Course Name Code Semester T+U Hours Credit ECTS
Introduction To Banach Spaces MAT 517 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. MAHPEYKER ÖZTÜRK
Course Lecturers
Course Assistants
Course Category Other
Course Objective

Understanding the relation between normed space and topological space by using the fundamental functionel analysis knowledge.Understanding the Hahn-Banach Extension Theorem and having knowledge about compact transformations.

Course Content

Preliminares, norms, properties of normed spaces, linear transformations between normed spaces, Baire Category Theorem, Hahn-Banach Extension Theorem, dual spaces, weak topologies, weak compactness,cusp points, linear transformations, conjugate transformations, compact transformations, Schauder basis, fixed points .

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she proves the theorems by using the knowledge of functionel analysis. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 He/she remembers the relation between normed spaces and topological spaces. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 He/she gains the ability of understanding the relations between mormed spaces and topological spaces. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she learns the definition and proof of Hahn-Banach theorem. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she proves the theorems by using Hahn-Banach Extension Theorem. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 He/she regognizes compact transformations. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Preliminares
2 Norms
3 Properties of normed spaces
4 Linear transformations between normed spaces
5 Baire Category Theorem
6 Hahn-Banach Extension Theorem
7 Dual spaces
8 Weak topologies
9 Weak Compactness
10 Cusp Points
11 Linear transformations
12 Conjugate transformations
13 Compact transformations
14 Schauder basis, fixed points
Resources
Course Notes
Course Resources

1-Robert E. Megginson, An Introduction to Banach space theory, Springer, 1998
2-Carl L. Devito, Functional Analysis and Linear operator theory, Addison-Wesley, 1990.

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 X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
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. X
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 X
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. X
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. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ödev 100
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 30 30
Performance Task (Laboratory) 1 30 30
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6