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 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