Information Package / Course Catalogue
Normed Spaces and Inner Product Spaces
Course Code: MTK567
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

This course aims to acquaint students with the fundamental notions of Normed and Inner Product Spaces including Normed linear spaces, linear subspaces, infinite series, convex sets, linear functionals, finite-dimensional spaces, dual space and second dual space, weak convergence, inner product spaces, orthogonal complements, Fourier series, Riesz representation theorem

Course Content

Normed linear spaces, linear subspaces, infinite series, convex sets, linear functionals, finite-dimensional spaces, dual space and second dual space, weak convergence, inner product spaces, orthogonal complements, Fourier series, Riesz representation theorem

Name of Lecturer(s)
Lec. Berna ARSLAN
Learning Outcomes
1.To be able to comprehend Normed spaces
2.To be able to comprehend İnner product spaces
3.To be able to develop mathematical sense
4.To be able to use mathematical concepts in solving certain types of problems
5.To be able to gain the skill of interpreting some interrelations among these concepts
Recommended or Required Reading
1.Topology and Normed Spaces, G. J. O. Jameson.
Weekly Detailed Course Contents
Week 1 - Theoretical
Normed linear spaces
Week 2 - Theoretical
Linear subspaces
Week 3 - Theoretical
Infinite series
Week 4 - Theoretical
Convex sets
Week 5 - Theoretical
Linear functionals
Week 6 - Theoretical
Finite-dimensional spaces
Week 7 - Theoretical
Dual space and second dual space
Week 8 - Theoretical
Weak convergence
Week 9 - Theoretical
Inner product spaces (Midterm)
Week 10 - Theoretical
Inner product spaces
Week 11 - Theoretical
Inner product spaces
Week 12 - Theoretical
Orthogonal complements
Week 13 - Theoretical
Fourier series
Week 14 - Theoretical
Riesz representation theorem
Assessment Methods and Criteria
Type of AssessmentCountPercent
Final Examination1%70
Assignment2%30
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Assignment230264
Midterm Examination140040
Final Examination150252
TOTAL WORKLOAD (hours)198
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
4
5
4
4
3
OÇ-2
4
5
4
4
3
OÇ-3
5
4
4
2
OÇ-4
5
4
4
4
4
2
OÇ-5
4
4
4
4
2
Adnan Menderes University - Information Package / Course Catalogue
2026