Differential Geometry (MAT417) | GSÜ - ECTS Information Guide

Content

Objective

Introduction to fundamental theorems and concepts in differential geometry

Course Content

Curves, surfaces, differential forms, first fundamental form, second fundamental form, Christoffel symbols, geodesics, Gauss's theorema egregium theorem, Gauss-Bonnet theorem, differentiable manifolds, tangent bundle, Lie derivative, Lie brackets, Lie groups, de Rham cohomology

Course Learning Outcomes

1. Understand how to study curves and surfaces
2. Understand the notions of differentiable varieties and the questions involved

Teaching and Learning Methods

Lectures and problem sets

References

Cours de mathématiques pures et appliquées : Algèbre et géométrie - Ramis, Warusfel, Moulin
Géométrie et calcul différentiel sur les variétés - Pham
Differential geometry of curves and surfaces - Do Carmo
Géométrie différentielle élémentaire - Paulin
Notes de cours de Géométrie différentielle - Oancea
Géométrie différentielle - Guedj
Lectures on the Geometric Anatomy of Theoretical Physics - Schuller

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Differential calculus
2	Differential forms
3	Curves
4	Surfaces
5	Tensors, quizz
6	First fundamental form
7	Second fundamental form
8	Midterm
9	Submanifold
10	Manifold
11	Tangent bundle
12	Lie brackets, Lie derivative
13	Lie group
14	de Rham Cohomology, quizz

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	14	60
Contribution of final exam to overall grade	1	40
Total	15	100

In-Term Studies
Activities	Number	Contribution
Assignments	10	5
Presentation	1	5
Midterm Examinations (including preparation)	1	30
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	2	20
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
Total	14	60

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways;		X
2	can properly state and use concepts and results of major mathematical interest;			X
3	masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools;				X
4	is able to express one’s mathematical ideas in an organised way both in written and oral forms;			X
5	understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...);				X
6	has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;		X
7	has a theoretical and practical knowledge in computer science well adapted for learning a programming language;			X
8	has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;		X
9	has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement;		X
10	masters French language as well as other foreign languages, to a level sufficient to study or work abroad.		X

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	4	56
Working Hours out of Class	14	5	70
Assignments	7	3	21
Midterm Examinations (including preparation)	2	6	12
Final Examinations (including preparation)	1	16	16
Total Workload			175
Total Workload / 25			7.00
Credits ECTS			7