Discussion Overview
The discussion centers around recommendations for mathematics books suitable for learning multivariable calculus, particularly for someone who is currently studying single-variable calculus and analysis through "baby Rudin." Participants explore various book options and their rigor, as well as the appropriateness of learning certain topics from Rudin.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant suggests learning multivariable calculus non-rigorously before tackling Rudin's analysis chapters 9-11.
- Another participant proposes finishing single-variable topics first and then learning multivariable material rigorously, questioning the choice of starting with Rudin.
- A participant recommends "Calculus vol. 2" by Apostol for its rigor but notes it may take considerable time to work through.
- Another suggestion is Lang's "Calculus of Several Variables" as a less rigorous but excellent introduction to the subject.
- Concerns are raised about learning differential forms from Apostol or Lang, with a recommendation for Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" as an alternative.
- One participant advises against learning measure theory and Lebesgue integration from Rudin, suggesting that other texts would be more suitable.
- Another participant emphasizes the need for both volumes of Apostol for a complete treatment of multivariable calculus.
Areas of Agreement / Disagreement
Participants express differing opinions on the best approach to learning multivariable calculus and the suitability of various texts, indicating that multiple competing views remain without a consensus on a single recommended book.
Contextual Notes
Participants highlight the limitations of certain texts regarding specific topics like differential forms and measure theory, indicating that the choice of book may depend on the learner's goals and prior knowledge.