Course Name Code Semester T+U Hours Credit ECTS
Fixed Point Theory In Metric Places I MAT 527 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. AYNUR ŞAHİN
Course Lecturers Doç.Dr. AYNUR ŞAHİN,
Course Assistants
Course Category Field Proper Education
Course Objective

The understanding of fixed point theory in metric spaces, the knowing of hyperbolic metric spaces and non-positive metric spaces, the learning of normal structures in metric spaces and ultrametric spaces

Course Content

Metric space, completeness, separability and connectedness, metric convexity and convexity structures, the basic fixed point theorems in metric space, metric spaces of non-positive curvature and their examples, some fixed point theorems in metric spaces of non-positive curvature, hyperbolic metric spaces and their properties, structure of the fixed point set in hyperbolic metric spaces, normal structures in metric space, stability and smoothness, ultrametric spaces and some fixed point results

# Course Learning Outcomes Teaching Methods Assessment Methods
Week Course Topics Preliminary Preparation
Resources
Course Notes
Course Resources

1) K. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, 1990.                                                                                               

2) M.R. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer, 1991.

3) M.A. Khamsi, W.A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and   Applied Mathematics, A Wiley-Intersicence Series of Texts, Monographs and Tracks, 2001.

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
2 Student follows the current journals in his/her field and puts forward problems.
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field.
5 Student uses different proof methods to come to a solution by analyzing the problems encountered.
6 Student determines the problems to be solved within his/her field and if necessary takes the lead.
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field.
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level.
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 50
1. Kısa Sınav 20
1. Ödev 15
2. Ödev 15
Total 100
1. Final 50
1. Yıl İçinin Başarıya 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Mid-terms 1 24 24
Assignment 2 8 16
Final examination 1 48 48
Hours for off-the-classroom study (Pre-study, practice) 14 1 14
Total Workload 150
Total Workload / 25 (Hours) 6
dersAKTSKredisi 6