This page contains some information that can be helpful before you register for the course. After registration, we will use ODTUclass. You should follow ODTUclass and check your emails regularly for important announcements during the semester.
Course Objectives
This is the second part of a classical graduate algebra course that covers some basic concepts in the theory of modules and fields.
Lecture Hours
The lectures will be in M203 – Tosun Terzioğlu Seminar Room.
- Monday 10:40-12:30
- Thursday 11:40-12:30
Homework, Exams, and Grading
Homework will be assigned on a regular basis, and there will be 4-6 homework sets by the end of the semester. There will be one midterm and a final. The time and the method of each exam will be announced later.
- Midterm, 30 points – around the 8th or 9th week.
- Final, 30 points – during the final exam period.
- Homework, 40 points.
Homework Policy: You should write your solutions on your own. You are allowed to consult other people’s solutions for homework problems, but you must express everything in your own words. If you copy a solution, which is referred to as cheating, you will probably gain nothing and may encounter penalties.
Textbooks
- Hungerford, Algebra.
- Dummit and Foote, Abstract Algebra, 3rd edition.
Tentative Course Outline
The course content, together with a tentative course outline, can be found below. We will attempt to cover the related parts of the above textbooks each week.
Modules
- Week 1: (Feb 17 – Feb 21) Modules, Homomorphisms and Exact Sequences.
- Week 2: (Feb 24 – Feb 28) Free Modules and Vector Spaces.
- Week 3: (Mar 3 – Mar 7) Projective and Injective Modules.
- Week 4: (Mar 10 – Mar 14) Hom and Duality. Tensor Products.
- Week 5: (Mar 17 – Mar 21) Modules Over a PID.
- Week 6: (Mar 24 – Mar 28) Modules Over a PID.
Fields
- Week 7: (Mar 31 – Apr 4) Field Extensions.
- Week 8: (Apr 7 – Apr 11) Fundamental Theorem of Galois Theory.
- Week 9: (Apr 14 – Apr 18) Fundamental Theorem of Galois Theory.
- Week 10: (Apr 21 – Apr 25) Splitting Fields, Algebraic Closure and Normality.
- Week 11: (Apr 28 – May 2) Galois Group of a Polynomial.
- Week 12: (May 5 – May 9) Finite Fields.
- Week 13: (May 12 – May 16) Separability.
- Week 14: (May 19 – May 23) Cyclic, Cyclotomic, and Radical Extensions.
- Week 15: (May 26 – May 30) Review.