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HU Credits:
6
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
2nd Semester
Teaching Languages:
English and Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Prof Eran Nevo
Coordinator Office Hours:
By appointment
Teaching Staff:
Prof Tomer Schlank,
Mr. Shai Keidar
Course/Module description:
Basic concepts in Algebraic Topology.
Prerequisites: Algebraic Structures 1, Intro. to Topology, Advanced Infinitesimal Calculus II
Course/Module aims:
Introduction to Algebraic Topology.
Learning outcomes - On successful completion of this module, students should be able to:
Basic concepts in Algebraic Topology.
Ability to construct and use of Homotopy and Homology.
Proving the fixed point theorems and other applications of homology and homotopy.
Ability to prove fundamental theorems in Algebraic Topology.
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Lecture + exercise
Course/Module Content:
A. Homotopy, the Fundamental Group, Cover Spaces, van Kampen theorem.
B. Construction of functors from the Homotopy category into the more accessible categories of Abelian Groups.
C. Singular Homology, conservation under Homotopy, short and long Exact Sequences, Mayer-Vietoris theorem.
D. Cohomology and Products.
E. Applications in Euclidean Spaces, Spheres, and Manifolds, the Duality Theorems.
Required Reading:
None
Additional Reading Material:
We will mainly use the book of
Hatcher, "Algebraic Topology"
Course/Module evaluation:
End of year written/oral examination 70 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 30 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
Take home exam.
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