• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Comprehend the basic principles and methods of Algebraic Topology

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Acquire scientific knowledge and work independently,
   3. Develop mathematical, communicative, problem-solving, brainstorming skills.

   Method of assessment

   1. Homework assignment
2. Compute fundamental group, homology and cohomology using the main methods of homological algebra

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   3. Acquire scientific knowledge and work independently,
   4. Develop mathematical, communicative, problem-solving, brainstorming skills.
   5. Support his/her ideas with various arguments and present them clearly to a range of audience, formally and informally through a variety of techniques

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Term paper
3. Construct topological spaces and maps with given invariants

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   3. Develop mathematical, communicative, problem-solving, brainstorming skills.

   Method of assessment

   1. Written exam

Contents
Week 1:	Fundamental Groups and its applications
Week 2:	Van-Kampen Theorem, Covering Spaces
Week 3:	Singular complexes and Singular Homology
Week 4:	Simplicial complexes and Simplicial Homology
Week 5:	Exact Sequences and excision
Week 6:	The equivalence of Simplicial and Singular Homology
Week 7:	CW-complexes and Cellular Homology
Week 8:	Mayer-Vietoris Sequences
Week 9:	Axioms for Homology Midterm Exam
Week 10:	Kohomoloji Grupları
Week 11:	Universal Coefficient Theorem
Week 12:	Cross product, cup product
Week 13:	Künneth Theorem
Week 14:	Homology and cohomology of manifolds. Duality Theorem.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Algebraic Topology, Allen Hatcher
Recommended readings:	A concise course in Algebraic Topology, J.Peter May
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	8	25
Other in-term studies:	-	0
Project:	14	20
Homework:	3,5,7,9,11,13	20
Quiz:	-	0
Final exam:	16	35
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	2	14
Practice, Recitation:	0	0
Homework:	4	6
Term project:	3	14
Term project presentation:	2	1
Quiz:	0	0
Own study for mid-term exam:	10	2
Mid-term:	3	1
Personal studies for final exam:	10	2
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)