MTK762 - ALGEBRAIC TOPOLOGY II

Course Name Code Semester Theory
(hours/week)		 Application
(hours/week)		 Credit ECTS
ALGEBRAIC TOPOLOGY II MTK762 2nd Semester 3 0 3 12
Prequisites
Course languageTurkish
Course typeElective 
Mode of DeliveryFace-to-Face 
Learning and teaching strategiesLecture
Discussion
Problem Solving
Other: homework  
Instructor (s)Assist. Prof. Dr. Sinem Onaran 
Course objectiveThis course is a sequel course to Algebraic Topology I. The aim of the course is to describe the relation between algebra and topology. 
Learning outcomes
  1. defines cohomology groups and computes cohomology of spaces,
  2. proves the universal coefficient theorem and applies the theorem,
  3. defines cup product,
  4. proves Künneth formula and does the computations using the formula,
  5. proves the Poincaré duality, learns its relation to orientation and homology
Course ContentCohomology Groups, Cohomology of spaces,
Universal coefficient theorem,
Cup product,
Künneth formula ,
Poincaré duality,
Orientation and homology
 
References Algebraic Topology, Allen Hatcher
Algebraic Topology, An Introduction W.S. Massey
An introduction to Algebraic Topology, J.J. Rotman
 

Course outline weekly

WeeksTopics
Week 1Cohomology Groups
Week 2Cohomology of spaces
Week 3Computations of Cohomology of spaces
Week 4Universal coefficient theorem
Week 5Computations using Universal coefficient theorem
Week 6Midterm exam
Week 7Cup product
Week 8Künneth formula
Week 9Computations with Künneth formula
Week 10Poincaré duality
Week 11Midterm exam
Week 12Orientation and homology
Week 13Duality theorem
Week 14Connections with Cup product
Week 15Final preparation
Week 16Final exam

Assesment methods

Course activitiesNumberPercentage
Attendance00
Laboratory00
Application00
Field activities00
Specific practical training00
Assignments630
Presentation00
Project00
Seminar00
Midterms130
Final exam140
Total100
Percentage of semester activities contributing grade succes760
Percentage of final exam contributing grade succes140
Total100

WORKLOAD AND ECTS CALCULATION

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 14 3 42
Laboratory 0 0 0
Application000
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)1412168
Presentation / Seminar Preparation000
Project000
Homework assignment620120
Midterms (Study duration)11515
Final Exam (Study duration) 11515
Total Workload3665360

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
12345
1. Deepens the concepts of mathematics in the level of expertise.    X
2. Grasps the inter-disciplinary interaction related to the area; reaches original results by using the specialist knowledge in analyzing and evaluating new ideas.  X  
3. Gains the ability to think independently and develops theoretical concepts.     X
4. Develops original mathematical models by using interrelations between mathematics and other disciplines and applies them to other disciplines.     
5. Uses high level research methods in studies in the area.   X 
6. Develops a new idea, method and/or application independently, finds a solution, and contributes to the progress in the area by carrying out original studies.     
7. Fulfills the leader role in the environments where solutions are thought for the area and/or inter-disciplinary problems.     
8. Develops continually the skills of creativity, decision making and problem solving.    X
9. Defends original opinions by communicating with experts in the area.     
10. Uses a foreign language- at least C1 Level-, communicates with foreign colleagues and follows the international literature.   X 
11. Follows the latest developments in the information and communication technologies and uses them in the area.     
12. Does research in national and international research groups.     
13. Makes strategic decision in the solution of problems in the area.     
14. Protects the rights of other researchers in regards to ethics, privacy, ownership and copyright.  X  

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest