All-encompassing book series of mathematics?

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SUMMARY

The discussion centers on the search for a comprehensive mathematics book series akin to the Landau-Lifschitz physics books, covering major fields such as algebra (group theory), topology (algebraic), differential geometry, analysis (including Fourier and vector analysis), functional analysis, and probability theory. Participants suggest alternatives like the "Mathematical Methods for Physicists" series, including titles by Boas, Arfken & Weber, and Riley, Hobson & Bence, which provide a unified treatment with physical examples. Additionally, the Schaum's Outlines are mentioned as a comprehensive resource, although they may lack depth in explanations.

PREREQUISITES
  • Familiarity with algebraic structures, specifically group theory.
  • Understanding of basic concepts in topology and differential geometry.
  • Knowledge of analysis techniques, including Fourier and vector analysis.
  • Basic principles of probability theory and statistics.
NEXT STEPS
  • Research "Mathematical Methods for Physicists" by Boas for a unified approach to mathematics in physics.
  • Explore "Mathematical Methods for Physicists" by Arfken & Weber for comprehensive coverage of mathematical techniques.
  • Investigate "Mathematical Methods for Physicists" by Riley, Hobson & Bence for additional physical examples and motivation.
  • Review Schaum's Outlines for a broad overview of mathematical topics, keeping in mind their concise explanation style.
USEFUL FOR

Students and professionals in mathematics and physics, educators seeking comprehensive teaching resources, and anyone interested in a unified approach to mathematical concepts applied in physical contexts.

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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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