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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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Inner product spaces
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R1: Section 5.3
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2
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Properties of inner product spaces
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R1: Section 5.3
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3
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Gram-Schmidt Process
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R1: Section 5.4
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4
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Orthogonal Complements
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R1: Section 5.5
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5
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Definition and Examples of Linear Transformations
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R1: Section 6.1
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6
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Kernel of a linear transformation
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R1: Section 6.2
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7
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Range and rank of a linear transformation
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R1: Section 6.2
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8
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Matrix of a linear transformation
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R1: Section 6.3
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9
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Similarity
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R1:Section 6.5
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10
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Eigenvalues and Eigenvectors
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R1: Section 7.1
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11
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Cayley-Hamilton`s Theorem and Applications
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R1: Section 7.1
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12
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Diagonalization and Similar Matrices
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R1: Section 7.2
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13
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Diagonalization of Symmetric Matrices
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R1: Section 7.3
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14
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General Examples
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R2. Lecture notes
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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 KARAASLAN
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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. Kolman, B. and Hill, D.R. ( 2004) Elementary Linear Algebra with Applications and Labs, Prentice-Hall, New Jersey
R2. Lecture Notes
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Supplementary Book
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SR1. Spence, L., Insel, A. and Friedberg, S. Elementary Linear Algebra A Matrix Approach. Pearson I.E. (2nd Edition)
SR2. Hoffman, K. and Kunze, R. (1971) Linear Algebra, 2nd Edition, Prentice-Hall, New Jersey,
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Goals
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The aim of this course is to introduce the students linear transformations theory by using Linear Algebra knowledge which is learned the previous semester. To teach the student concept of Linear transformations, representation by matrices, special forms (diagonal, triangular), and besides these, to teach inner products and dual spaces. to the very heart of the subject including topics such as inner product spaces and linear mappings on them
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Content
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Inner product space, linear transformation, Eigenvalues and Eigenvectors of matrices, diagonalization of 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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-
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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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