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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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Matrices and Basic Operations of Matrices
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R1: Section 1.1,1.2,1.3,1.4
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2
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LU Decomposition of a Matrix
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R1: Section 3.5
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3
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Eigenvalues and Eigenvectors of a Matrix and Related Properties
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R1: Section 5.1, 5.2, 5.3
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4
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Linear Independent Eigenvectors
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R1: Section 5.4, 5.5
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5
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Power Methods
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R1: Section 5.6
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6
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Polynomial of a Matrix in Distinct and General Cases
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R1: Section 7.3, 7.4
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7
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Generalized Eigen Vectors
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R1: Section 9.1,9.2,9.3, 9.4
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8
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Chains
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R1: Section 9.5
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9
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Canonical Basis
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R1: Section 9.6
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10
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Jordan Canonical Forms of Matrices
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R1: Section 9.7
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11
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Complex Inner Product and Self Adjoint Matrices
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R1: Section 10.1, 10.2
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12
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Real Symmetric and Orthogonal Matrices
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R1: Section 10.3,10.4
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13
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Hermitian and Uniter Matrices
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R1: Section 10.5,10.6
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14
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Positive Definite Matrices
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R1: Section 10.8
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Assoc. Prof. Dr. Faruk KARASLAN
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Instructors
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-
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Assistants
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-
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Resources
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R1. Bronson, R. (1991). Matrix methods: An introduction. Gulf Professional Publishing.
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Supplementary Book
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SR1. Abadir, K. M. and Magnus, J. R. (2005). Matrix algebra (Vol. 1). Cambridge University Press.
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Goals
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Learning of some advanced subjects related to matrices.
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Content
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Basic Matrices, LU decompositions, eigenvalue and eigenvectors, Jordan canonical form of a matrix, special matrices.
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Program Learning Outcomes |
Level of Contribution |
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1
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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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3
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2
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Ability of abstract thinking
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3
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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3
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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-
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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2
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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-
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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-
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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-
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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-
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11
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Being able to produce projects and organize events with social responsibility awareness
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-
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12
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Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
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-
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13
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Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
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-
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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-
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