Syllabus-modern-geometry-about-the-history-of-older-mathematician

Major Math

1. Republic of the Philippines
JOSE RIZAL MEMORIAL STATE UNIVERSITY
The Premier University in Zamboanga del Norte
KATIPUNAN CAMPUS

COLLEGE OF EDUCATION
Program: BACHELOR OF SECONDARY EDUCATION – MATHEMATICS/SCIENCE
Department: COLLEGE OF EDUCATION
Instructor: MA.BETTY P. DECIN
COURSE SYLLABUS
Pre-Requisites:
Unit of Credit: 3 Units
No. of Hours:
Course Code MATH 115
Day & Time: TTH (7:30AM – 9:00AM)
Room: CED Room 3
Consultation Hours:
Course Title MODERN GEOMETRY
CORE VALUES
Humane Trust
Innovative Excellence
Transformational Communication
VISION
A dynamic and diverse internationally recognized University.
A dynamic, inclusive and regionally-diverse university in Southern Philippines.
MISSION
Jose Rizal Memorial State University pledges to deliver effective and efficient services along research, instruction, production, and extension.
It commits to provide advanced professional, technical and technopreneurial training with the aim of producing highly competent, innovative and
self-renewed individuals.
GOALS
G - lobally competitive educational institution;
R - esilient to internal and external risks and hazards;
I - nnovative processes and solutions in research translated to extension engagements;
P - artnerships and collaborations with private enterprise, other HEIs, government agencies, and alumni;
S - ound Fiscal Management and Participatory Governance.
Program Outcome/s
At the end of the course, the pre-service teachers should be able to:
(from CMO No. 75, s. 2017, p. 3 and 5):
6.2.b. Demonstrate mastery of subject matter/discipline
6.3.3.a. Exhibit competence in mathematical concepts and procedures
6.3.3.b. Exhibit proficiency in relating mathematics to other curricular areas
Course Description
This course seeks to enrich students’ knowledge of Euclidean Geometry. It discusses the properties and applications of other types of geometries
such as hyperbolic and elliptical geometries, finite geometry, and projective geometry. Students will advance their skills in the use of the axiomatic
method and in writing proofs which are both important in higher mathematics.
Course Outcomes Learning Outcomes Topics References Learning Learning Formative Summative
Registration No. 62Q15965
INSTITUTIONAL LEVEL
JRMSU-CED-017

2. Activities Materials Assessment Assessment
Recite the VMGO of
JRMSU
Present a role play
highlighting
dynamism in
developing the
attributes of VMGO
At the end of the period, the
students should be able to:
1.Memorize and recite the
VMGO of JRMSU.
Act out different situations
applying the attributes of the
VMGO.
Introduction of VMGOs,
GAD, and Course Syllabus
University Code
www.jrmsu.edu.ph
Listens
attentively to
discussion of
the VMGO of
JRMSU.
Watches a video
clip of JRMSU’s
achievements
and challenges
to the students.
LCD Projector,
Laptop, video
clip
Posting
comments or
videos
Group
Recitation
Recite the
VMGO of
JRMSU
Present a role
play
highlighting
dynamism in
developing the
attributes of
VMGO
At the end of the
course, the pre-
service teachers
should be able to:
A. Demonstrate
understanding of the
5th Postulate and
how it led to the
emergence of other
types of geometry;
At the end of the session/s, the
preservice teachers should be
able to:
• Discuss theorems familiar
from high school geometry the
traditional viewpoint
• Discover any hidden
assumptions that are made by
Euclid in his axioms and
proofs , or appeals to intuition
instead of logic
Unit 1. CLASSICAL
EUCLIDEAN GEOMETRY
1. The origins of geometry
2. Undefined terms
3. Euclid's first four
postulates
4. The parallel postulate
5. Attempts to
Week 1-3
Greenberg, M. (1974).
Smart, J. (1998).
1. Interactive
Discussion
2. Problem-
solving
(Individual)
A. Given some
figures,
students are
asked to solve
the problem
using the
postulates
presented.
B. The students
are asked to
prove some
postulates
discussed.
3. Board work
A. Some
students are
asked to write
the solutions of
the problems on
the board and
then explain it.
Handouts
Visual aids
Formative
assessment:
1. Oral
Recitation
2. Pen and
paper quiz
3. Class
participation
4. Seatwork
Unit Test

