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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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Definition of group and some examples of groups
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R1. Lecture Notes
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2
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Permutation groups
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R1. Lecture Notes
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3
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Subgroups and Cyclic groups
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R1. Lecture Notes
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4
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Normal subgroups and quotient groups
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R1. Lecture Notes
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5
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Group homomorphism and isomorphisms
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R1. Lecture Notes
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6
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Direct product groups
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R1. Lecture Notes
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7
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Ring and subring
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R1. Lecture Notes
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8
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Integral domain and field
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R1. Lecture Notes
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9
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Ideals and quotient rings
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R1. Lecture Notes
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10
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Vector spaces and subspsces
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R1. Lecture Notes
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11
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Base and dimension of a vector space
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R1. Lecture Notes
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12
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Inner product spaces
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R1. Lecture Notes
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13
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Linear transformations
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R1. Lecture Notes
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14
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Matrix of a linear transformations
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R1. Lecture Notes
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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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Assoc. Prof. Dr. Faruk KARAASLAN
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Instructors
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-
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Assistants
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Assoc. Prof. Dr. Nihal BİRCAN KAYA
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Resources
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K1. John B. Fraleigh, Soyut Cebire Giriş, (Çevirenler: Prof. Dr. Mehmet Terziler, Yrd. Doç. Dr. Tahsin Öner) Palme Yayıncılık, Ankara 2013
K1. D.S. Malik, John N. Mordeson, M.K. Sen, Fundamentals of Abstract Algebra,1997
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Supplementary Book
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K1. I.N. Herstein, Topics in Algebra, 2. Edition, John Wiley and Sons 1975, Singapore
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Goals
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To teach fundamental concepts related to group, ring, vector spaces, inner product spaces, and linear transformations.
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Content
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Group, ring, integral domain, field, ideals, quotient rings, vector spaces, inner product spaces, linear transformations.
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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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3
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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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3
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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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-
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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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Make use of the necessary computer softwares and information technologies related to Mathematics
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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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