Discussion Overview
The discussion revolves around the comparison of Tom Apostol's "Calculus Vol. 1" and Michael Spivak's "Calculus" in the context of a proof-oriented calculus course. Participants explore the suitability of each text for covering topics such as the axioms for real numbers, Riemann integrals, limits, derivatives, the fundamental theorem of calculus, Taylor's theorem, infinite series, power series, and elementary functions. Additionally, there are inquiries about the level of Apostol's Vol. 2 compared to Spivak's "Calculus on Manifolds" and its adequacy as a foundation for linear algebra studies.
Discussion Character
- Debate/contested
- Conceptual clarification
- Technical explanation
Main Points Raised
- Some participants suggest that Spivak's text is more enjoyable for students, while Apostol's may be perceived as more scholarly.
- One participant notes that Spivak's treatment of multivariable calculus is more condensed and at a higher level than Apostol's, specifically mentioning the use of differential forms in Spivak's work.
- Another participant expresses a preference for Apostol's Volume 1 over Spivak's, but cautions that those new to proofs might find Spivak more accessible.
- Concerns are raised about Apostol's Volume 2, with one participant stating it covers too many subjects too briefly and recommending a more thorough study of linear algebra with Lang instead.
- There is a suggestion that Spivak's "Calculus on Manifolds" requires more background in linear algebra and real analysis than what is provided in Apostol's texts.
- One participant explicitly states a preference for Spivak over Apostol, indicating a lack of appreciation for Apostol's book.
Areas of Agreement / Disagreement
Participants express differing opinions on the merits of Apostol's and Spivak's texts, with no consensus reached on which is definitively better for a proof-oriented calculus course. Preferences vary based on personal experiences and perceived accessibility of the material.
Contextual Notes
Participants mention varying levels of difficulty and content coverage in Apostol's and Spivak's texts, indicating that the suitability of these books may depend on the reader's prior experience with proofs and related mathematical concepts.
Who May Find This Useful
Students and educators considering proof-oriented calculus texts, particularly those interested in the comparative strengths and weaknesses of Apostol's and Spivak's approaches.