Course Name Code Semester T+U Hours Credit ECTS
Homological Algebra MAT 609 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level Doctorate Degree Course Type Optional Course Coordinator Prof.Dr. MEHMET ÖZEN Course Lecturers Course Assistants Course Category Course Objective To introduce subject of base abstract algebra Course Content Algebraic structure, homological algebra
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will have learnt the most important notions of homological algebra. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 Students will have learnt the basic methods of homological algebra. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 Students will have discussed such topics as chain complexes and spectral sequences. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 Students will have done applications to subjects such as cohomology of groups and Hochschild cohomology of algebras. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 Students will have acquired an intoduction to classical homological algebra which provides a link with the modern approach via derived categories. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 Students will have learnt about modules such as projective, injection, and free modules. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Basic concepts
2 Modules
3 Submodules
4 Homomorphism
5 Homological structure
6 Complete sequences
7 Complete sequences
8 Projective modules
9 Injection modules
10 Generator, base
11 Free modules
12 Free moduless
13 Tensor product
14 Tensor product
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ödev 10
2. Kısa Sınav 10
1. Kısa Sınav 10
1. Ara Sınav 70
Total 100
1. Final 50
1. Yıl İçinin Başarıya 50
Total 100