GEOMETRIES

Course Code:

MATH 411

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Course Language:

English

Course Objectives:

To provide information about the fundamental concepts of geometries defined by invariants of transformations on two dimensional spaces of constant curvature.

Course Content:

Plane Euclidean geometry, Affine transformations in the Euclidean plane, Finite groups of isometries of Euclidean plane, Geometry on sphere, The projective plane, The hyperbolic plane.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Learns the geometry on plane	1	A
2) Learns the geometry on sphere	1	A
3) Learns the geometry on hyperbolic plane	1	A
4) Learns the transformations on plane	1	A
5) Learns the transformations on sphere	1	A
6) Learns the transformations on hyperbolic plane	1	A

Course Flow

Week	Topics	Study Materials
1	Plane Euclidean Geometry	From textbook Chapter 1
2	Plane Euclidean Geometry	Chapter 1
3	Plane Euclidean Geometry	Chapter 1
4	Affine transformations in Euclidean Plane	Chapter 2
5	Affine transformations in Euclidean Plane	Chapter 2
6	Finite Group of Isometries of Euclidean Plane	Chapter 3
7	MIDTERM and discussion of solutions)
8	Geometry on Sphere	Chapter 4
9	Geometry on Sphere	Chapter 4
10	Geometry on Sphere	Chapter 4
11	The Projective plane	Chapter 5
12	Distance geometry on Projective Plane	Chapter 6
13	The Hyperbolic Plane	Chapter 7
14	The Hyperbolic Plane	Chapter 7

Recommended Sources

Textbook	P. J. Ryan, Euclidean and Non-Euclidean Geometry An analytic Approach, Cambridge, 1997
Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes
Assignments
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

COURSE CATEGORY

Expertise/ Field Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)			x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems					x
5	Consciousness of professional ethics and responsibilty			x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest				x
8	Ability to learn, choose and use necessary information technologies			x
9	Lifelong education					x

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Mid-terms (Including self study)	1	24	24
Final examination (Including self study)	1	36	36
Total Work Load			172
Total Work Load / 25 (h)			6.88
ECTS Credit of the Course			7

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