SUMMARY
The forum discussion centers on the suitability of Serge Lang's "Fundamentals of Differential Geometry" for beginners in the subject. Participants recommend starting with Lang's book but caution that it may be too abstract for those with limited mathematical background. Alternative suggestions include Do Carmo's "Differential Geometry of Curves and Surfaces" and John Lee's series on manifolds for a more accessible introduction. The conversation highlights the need for foundational knowledge in topology and the importance of selecting appropriate texts for learning differential geometry, especially for applications in physics.
PREREQUISITES
- Basic understanding of topology from an Analysis II course
- Familiarity with calculus and mathematical analysis
- Interest in applications of differential geometry in physics
- Willingness to engage with mathematical rigor
NEXT STEPS
- Explore Do Carmo's "Differential Geometry of Curves and Surfaces" for a practical introduction
- Study John Lee's series: "Topological Manifolds," "Smooth Manifolds," and "Riemannian Manifolds" for comprehensive understanding
- Read Wald's "General Relativity" for applications of differential geometry in physics
- Investigate Pressley's "Elementary Differential Geometry" for a modern exposition of the subject
USEFUL FOR
Students of mathematics and physics, particularly those interested in self-learning differential geometry and its applications in mechanics and general relativity.
