IMM Pakistan Student 2025 - 2027
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IMM Pakistan / 2022 - 2023
Advanced Differential Geometry
TEACHING TEAM
Course description
Course description
Differential Geometry is the study of smooth spaces using the notion of a smooth manifold which can be thought of as a generalization of smooth surfaces in three dimensional space. Moreover the possible geometric structures on these manifolds are of interest, examples of such structures include vector bundles, vector fields, derivations, differential forms and integrals.
This course covers the fundamentals of Differential Geometry: Local and global geometry of curves and surfaces, Frenet frames, Total curvature, Minimal surfaces, Geodesics, Gaussian curvature, Differentiable manifolds, Tangent bundles, and Riemannian manifolds.
Upon successful completion, students will have the knowledge and skills to:
1. Explain the concepts and language of differential geometry and its role in modern mathematics.
2. Analyse and solve complex problems using appropriate techniques from differential geometry with mathematical rigour
A complete list course overview can be found here.
Course materials
Course materials
References
References
The main references are:
- do Carmo, M. P. (2017). Differential Geometry of Curves and Surfaces (Revised and updated 2nd ed.). Dover Publications.
- Spivak, M. (1979). A Comprehensive Introduction to Differential Geometry, Volume 2 (2nd ed.). Publish or Perish, Inc.
- Kühnel, W. (2015). Differential Geometry: Curves — Surfaces — Manifolds (3rd ed.; Student Mathematical Library, Vol. 77). American Mathematical Society.
Additional resources:
The lecture notes of Dr. Azar
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Applicants Are Divided Into Two Groups: "International Applicants" Who Have Foreign Citizenship And "Pakistani Applicants" Who Either Hold Pakistani Citizenship, Have Dual Citizenship, Or Are Pakistanis Residing Outside The Country.
