MC 109 Modern Geometry Syllabus PDF

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The Great Plebeian College College Department Course SyllabusCourse Code/TitleMC109 Modern GeometryDay/Time/Room MWF 3:00PM-4:00PM Instructor Patrick Dave R. Consay Consultation Hours8:00AM - 8:00PMCourse Description :This course seeks to enrich students’ knowledge of Euclidean Geometry. It discusse...

Description

The Great Plebeian College College Department Course Syllabus Course Code/Title Day/Time/Room Instructor Consultation Hours

MC109 Modern Geometry MWF 3:00PM-4:00PM Patrick Dave R. Consay 8:00AM - 8:00PM

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

Learning Outcomes (LOs) Graduate Attributes LO1: Expert Learner

LO2: Critical and Creative Thinker

       

At the end of the course, the students will be able to: Identify various types of geometric problems Identify what variables are needed and what are not in solving problems Realize how important measurements are in geometry Use inductive reasoning to find a pattern Demonstrate understanding of mathematics as a dynamic field relative to the emergence of the different types of geometries. Derive formulas in solving related problems Relate to settings and circumstances that requisites mathematical concepts Show critical thinking and logical reasoning in using the axiomatic method when constructing proofs for nonEuclidean geometric propositions

LO3: Fluent and Effective Communicator

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Demonstrate clarity in communicating statistical problems Express data analysis, processes and solutions in written or oral form

LO4: Expert Self

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Exhibit proficiency in analyzing data by using appropriate technology for informed decision-making Display competence in demonstrating knowledge about geometry.

LO5: Expert Doer

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LO6: Expert Community Participant

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Demonstrate understanding of the 5th Postulate and how it led to the emergence of other types of geometry Illustrate examples that apply geometrical concepts 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 Apply knowledge about geometry in various activities done in the community

LO7: Expert Agent of Change

 Appreciate statistics by advocating the use of geometry in our daily life especially in architecture and engineering

Final Course Output LEARNING OUTCOME LO1, LO2, LO3, LO6

LO1, LO2, LO3

LO1, LO2, LO3, LO4, LO5, LO6, LO7

             

REQUIRED OUTPUT Module Activities Online Quizzes Assignments Examinations Module Activities Take-home Quizzes Assignments Examinations Online Group Works/Activities Video Presentation Module Activities Take-home Quizzes Assignments Examinations

DUE DATE Week 4

Week 9

Week 14

LO1, LO2, LO3, LO5, LO6, LO7

      

Learning Plan LOs Topics LO1 LO2 LO3 LO4 LO5

Week 19

Compilation of all Modules Video Presentation Online Group Works/Activities Module Activities Presentation/Demonstration Assignments Examinations

 CLASSICAL EUCLIDEAN GEOMETRY  The origins of geometry  Undefined terms  Euclid's first four postulates  The parallel postulate  Attempts to prove the parallel postulate

Week # 1-4

Experiential Learning Activities Discussions through modules/handouts; Video Discussions; via Google Classroom; and via Google Meet

References    

Week 5 (EXAM WEEK)

Batten, L. (1997). Combinatorics of Finite Geometries. Cambridge University Press. Greenberg, M. (1974). Euclidean and NonEuclidean Geometries: Development and Histories. W.H. Freeman. Ryan, P. (1986). Euclidean and NonEuclidean Geometry. Cambridge University Press. Smart, J. (1998). Modern Geometries. Brooks/ Cole..

LO1 LO2 LO3 LO4 LO5

LO1 LO2 LO3 LO4 LO5

 NEUTRAL GEOMETRY      

6-9

Alternate interior angle theorem Exterior angle theorem Measure of angles and segments Saccheri-Legendre theorem Equivalence of parallel postulates Angle sum of a triangle

 HISTORY OF THE PARALLEL POSTULATE  Proclus  Wallis  Saccheri  Clairaut  Legendre  Lambert and Taurinus  Farkas Bolyai

Discussions through modules/handouts; Video Discussions; via Google Classroom; and via Google Meet

   

11-14

Week 10 (EXAM WEEK) Discussions through modules/handouts; Video Discussions; via Google Classroom; and via Google Meet

   

Week 15 (EXAM WEEK)

Batten, L. (1997). Combinatorics of Finite Geometries. Cambridge University Press. Greenberg, M. (1974). Euclidean and NonEuclidean Geometries: Development and Histories. W.H. Freeman. Ryan, P. (1986). Euclidean and NonEuclidean Geometry. Cambridge University Press. Smart, J. (1998). Modern Geometries. Brooks/ Cole.. Batten, L. (1997). Combinatorics of Finite Geometries. Cambridge University Press. Greenberg, M. (1974). Euclidean and NonEuclidean Geometries: Development and Histories. W.H. Freeman. Ryan, P. (1986). Euclidean and NonEuclidean Geometry. Cambridge University Press. Smart, J. (1998). Modern Geometries. Brooks/ Cole..

LO1 LO2 LO3 LO4 LO5 LO6 LO7

 HYPERBOLIC AND NONEUCLIDEAN GEOMETRY  Janos Bolyai  Gauss  Lobachevsky  Subsequent developments  Hyperbolic geometry

16-19

Discussions through modules/handouts; Video Discussions; via Google Classroom; and via Google Meet

   

Batten, L. (1997). Combinatorics of Finite Geometries. Cambridge University Press. Greenberg, M. (1974). Euclidean and NonEuclidean Geometries: Development and Histories. W.H. Freeman. Ryan, P. (1986). Euclidean and NonEuclidean Geometry. Cambridge University Press. Smart, J. (1998). Modern Geometries. Brooks/ Cole..

Week 20 (EXAM WEEK) Grading System Prelim Grade: Requirements Class Standing 2/3 of the Final Grade Attendance Assignments Quizzes Module Activities Compilation of all Modules Sub-total Major Examination 1/3 of the Final Grade Total Midterm Grade (MG) = 30% Prelim Grade + 70% Tentative Midterm Grade Semi-Final Grade (SFG) = 30% Midterm Grade + 70% Tentative Semi-Final Grade Final Grade (FG) = 30% Semi-Final Grade + 70% Tentative Final Grade Note: Grades should be ROUNDED OFF only in the Final Grade

Total 67% 20%

80%

100% 33% 100%

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..

Websites 

https://www.isinj.com/mt-usamo/Advanced%20Euclidean%20Geometry%20-%20Roger%20Johnson%20(Dover,%201960).pdf

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https://www.math.ksu.edu/~dbski/writings/further.pdf

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https://www.aproged.pt/biblioteca/planeandsolidgeometry.pdf

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http://math.fau.edu/yiu/AEG2013/2013AEG.pdf

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https://people.math.sc.edu/sharpley/math532/Book_Gilbert.pdf

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https://www.christianbook.com/advanced-geometry-pdf-janice-wendling/9781773445687/pd/29694DF

Prepared by: ___________________________________________ PATRICK DAVE R. CONSAY CTE Instructor Noted by: _____________________ __________________ ________ MA. CORAZON C, COLENDRINO, PhD Vice President for Academic Affairs/ __________________________________________ Dean, _____ FRANCY C. CELZO, MPACollege of Teacher Education OIC School President

__________________________________________ _____ MARILOU R. RAPATALO, MaEd School Registrar...