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| MAT4015 | Field extensions and Galois Theory | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Osman KAZANCI | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The main of this course is introduce the concepts of algebraic extensions of fields, Normal and separable extensions and finally how all finite fields can be constructed. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn the significance and properties of the minimal polynomial, | 5,6 | | | LO - 2 : | learn the concept of field extensions and properties of the algebraic element, | 5,6 | | | LO - 3 : | learn how to establish and use the concept of the degree of an extension | 5,6 | | | LO - 4 : | learn to construct splitting fields, normal extensions and algebraic closed fields, | 5,6 | | | LO - 5 : | learn fundamental theorems of algebra. | 5,6 | | | LO - 6 : | learn how to construct finite fields | 5,6 | | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Introduction, (basic concepts of Rings, Polynominal rings and Vector spaces) Algebraic extensions of fields, Normal and Separable extensions, Introduction to Galois Theory. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction | | | Week 2 | Basic properties of Rings | | | Week 3 | Polynominal rings | | | Week 4 | Vector spaces | | | Week 5 | Extensions of fields | | | Week 6 | Algebraic extensions of fields | | | Week 7 | Algebraically closed fields | | | Week 8 | Splittings fields | | | Week 9 | Midterm-exam | | | Week 10 | Normal extensions | | | Week 11 | Multiple roots | | | Week 12 | Sonlu cisimler | | | Week 13 | Separable extension | | | Week 14 | The characterization of finite field | | | Week 15 | Introduction to Galois Theory. | | | Week 16 | End-of-term exam | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 26/11/2021 | 1.5 | 50 | | End-of-term exam | 16 | 14/01/2022 | 1.5 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 5 | 1 | 5 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 159 |
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