

Solve problems using permutations and combinations. x x x x x x x x x x

*PROGRAM OUTCOMES (adapted from CHED CMO no. 42 s. 2017):

The minimum standards for the BS Statistics program are expressed in the following
minimum set of learning outcomes:

1. Common to all baccalaureate programs in all types of schools

a) articulate the latest developments in their specific fields of practice (PQF level 6
descriptor);
b) effectively communicate orally and in writing using both the English and Filipino
languages;
c) work effectively and independently in multi-disciplinary and multi-cultural teams
(PQF level 6 descriptor);
d) demonstrate professional, social, and ethical responsibility, especially in practicing
intellectual property rights and sustainable development; and,
e) preserve and promote "Filipino historical and cultural heritage" (based on RA
7722).

2. Common to Science and Mathematics programs

Graduates of the Science and Mathematics programs are able to:
f) demonstrate broad and coherent knowledge and understanding in the core areas
of statistical theory and statistical modeling;
g) apply critical and problem solving skills using the scientific method;
h) interpret scientific data and make judgments that include reflection on relevant
scientific and ethical issues;
i) carry out basic mathematical and statistical computations and use appropriate
technologies in the analysis of data;
j) communicate information, ideas, problems, and solutions, both orally and in
writing, to other scientists, decision-makers and the public;
k) relate science and mathematics to the other disciplines;
l) design and perform safe and responsible techniques and procedures in laboratory
of field practices;
m) critically evaluate inputs from others;
n) appreciate the limitations and implications of science in everyday life; and
o) commit to the integrity of data.

3. Specific to the Bachelor of Science in Statistics Program

The scientific process involved in the statistical science includes the generation/
compilation of data, extraction/aggregation of information through statistical analysis, and
utilization of information in decision-making.
 The BS Statistics program is intended to develop students with competencies in the
generation of timely, relevant, and accurate/reliable data in solving problems in aid of
decision-making and policy formulation, in making valid and meaningful decisions from
statistical analysis, and in effectively communicating results of statistical research/activities
(Data Scientist).

Graduates of BS Statistics are able to:

p) demonstrate broad and coherent knowledge and understanding in the core areas
of statistics, computing, and mathematics;
q) translate real-life problems into statistical problems;
r) generate information involving the conceptualization of a strategy for generating
timely and accurate/reliable data, organizing a process for putting together or
compiling the needed data, and transforming available data into relevant and
useful forms; and,
s) identify appropriate statistical tests and methods and use these properly for the
given problems, select optimal solutions to problems, and make decisions in the
face of uncertainty.

METHODS FOR ASSESSING THE EXPECTED LEARNING OUTCOMES

Learning and Teaching Modes

The course concepts will be taught onsite using slide/beamer presentations and lecture notes.
The lectures will be enhanced by utilizing class discussions and consultations. The learners’
skills and competencies will be assessed through quizzes, problem sets, and exams.
 COURSE COVERAGE

Suggested
Teaching and Resources/ Suggested Assessment
Week Learning Outcome/s Tools/Activit
Course Topic Learning Strategies References Output(s)
ies

I. Review: The Real Number System 1.1 define and explain the basic - class lecture/ - book - answers - quiz and
A. Mathematical Systems concepts of a mathematical discussion references to quiz problem
system - lecture notes and set
B. Subsets of the Real Number - independent study
System 1.2 illustrate the different - guided class problem
1 C. Cartesian Products mathematical axioms discussions set
1.3 compare the different subsets of
ℝ
1.4 define and illustrate a Cartesian
product
II. Logic 2.1 define and illustrate a proposition - class lecture/ - book - answers - quiz and
A. Introduction to Logic or a mathematical statement presentation references to quiz problem
B. Compound Statements and Truth Tables 2.2 distinguish the different types of - independent study - lecture notes and set
- Basic Logical Operations a compound statement - guided class problem
_ The Truth Table 2.3 determine the truth value of a discussions set
_ Conditional Propositions simple or compound statement
_. Logical Equivalence 2.4 determine the logical
C. Quantified Statements equivalence of two
- Propositional Function mathematical statements
2.5 determine the truth value of
2-5 - Universally and Existentially Quantified
statements containing
Statements quantifiers
D. Proving the Validity of an Argument 2.6 find out the validity of a
- Proving Using the Truth Table statement
- Proving Using the Rules of Inference 2.7 prove a statement using a truth
table
- Proving an Argument that has a Quantified
2.8 prove a statement using the
Statement
rules of inference
E. Methods of Proof 2.9 prove a statement either
- Using Definitions in Proofs directly or indirectly
- Proving P → Q
 - Direct Method 2.10 prove a
- Proof by Contradiction statement
- Proof by Contrapositive inductively
- Special Case: Proving 2.11 prove equivalent statements
- (p1 v p2) → q 2.12 disprove a statement by
- Proving the Logically Equivalent Statements providing a
- Proving the biconditional P ↔ Q counterexample
- Proving Equivalent 2.13 prove or disprove quantified
Statements statements
2.14 prove statements concerning
- Disproving P → Q
existence and uniqueness
- Proving or Disproving Quantified Statements
- Proving or Disproving - Quantified
Statements with one variable
- Proving or Disproving - Quantified
Statements with two variables
F. Mathematical Induction
G. Existence Theorem
H. Uniqueness Theorem

