Theory of Manifolds (MAT457) | GSÜ - ECTS Information Guide

Theory Topics
Week	Weekly Contents
1	Review of multivariable differential calculus: differentiability, inverse function theorem, and constant rank theorem.
2	Differentiable manifolds: charts, atlases, changes of coordinates, and dimension.
3	Fundamental examples of manifolds: spheres, tori, projective spaces, and matrix groups.
4	Smooth maps between manifolds and diffeomorphisms.
5	Tangent spaces: definitions using curves and derivations; examples.
6	Tangent maps, chain rule, and the inverse function theorem on manifolds.
7	Submanifolds; immersions, submersions, embeddings, and the regular value theorem.
8	Midterm
9	Tangent and cotangent bundles; vector fields and integral curves.
10	Exterior algebra and differential forms; pullbacks of differential forms.
11	Exterior derivative; closed and exact forms.
12	Orientation, manifolds with boundary, and integration of differential forms.
13	Stokes’ theorem and classical applications.
14	Introduction to de Rham cohomology; applications to curves and surfaces; general review.

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	2	50
Contribution of final exam to overall grade	1	50
Total	3	100

In-Term Studies
Activities	Number	Contribution
Assignments	0	0
Presentation	0	0
Midterm Examinations (including preparation)	1	40
Project	1	10
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
Make-up	0	0
Total	2	50

Activities	Number	Period	Total Workload
Class Hours	14	3	42
Working Hours out of Class	13	3	39
Assignments	0	0	0
Presentation	0	0	0
Midterm Examinations (including preparation)	1	10	10
Project	1	10	10
Laboratory	0	0	0
Other Applications	0	0	0
Final Examinations (including preparation)	1	12	12
Quiz	0	0	0
Term Paper/ Project	0	0	0
Portfolio Study	0	0	0
Reports	0	0	0
Learning Diary	0	0	0
Thesis/ Project	0	0	0
Seminar	0	0	0
Other	0	0	0
Make-up	0	0	0
Yıl Sonu	0	0	0
Hazırlık Yıl Sonu	0	0	0
Hazırlık Bütünleme	0	0	0
Total Workload			113
Total Workload / 25			4.52
Credits ECTS			5

Theory of Manifolds