Should You Choose Classical or Modern Texts for Studying Curved Surfaces?

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    Studying Surfaces
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SUMMARY

The discussion centers on the choice between classical texts, such as Gauss's "General Investigations on Curved Surfaces" and Euler's works, versus modern texts for studying curved surfaces. Participants highlight that Spivak's book effectively bridges classical concepts with modern interpretations, making it a valuable resource for understanding Gauss and Riemann. The consensus suggests that both classical and modern texts have their merits, and utilizing Spivak's work allows for a comprehensive understanding of the subject.

PREREQUISITES
  • Familiarity with differential geometry concepts
  • Understanding of Gauss's and Riemann's contributions to mathematics
  • Knowledge of mathematical terminology used in classical texts
  • Exposure to modern mathematical literature and its language
NEXT STEPS
  • Read Spivak's "Calculus on Manifolds" for a modern interpretation of classical concepts
  • Explore Gauss's "General Investigations on Curved Surfaces" for foundational knowledge
  • Study Riemann's works to understand the evolution of concepts in curved surfaces
  • Investigate contemporary texts on differential geometry for state-of-the-art methodologies
USEFUL FOR

Students of mathematics, educators in geometry, and researchers interested in the historical and modern approaches to curved surfaces will benefit from this discussion.

mathnerd15
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I wonder if one should study books like Gauss's General Investigations on Curved Surfaces or Euler's works or there are more modern texts that are state of the art?
 
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spivak's book helps explain gauss and riemann in modern language, so you can do both.
 

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