Week |
Subject |
Related Preparation |
1) |
Hilbert Spaces: HilbertAdjoint Operator. |
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2) |
SelfAdjoint, Unitary and Normal Operators. |
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3) |
Fundamental Theorems for Normed and Banach Spaces: Zorn’s Lemma,HahnBanach Theorem. |
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4) |
HahnBanach Theorem for Complex and Normed Spaces, and It’s Application to C[a,b]. |
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5) |
Adjoint Operator. |
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6) |
Reflexive Spaces. |
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7) |
Category Theorem, Uniform Boundedness Theorem, and Applications. |
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8) |
Convergence: Strong and Weak Convergence. |
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9) |
Convergence of Sequences of Operators and Functionals. |
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10) |
Open Mapping theorem. |
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11) |
Closed Linear Operators and Closed Graph Theorem. |
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12) |
Banach Fixed Point Theorem: Application of Banach’s Theorem to Linear Equations. |
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13) |
Application of Banach’s Theorem to Linear Equations, Differential Equations, and Integral Equations. |
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14) |
Approximation Theory: Approximation in Normed Spaces, Uniqueness and Strict Convexity.
Uniform Approximation, Chebyshev Polynomials, Approximation in Hilbert Spaces.
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Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other. |
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2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
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3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
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4) |
Ability to make individual and team work on issues related to working and social life. |
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5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
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6) |
Ability to use mathematical knowledge in technology. |
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7) |
To apply mathematical principles to real world problems. |
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8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
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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. |
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10) |
To apply mathematical principles to real world problems. |
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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. |
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12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |
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