COURSE UNIT TITLE

: GEOMETRY

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4068 GEOMETRY ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course aim to introduce students to the foundations of Euclidean and Non-Euclidean geometries.

Learning Outcomes of the Course Unit

1   will be able to know difference between Affine and Euclidean spaces
2   will be able to know the isometries of Euclidean spaces
3   will be able todefine projective space
4   will be able to state Euclid s axioms and postulates
5   will be able to explain the role of the Parallel Postulate in the development of geometry from classical to modern times
6   will be able to know at least one model of Hyperbolic spaces

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Afine spaces, Affine mappings, The theorems of Thales, Pappus and Desargues
2 Barycentric coordinates, Convexity, Cartesian coordiantes in affine geometry
3 Euclidean Geometry, Isometries, The group of linear isometries
4 Angles, isometries and rigid motions in the plane, Plane similarities, Inversions and pencils of circles
5 Isometries and rigid motions in space, The vector product with area computations, Spheres, Spherical triangles
6 Polyhedra, Regular polyhedra, Euler formula, Platonic solids and their symmetry groups
7 Projectivespaces, Projective duality,
8 Projective transformations
9 The cross-ratio, The complex projective line and Möbius transformations
10 Conics and Quadrics
11 The postulate s of Euclid and existence of Non-Euclidean geometries.Elliptic geometry: spherical and projective models, streographic projection
12 Spherical triangles and spherical trigonometry, Spherical motions
13 Models for Hyperbolic spaces: The Klein-Beltrami model, The Poincaré disk model, The Poincaré half plane model, The Lorentz Model
14 Relations between hyperbolic planes, Hyperbolic motions, Hyperbolic triangles and hyperbolic trigonometry

Recomended or Required Reading

Textbooks:
1. Audin, M., Geometry, Springer, 2002, ISBN 978-3540434986
2. Rees, E. G., Notes on Geometry, Springer, 2005, ISBN 978-3540120537
3. Reid,M., Szendroi, B., Geometry and Topology, Cambridge University Press, 2005, ISBN 978-0521613255
Supplementary Books:
4. Berger, M., Geometry I, Springer, 2009, ISBN 978-3540116585
5. Berger, M., Geometry II, Springer, 2009, ISBN 978-3540170150
6. Greenberg, M. J., Euclidean and Non-Euclidean Geometries: Development and History, 4th ed., W. H. Freeman Publishing, 2007, ISBN 978-0716799481
7. Holme, A., Geometry: our cultural heritage, 2nd ed., Springer, 2010, ISBN 978-3642144400
8. Richter-Gebert, J., Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry, Springer, 2011, ISBN 978-3642172854
9. Stillwell, J., The Four Pillars of Geometry, Springer, 2010, ISBN 978-1441920638

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 QUZ QUIZ
3 ASG ASSIGNMENT
4 FIN FINAL EXAM
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + FIN * 0.50
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

30% (Midterm examination) +10%(Quiz)+%10(Homework assignment)+50% (Final examination)

Language of Instruction

English

Course Policies and Rules

The student is responsible for attending 70% of the courses throughout the semester. Action will be taken within the framework of the relevant regulations regarding unethical behavior that may occur in classes and exams. You can obtain the DEU Faculty of Science teaching and exam practice principles regulation from http://web.deu.edu.tr/fen.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Phone: +90 232 301 8585
Office: B212 (Mathematics Department)

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparation before/after weekly lectures 13 3 39
Preparation for Mid-term Exam 1 20 20
Preparation for Final Exam 1 20 20
Preparation for quiz etc. 2 8 16
Preparing assignments 2 9 18
Midterm 1 2 2
Quiz etc. 2 1 2
Final 1 2 2
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.153333433
LO.2543333334
LO.354333343344
LO.45533533
LO.55534345334
LO.653433443344