Course Name Code Semester T+U Hours Credit ECTS
Complex Manifolds I MAT 627 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Doç.Dr. MAHMUT AKYİĞİT
Course Lecturers
Course Assistants
Course Category
Course Objective The complex structures and manifolds course aims to give the fundamental knowledge for the studies of graduate students who study at topology, algebra and geometry branch.
Course Content Riemann manifolds, Complex vector fields, Complex structures, complex torsion, Complex coordinate system, Holomorphic function holomorphic map, Holomorphic forms and vector fields, Holomorphic line bundles, Complex manifolds: definition and examples, Holomorphic functions on complex manifolds, Complex submanifolds, Almost complex manifolds nijenhuis tensor, Complex tangent vector infinitezimal otomorfizm, Compact complex manifold, The examples of complex manifolds
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she learns concept of Riemann manifolds Lecture, Question-Answer, Drilland Practice, Brain Storming, Problem Solving, Testing, Homework,
2 He/she defines complex structures Lecture, Question-Answer, Drilland Practice, Brain Storming, Self Study, Problem Solving, Testing, Homework,
3 He/she learns holomorphic fonctions Lecture, Question-Answer, Drilland Practice, Brain Storming, Self Study, Problem Solving, Homework, Testing,
4 He/she realizes complex manifolds Brain Storming, Self Study, Problem Solving, Lecture, Question-Answer, Drilland Practice, Testing, Homework,
5 He/she establishes between the Riemann manifold and complex manifolds Lecture, Question-Answer, Drilland Practice, Brain Storming, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Riemann manifolds
2 Complex vector fields
3 Complex structures and complex torsion
4 Complex coordinate system
5 Holomorphic function and holomorphic map
6 Holomorphic forms and vector fields
7 Holomorphic line bundles
8 Complex manifolds: definition and examples
9 Holomorphic functions on complex manifolds
10 Complex submanifolds
11 Almost complex manifolds nijenhuis tensor,
12 Complex tangent vector infinitezimal otomorfizm
13 Compact complex manifold
14 The examples of complex manifolds
Resources
Course Notes 1.) Daniel Huybrechts, Complex geometry, Springer, 1965.<br>2.) Kunihiko Kodaira, Complex manifold and deformation of complex structures, Springer, 1981.
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
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
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
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
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
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
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
1. Ödev 10
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 10 10
Quiz 1 10 10
Assignment 2 16 32
Final examination 1 10 10
Total Workload 158
Total Workload / 25 (Hours) 6.32
dersAKTSKredisi 6