All-encompassing book series of mathematics?

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Discussion Overview

The discussion revolves around the search for a comprehensive book series in mathematics that parallels the Landau-Lifschitz series in physics. Participants explore the idea of a series that covers major mathematical fields while incorporating physics for motivation and examples.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about a series that encompasses various fields of mathematics, including algebra, topology, differential geometry, analysis, functional analysis, PDEs, ODEs, probability, and statistics, while also drawing on physics.
  • Another participant mentions the Springer Undergraduate Math Series, noting that it is not a single series but rather a collection of works by different authors.
  • A different viewpoint suggests that "Mathematical Methods for Physicists" textbooks, such as those by Boas or Arfken & Weber, might meet the criteria, although they may be more concise than desired.
  • One participant points to Schaum's Outlines as a potentially comprehensive resource, though they caution that the explanations may be straightforward and not cover every topic exhaustively.

Areas of Agreement / Disagreement

Participants express differing opinions on the availability and suitability of existing resources, indicating that no single consensus exists regarding a perfect series that meets the initial inquiry.

Contextual Notes

Some responses highlight the limitations of the suggested resources, such as varying levels of depth, coverage, and pedagogical style, which may not fully align with the original request.

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Hi,

I was wondering if there exists a series, much like the Landau-Lifschitz physics books, that covers every major field of mathematics in a rich, lucid and pedagogical fashion, and at the same time drawing heavily on physics for examples and motivation.

It should at least include:
algebra (group theory), topology (algebraic), (complex) differential geometry, analysis (fourier analysis, vector analysis and other basics), functional analysis, theory of PDEs and ODEs, probability theory and perhaps statistics.

Thanks for any input.
 
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Springer does this, but its not really a series as its written by different authors. Still, its called an Undergradute Math Series.
 
It sounds like you're describing any of the multitude of "Mathematical Methods for Physicists" textbooks like Boas or Arfken & Weber or Riley, Hobson & Bence. They might be a bit terser than what you're looking for, but on the other hand, any of those books will have a more uniform and unified treatment and more physical examples and motivation than individual texts on each of those topics.
 
If it's a series of books, the schaum's outlines are quite comprehensive (no garuntees that they cover ALL of it though). Beware though, they have quite a no-frills explanation technique.

V
 

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