3. B. Demonstrate
knowledge of the
similarities and
differences among
the different
geometric types in
terms of concepts,
models, and
properties with or
without the use of ICT
tools ;
At the end of the session/s, the
preservice teachers should be
able to:
• discuss the different methods
of proving mathematical
statements
• develop the idea of
nontraditional models and
types of geometry
Unit 2 MODERN APPROACH
TO AXIOMATICS
1. Informal logic
2. Theorems and proofs
3. RAA proofs
4. Negation
5. Quantifiers
6. Implication Law of
excluded middle and proof
by cases
7. Incidence geometry
Models
8. Isomorphism of models
Week 4-7
Greenberg, M. (1974).
Smart, J. (1998).
1. Interactive
Discussion
2. Problem-
solving
(Individual)
A. The students
are asked to
prove some
problems
related to the
topics
discussed.
3. Boardwork
A. Some
students are
asked to write
the solutions of
the problems on
the board and
then explain it.
Handouts
Visual aids
Formative
assessment:
1. Oral
Recitation
2. Pen and
paper quiz
3. Class
participation
4. Seatwork
Unit Test
C. Show critical
thinking and logical
reasoning in using the
axiomatic method
when constructing
proofs for non-
Euclidean geometric
propositions;
At the end of the session/s, the
preservice teachers should be
able to:
• Discuss a version of Hilbert's
axioms of incidence and
betweenness and prove many
of the theorems that were
taken for granted by Euclid in
his Elements
• Show how the notions of
incidence and betweeness can
be developed without
appealing to geometric
intuitions.
Unit 3 HILBERT’S AXIOMS
1. Flaws in Euclid
2. Axioms of betweenness
3. Axioms of congruence
4. Axioms of continuity
5. Axiom of parallelism
Week 8-10
Greenberg, M. (1974).
Ryan, P. (1986).
Smart, J. (1998).
1. Interactive
Discussion
2. Problem-
solving
(Individual)
A. The students
are asked to
prove some
problems
related to the
topics
discussed.
3. Boardwork
A. Some
students are
asked to write
the solutions of
the problems on
the board and
then explain it.
Handouts
Visual aids
Pretest
Quiz
Unit Test
Major Exam

4. Midterm Coverage
1.The ability to
construct
classroom tests
and assessments
that measure a
variety of learning
outcomes, from
simple to
complex.
t the end of the session/s, the
preservice teachers should be
able to:
• define neutral geometry
• prove the rest of Hilbert's
axioms, and develop (some of)
Euclidean geometry from the
modern point of view
Unit 4 NEUTRAL GEOMETRY
1. Geometry without the
parallel axiom
2. Alternate interior angle
theorem
3. Exterior angle theorem
4. Measure of angles and
segments
5. Saccheri-Legendre
theorem
6. Equivalence of parallel
postulates
7. Angle sum of a triangle
Week 11-13
Ryan, P. (1986).
Smart, J. (1998).
1. Interactive
Discussion
2. Problem-
solving
(Individual)
A. The students
are asked to
prove some
problems
related to the
topics
discussed.
3. Boardwork
A. Some
students are
asked to write
the solutions of
the problems on
the board and
then explain it.
Visual
aids/PPT
presentation
Laptop
Projector
Formative
assessment:
1. Oral
Recitation
2. Pen and
paper quiz
3. Class
participation
4. Seatwork
Unit Test
Midterm
Examination
2.The ability to
obtain assessment
information from
classroom
observations, peer
appraisals and
self-report.
At the end of the session/s, the
preservice teachers should be
able to:
• discuss the role of the
parallel postulate in Euclidean
geometry
• investigate the question of
whether or not the parallel
postulate is necessary for
geometry
• discuss statements in
geometry that are equivalent
to the parallel postulate
UNIT 5 HISTORY OF THE
PARALLEL POSTULATE
1. Proclus
2. Wallis
3. Saccheri
4. Clairaut
5. Legendre
6. Lambert and Taurinus
7. Farkas Bolyai
Week 14-15
Batten, L. (1997).
Ryan, P. (1986).
Smart, J. (1998).
1. Interactive
Discussion
2. Problem-
solving
(Individual)
A. The students
are asked to
prove some
problems
related to the
topics
discussed.
3. Boardwork
A. Some
students are
asked to write
the solutions of
the problems on
the board and
Visual
aids/PPT
presentation
Laptop
Projector
Formative
assessment:
1. Oral
Recitation
2. Pen and
paper quiz
3. Class
participation
4. Seatwork
Unit Test