6 1ST LONG EXAM* (Chapters 1 & 2)

III. Set Theory 3.1 define and illustrate a set, its - class lecture/ - book references - answers - quiz and
A. Universal Sets and Subsets subsets, and the universal set presentation - lecture notes to quiz problem
- Ways of Specifying a Set 3.2 enumerate the properties of set - independent and set
- Set Inclusion inclusion study problem
3.3 perform the different set set
- Equality of Two Sets - guided class
B. Set Operations operations discussions
3.4 define and utilize the generalized
- Definition of Terms
set operations
7-8 - Properties of Set Operations
3.5 discuss the properties of set
C. Generalized Operations operations and generalized set
- Definition of Generalized Operations operations
- Properties of Generalized Operations 3.6 define and illustrate classes of sets
D. Classes of Sets 3.7 determine whether two sets are
- The Class of Sets and the Power Set disjoint
- Pairwise Disjoint Sets 3.8 find a partition a set
3.9 define and illustrate fields and
- Partition of a Set
sigma-fields
 E. Fields and Sigma-Fields 3.10 determine the monotonicity of a
- Field and Minimal Field sequence of sets
- Sigma-Field and Minimal Sigma-Field 3.11 find the limit of a monotone
- The Borel Field sequence of sets
F. Sequence of Sets

IV. Functions 4.1 differentiate a function from a - class lecture/ - book references - answers - quiz and
A. Relations and Functions relation presentation - lecture notes to quiz problem
- Relations 4.2 show whether a function is one-to- - independent and set
- Functions one study problem
4.3 show whether a function is onto set
9 B. One-to-One and Onto Functions - guided class
C. Special Types of Functions 4.4 find the inverse of a function (if it discussions
exists)
- Inverse Function
4.5 illustrate a set function and an
- Set Function indicator function
- Indicator Function

10 2ND LONG EXAM* (Coverage: Chapters 3 & 4)

V. Sequences and Sets 5.1 define a sequence and illustrate - class lecture/ - book references - answers - quiz
A. Sequences 5.2 distinguish an arithmetic sequence presentation - lecture notes to quiz and problem
- Sequence and Strings and a geometric sequence - independent and set
- Special Types of Sequence 5.3 discuss the properties of study problem
summation set
B. The Summation Notation - guided class
- Properties of Summation 5.4 use the Binomial Theorem to discussions
- Changing the Index and Limits of a Sum expand powers of binomials
5.5 define a series and illustrate
11 -12 - Summation of the First n terms of an
5.6 find the series expansion of a
Arithmetic and Geometric Sequence function using Taylor series
C. Series and Expansions
- Infinite Series and Its Convergence
- Taylor Expansion of f(x)
D. Other Special Sums
- Telescopic Series
- Square of a Sum
 VI. Counting Techniques 6.1 define equivalent sets and - class lecture/ - book references - answers - quiz and
A. Cardinality illustrate presentation - lecture notes to quiz problem
- Equivalent Sets 6.2 determine the cardinality of a set - independent and set
- Cardinal of Sets 6.3 make use of the Fundamental study problem
Principle of Counting set
B. Basic Principles of Counting - guided class
13 C. Permutations and Combinations 6.4 count the number of different discussions
permutations and combinations
- Definition of Terms
- Counting Permutations and Combinations
- Cardinality of New Sets Formed Through
Set Operations
- Special Results on Balls in Urns
14 3RD LONG EXAM* (Coverage: Chapters 5 & 6)
16 FINAL EXAMINATION (Coverage: All Chapters)
42.0
Learning Resources

I. References
1. A First Course in Probability Tenth Edition by Ross (2018)
2. Basic Analysis I: Introduction to Real Analysis Volume 1 Fifth Edition by Lebl (2018)
3. Calculus Eleventh Edition by Larson and Edwards (2017)
4. Calculus: Early Transcendentals Third Edition by Briggs et. al. (2018)
5. Calculus: Single and Multivariable Seventh Edition by Hughes-Hallett et. al. (2020)
6. Combinatorial Mathematics First Edition by West (2020)
7. Combinatorics Through Guided Discovery by Bogart (2017)
8. Combinatorics: A Problem-Based Approach First Edition by Mladenovic (2019)
9. Combinatorics: A Very Short Introduction Illustrated Edition by Wilson (2016)
10. Conceptions of Set and the Foundations of Mathematics by Incurvati (2020)
11. Concise Introduction to Logic and Set Theory First Edition by Jebril et. al. (2021)
12. Discrete Mathematics and Its Applications Eighth Edition by Rosen (2018)
13. Discrete Mathematics Eighth Edition by Johnsonbaugh (2017)
14. Discrete Mathematics with Applications Fifth Edition by Epp (2019)
15. Discrete Mathematics: An Open Introduction Third Edition by Levin (2018)
16. Elementary Statistics Thirteenth Edition by Triola (2017)
17. Elementary Statistics: A Step-By-Step Approach Tenth Edition by Bluman (2017)
18. Introduction to Logic by Lisle (2018)
19. Introduction to Logic Fifteenth Edition by Copi et. al. (2019)
20. Introduction to Probability Second Edition by Blitzstein and Hwang (2019)
21. Introduction to Real Analysis Third Edition by Stoll (2021)
22. Introductory Combinatorics Fifth Edition by Brualdi (2017)
23. Logic and Philosophy: A Modern Introduction Thirteenth Edition by Kahane et. al. (2021)
24. Logic: A Complete Introduction by Lee (2017)
25. Logic: An Emphasis on Formal Logic Fourth Edition by Baronett (2018)
26. Naïve Set Theory by Halmos (2017)
27. Probability and Statistics Fourth Edition by DeGroot and Schervish (2018)
28. Probability for the Enthusiastic Beginner by Morin (2016)
29. Pure Mathematics for Beginners by Warner (2018)
30. Set Theory for Beginners by Warner (2019)
31. Set Theory: A First Course First Edition by Cunningham (2016)
Rubric 1 for Problem Solving
Category 4 - Exemplary 3 - Proficient 2 - Developing 1 - Needs
development
Plan The group identifies The group identifies The group identifies The group is unable
the key elements of the key elements of the key elements of to identify the key
the problem and the problem and the problem and elements of the
clearly outlines the clearly outlines the clearly outlines the problem and/or the
objectives in an objectives in an objectives in an objectives without a
effective manner with effective manner with effective manner great deal of
no assistance. little assistance. with assistance. assistance.

Process The group develops The group develops The group develops The group is unable
strategies that are strategies that are strategies that are to develop strategies
insightful and use insightful and use insightful and use that are insightful and
logical reasoning to logical reasoning to logical reasoning to logical without a
reach accurate results reach accurate results reach accurate great deal of
with no assistance. with little assistance. results with assistance.
assistance.

Evaluation The group determines The group The group The group
whether the results determines whether determines whether determines whether
are accurate and the results are the results are the results are
reflects on any issues, accurate and reflects accurate and accurate and reflects
mistakes, or on any issues, reflects on any on any issues,
misunderstandings mistakes, or issues, mistakes, or
encountered during misunderstandings mistakes, or misunderstandings
the problem-solving encountered during misunderstandings encountered during
process with no the problem-solving encountered during the problem-solving
assistance. process with little the problem solving process without a
assistance. process with great deal of
assistance. assistance.

Construct The group constructs The group constructs The group The group constructs
Representation a representation a representation constructs a a representation
(chart, written, verbal) (chart, written, representation (chart, written,
that accurately reflects verbal) that (chart, written, verbal) that
the problem and aids accurately reflects verbal) that accurately reflects
in solving the the problem and aids accurately reflects the problem and aids
problem with no in solving the the problem and in solving the
assistance. problem with aids in solving the problem without a
little assistance. problem with great deal of
assistance. assistance.
COURSE REQUIREMENTS

Coverage of each exam will be announced at least

1 week before the exam schedule.
Long Exams 60% 1ST – Chapters 1 & 2
2ND – Chapters 3 & 4
3RD – Chapters 5 & 6
Final Exam This covers all six chapters in STAT 117.
20%

Assignments/Problem Sets, Each quiz covers all topics discussed per

Quizzes, etc. 20% chapter.

Total 100%

GRADING SYSTEM

[95.00, 100.00] 1.00 [68.00, 72.00) 2.50

[90.00, 95.00) 1.25 [64.00, 68.00) 2.75
[85.00, 90.00) 1.50 [60.00, 64.00) 3.00
[80.00, 85.00) 1.75 [55.00, 60.00) 4.00
[76.00, 80.00) 2.00 [0, 55.00) 5.00
[72.00, 76.00) 2.25 Passing Grade 60.00 (3.00)

CLASS POLICIES

Classes will be done in a face-to-face session. Further instructions on class

assignments/problem sets shall be given or posted in UVEC (University Virtual Education
Commons) or through UP Mail.

1. Students are encouraged to come to class on time.

2. Class activities and assignments shall be submitted at a given period (refer to the given
assignment guide). Submissions must be on or before the deadline. Late submissions
will not be accepted and is considered a zero score. Make sure to accomplish class works
right away (if possible) to keep oneself from getting overwhelmed from loads of class
works.
3. Class participation is encouraged with a sense of respect. In the middle of the discussion,
student should raise his/her hand if he/she has questions or clarifications on the topic.
 4. To avoid class interruptions, refrain from doing unnecessary activities such as doing
problem sets or projects for other courses, watching videos, and making unnecessary
noises while the class is ongoing.
5. If a student is caught cheating in any form (e.g., plagiarism, making others do their
assigned tasks) concerning the requirements of the course, he or she will receive a final
grade of 5.00 and his/her case will be sent to the Student Disciplinary Tribunal for further
action by the University.
6. Attendance shall be recorded. This is monitored before every regular class session, and
timely submission of class works. By university rules, the maximum number of allowable
absences is only 6, excused or unexcused. If the student exceeds 6 absences, then s/he
is urged to drop the course, or s/he will risk getting a grade of 5.00.
7. In an event that a student is not able to attend the class, he/she should send an e-mail
to the teacher stating the reason for absence.
8. There will be 3 long exams and 1 final comprehensive exam. All exams will be done
onsite during class hours.
9. Make-up exams will only be given to students with a valid reason as specified in #10. If
the absence is not valid, the student is given a score of zero in that examination.
10. Excused absences are those due to illness, death of an immediate family member, or
any official university-related activity that requires the student’s attendance or
representation. Documents of certification or proof with contact details should be
submitted immediately. Otherwise, the absence will be unexcused.
11. No make-up quizzes or class activities will be given, excused or unexcused.
12. If a grade of 4.00 is incurred, the student needs to take a removal exam. An INC grade
would require the student to complete the course requirement. One year is given to
complete his/her course deficiencies, otherwise, the student will get a grade of 5.00 in
the course.
13. Dropping of the course must be done officially through the Office of the University
Registrar (OUR).

ABOUT THE INSTRUCTOR

Mr. Jayno M. Gerzon, a BS Mathematics graduate of the University of the Philippines

Cebu.

Email: jmgerzon@up.edu.ph
Consultation Hours: MTh 1:30 - 3:00 PM
TF 12:30 - 4:00 PM

Clarifications and other class concerns shall be addressed during class hours and consultation
period.
IMPORTANT REMINDER ON THE COURSE PACK:

The course pack provided to you in any form is intended only for your use in connection with
the course that you are enrolled in. It is not for distribution or sale. Permission should be
obtained from your teacher for any use other than for what it is intended.