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