5. then explain it.
D. Demonstrate
understanding of
mathematics as a
dynamic field relative
to the emergence of
the different types of
geometries.
At the end of the session/s, the
preservice teachers should be
able to:
• differentiate hyperbolic and
Euclidean geometry.
• discuss some of the
important theorems in
hyperbolic geometry.
discuss models of hyperbolic
geometry
• justify the (relative)
consistency of hyperbolic
geometry.
• explain how non-Euclidean
geometry led to revolutionary
ideas such as Einstein's theory
of relativity, or new fields such
as differential geometry
UNIT 6 HYPERBOLIC AND
NON-EUCLIDEAN GEOMETRY
1. Janos Bolyai
2. Gauss
3. Lobachevsky
4. Subsequent
developments
5. Hyperbolic geometry
6. Angle sums (again)
7. Similar triangles
8. Consistency of hyperbolic
geometry
9. The Beltrami-Klein model
10. The Poincare models
11. Perpendicularity in the
12. Beltrami-Klein model
Week 16-18
Batten, L. (1997).
Ryan, P. (1986).
1. Interactive
Discussion
2. Problem-
solving
(Individual)
A. The students
are asked to
prove some
problems
related to the
topics
discussed.
3. Boardwork
A. Some
students are
asked to write
the solutions of
the problems on
the board and
then explain it.
Visual
aids/PPT
presentation
Laptop
Projector
Formative
assessment:
1. Oral
Recitation
2. Pen and
paper quiz
3. Class
participation
4. Seatwork
Unit Test
Major Exam
Final Coverage
References
Batten, L. (1997). Combinatorics of Finite Geometries. Cambridge University Press.
Greenberg, M. (1974). Euclidean and Non-Euclidean Geometries: Development and Histories. W.H. Freeman.
Ryan, P. (1986). Euclidean and Non-Euclidean Geometry. Cambridge University Press.
Smart, J. (1998). Modern Geometries. Brooks/ Cole.
Grading Plan
The following are the criteria for grading:
30%- Major Examination (Midterm or Final)
30%- Quizzes/Attendance
40% - Performance Tasks (projects/assignments/activities/recitations, seat works, output)
100%
Transmutation shall be based on 0 = 50% grading system
General Average (GA) is the grade that appears in the transcript of records for a certain course which is 50% of the Midterm Grade + 50% of the Final grade).

6. Classroom Rules of Conduct
1.Attendance:
a.Students who are absent for more than 20% of the total number of class hours (54 in a 3-unit course) may be dropped from the course/subject.
b.Any student who finds it necessary to be absent from class must present a letter of excuse to his/her instructor.
c.If a student’s absences reach ten (10) times, the instructor/professor may recommend to the Dean that the said student be dropped from the course or be given a grade of 5.0.
2.Course requirements must be submitted on time.
3.Plagiarism is strictly prohibited. Be aware that plagiarism in this course would include not only using another’s words, but another’s specific intellectual posts in social media.
4.Assignments must be done independently and without reference to another student’s work. Any outside sources used in completing an assignment, including internet references must
be fully cited on any homework assignment or exercise.
5.All students should feel free to talk to the instructor face-to-face or through media during office hours.
Adopted from: MathematicsSyllabiCompendium.pdf
Prepared:
MA.BETTY P. DECIN,EdD
Instructor
Reviewed:
BETTY P. DECIN,EdD
Chairperson, BSED Program
Noted:
HERMIE V. INOFERIO, Ph. D.
Associate Dean, College of Education
Approved/Disapproved:
JAY D. TELEN, Ph. D.
Vice President for Academic Affairs
Date: Date: Date: Date: