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Week
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Topics
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Study Metarials
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1
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Ordered vector spaces, Riesz spaces
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R1-Section 1.1
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2
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Archimedean Riesz spaces
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R1-Section 1.1
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3
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Positive operators, Regular operators
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R1-Section 1.1
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4
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Dedekind completeness, Riesz-Kantorovich Theorem
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R1-Section 1.1
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5
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Extensions of positive operators
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R1-Section 1.2
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6
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Extensions of positive operators and their applications
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R1-Section1.2
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7
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Ideals in Riesz spaces and their examples
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R1-Section 1.2
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8
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Bands in Riesz spaces and their examples
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R1-Section 1.2
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9
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Extreme points
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R1-Section1.3
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10
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Order projections
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R1-Section 1.3
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11
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Order continuous operators
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R1-Section1.3
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12
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Examples of order continuous operators
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R1-Section 1.3
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13
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Positive linear functionals
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R1-Section 1.4
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14
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Examples of positive linear functionals
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R1-Section 1.4
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Prof. Dr. Faruk POLAT
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Instructors
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1-)Profesör Dr. Faruk Polat
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Assistants
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The related lecturers of the department
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Resources
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R1. Aliprantis,C.D., and Burkinshaw, O., (1985), Positive Operators
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Supplementary Book
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SR1. Luxemburg,W.A.J.,and Zaanen, A.C., (1971), Riesz SpacesI
SR2. D.H. Fremlin, Topological riesz spaces and measures theory, Cambridge Uni. Press, 2998.
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Goals
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To apply the concepts and technics of functional analysis to ordered vector spaces and operators between them.
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Content
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Ordered vector spaces, Riesz spaces, Archimeden Riesz spaces, Positive operators, Regular operators,
Dedekind completeness, Riesz - Kantorovic Theorem, The extensions of positive operatorsi, Ideals in Riesz spaces, bands in Riesz spaces, Extremum points, Order projections, Order continuous operators, Positive linear functionals
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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4
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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-
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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5
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4
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Analyze mathematical problems by using the gained research methods
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-
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5
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Conduct independently a study requiring speciliaty in Mathematics
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-
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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-
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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4
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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-
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9
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Uses computer software and information technologies related to the field of mathematics at an advanced level.
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-
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10
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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-
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