Week |
Subject |
Related Preparation |
1) |
Introduction: Metric Space, Open set, Closed set, Neighborhood. |
|
2) |
Sequences: Boundedness, Convergence, Cauchy Sequence, Seperability. |
|
3) |
Completeness and Completion of Metric Spaces. |
|
4) |
Examples. Completeness Proofs. |
|
5) |
Vector spaces: Subspace, Dimension, Hamel Basis. |
|
6) |
Normed Spaces, Banach Spaces: Normed Space, Banach Space, Further Properties of Normed Spaces. |
|
7) |
Finite Dimensional Normed Spaces and Subspaces, Compactness and Finite Dimension. |
|
8) |
Linear Operators: Some Properties. |
|
9) |
Applications of Bounded and Linear Operators. |
|
10) |
Functionals: Linear Functionals, Normed Spaces of Operators |
|
11) |
Dual Space: Algebric Dual and Continuous Dual. |
|
12) |
Inner Product Spaces, Hilbert Spaces: Inner Product Space Hilbert Space, Further Properties of Inner Product Spaces, Parallelogram Law. |
|
13) |
Orthogonal Complements and Direct Sums. |
|
14) |
Orthonormal Sets and Sequences, Total Orthonormal Sets and Sequences, representation of Functionals on Hilbert Spaces, Hilbert adjoint Operator. |
|
|
Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other.
|
4 |
2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
|
4 |
3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
5 |
4) |
Ability to make individual and team work on issues related to working and social life. |
|
5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
4 |
6) |
Ability to use mathematical knowledge in technology. |
5 |
7) |
To apply mathematical principles to real world problems. |
5 |
8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
4 |
9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
5 |
10) |
To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. |
|
11) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
4 |
12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |
4 |