DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Field Theory Course Code : MT 412 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Spring (16 Weeks) ECTS : 5 Name of Lecturer(s) : Prof.Dr. HAYRULLAH AYIK Learning Outcomes of the Course : Explains the concept of field extension with examples. Defines the concept degree of an extension. Is able to explain constructable and unconstructable figures using extensions. Defines a finite field and can build finite fields. Finds splitting field of a polynomial. Defines normal and separable extensions and gives examples. Is able to define the Galois group of an extension and finds the Galois group a given extension. Defines the Galois relation for an extension, decides whether or not the relationshipis is bijection. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : Genaral aim of this course is to teach the Galois theory and some of its results. Course Contents : Review of theory of rings, field extension, simple and transcendental extensions, degree of an extension, ruler and compass constructions, Galois group of an extension, splitting fields, normal and separable extensions, solution of equations by radicals. Language of Instruction : Turkish Work Place : Faculty of Arts and Sciences Annex Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Review of basic concepts from Ring theory none Lecture and discussion 2 Decomposition in polynomial rings Review of related concepts from lecture notes and sources Lecture and discussion 3 Field extensions Review related concepts from lecture notes and sources Lecture and discussion 4 Classification of simple extensions Review of related concepts from lecture notes and sources Lecture and discussion 5 Degree of an extension Review of related concepts from lecture notes and sources Lecture and discussion 6 Ruler and compass construction Review of related concepts from lecture notes and sources Lecture and discussion 7 Principles of the Galois Theory Review of related concepts from lecture notes and sources Lecture and discussion 8 Mid-term exam Review of topics discussed in the lecture notes and sources Written exam 9 Splitting fields Review of related concepts from lecture notes and sources Lecture and discussion 10 Finite filelds Review of related concepts from lecture notes and sources Lecture and discussion 11 Monomorphisms between fields and Galois Groups Review of related concepts from lecture notes and sources Lecture and discussion 12 Normal and separable extensions Review of related concepts from lecture notes and sources Lecture and discussion 13 Normal closure Review of related concepts from lecture notes and sources Lecture and discussion 14 Galois relation of an extension. Review of related concepts from lecture notes and sources Lecture and discussion 15 Galois relation of an extension Review of related concepts from lecture notes and sources Lecture and discussion 16/17 Final exam Review of topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)   I. Stewart, Galois Theory, Chapman and Hall, London 1973 Required Course Material(s)  John M. Howie, Fields and Galois theory, Springer- verlag London, 2006   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 1 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 5 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 2 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 2 6 Expresses clearly the relationship between objects while constructing a model 0 7 Draws mathematical models such as formulas, graphs and tables and explains them 2 8 Is able to mathematically reorganize, analyze and model problems encountered. 3 9 Knows at least one computer programming language 1 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 119 Total Workload / 25 (h): 4.76 ECTS Credit: 5