Master Program in Mathematics

Algebraic Topology(MATH 522)

Content
Course Code Course Name Semester Theory Practice Lab Credit ECTS
MATH 522 Algebraic Topology 1 3 0 0 3 7
Prerequisites
Admission Requirements
Language of Instruction English
Course Type Elective
Course Level Masters Degree
Course Instructor(s) Serap GÜRER serapgurer@gmail.com (Email)
Assistant
Objective This is a course on the homology theories of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.
Content Simplicial Homology, Singular Homology, Cellular Homology, Homological algebra, Cohomology, and Poincare duality.
Course Learning Outcomes
Teaching and Learning Methods
References Algebraic Topology, Alain Hatcher
Print the course contents
Weekly Contents
Theory Topics
Week Weekly Contents
1 Simplical Homology
2 Singular Simplices and Chains
3 Homology, Categories, Functors, Natural Transformations
4 Homotopy Invariance of Homology, Relative Homology
5 The Homology Long Exact Sequence, Excision and Applications
6 The Eilenberg Steenrod Axioms and the Locality Principle
7 Exam
8 CW-Complexes, Homology of CW-Complexes
9 Real Projective Space, Euler Characteristic and Homology Approximation
10 Tensor Product, Tensor and Tor
11 Universal Coefficient Theorem, Künneth and Eilenberg-Zilber
12 Coproducts, Cohomology
13 Products in Cohomology, Cup Product (cont.)
14 Poincaré Duality
Practice Topics
Week Weekly Contents
Assessment System
Contribution to Overall Grade
  Number Contribution
Toplam 0 0
In-Term Studies
  Number Contribution
Toplam 0 0
Relation of Proficiency
No Program Learning Outcomes Contribution
1 2 3 4 5
ECTS
Activities Number Period Total Workload
Total Workload 0
Total Workload / 25 0.00
Credits ECTS 0
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