Master Program in Mathematics

Differential Topology(MATH 523)

Content
Course Code Course Name Semester Theory Practice Lab Credit ECTS
MATH 523 Differential Topology 2 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 course is an introduction to smooth manifolds and their topology (differential topology).
Content In the first part of the course, we will introduce basic objects on smooth manifolds, including: differentiable manifolds, smooth maps, tangent and cotangent vectors, differential forms, integration, stokes theorem and de Rham cohomology. In the second part, we will study differential topology (topology of smooth manifolds), including: Whitney immersion and embedding theorems, approximation theorem, Sard theorem, transversality, intersection numbers, Morse functions and Morse theory.
Course Learning Outcomes
Teaching and Learning Methods
References 1)John Lee, Introduction to smooth manifolds?
2)Victor Guillemin & Alan Pollack, Differential topology
Print the course contents
Weekly Contents
Theory Topics
Week Weekly Contents
Practice Topics
Week Weekly Contents
Assessment System
Contribution to Overall Grade
  Number Contribution
Contribution of in-term studies to overall grade 4 15
Contribution of final exam to overall grade 1 40
Toplam 5 55
In-Term Studies
  Number Contribution
Assignments 0 0
Presentation 0 0
Midterm Examinations (including preparation) 0 0
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 0 0
Term Paper/ Project 0 0
Portfolio Study 0 0
Reports 0 0
Learning Diary 0 0
Thesis/ Project 0 0
Seminar 0 0
Other 0 0
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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