Which is More Mathematical: The Princeton Companion or Mathematics for Physics?

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The discussion compares "The Princeton Companion to Applied Mathematics" and "Mathematics for Physics" by Michael Stone and Paul Goldbart in terms of mathematical rigor and applicability. "Mathematics for Physics" is noted for its streamlined presentation and focus on essential mathematical concepts relevant to physics, making it more suitable for learning foundational mathematics that may not be covered in standard undergraduate courses. In contrast, "The Princeton Companion" serves as a comprehensive reference that includes a wide range of specialized topics such as asymptotics and mathematical modeling, but is perceived as less effective for direct learning due to its sprawling nature. Overall, "Mathematics for Physics" is considered more mathematically advanced and rigorous for students seeking a focused approach to applied mathematics in physics.
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Which is more mathematical among The Princeton Companion to Applied Mathematics and Mathematics for Physics by Michael Stone and Paul Goldbart?
Both of them are applied mathematics books. What are the main differences between them? Which is more mathematical i.e. mathematically advanced, mathematically rigorous?
 
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Mathematics for Physics is more streamlined in its presentation, and covers the most important mathematics for physics that might not be covered in the mathematics classes required for a typical undergraduate degree. The Princeton Companion is a nice reference, but it... sprawls a bit. It does cover quite a few interesting specialized topics like asymptotics, mathematical modeling, etc. , but I don't feel that the Princeton Guide is as good for learning from.
 
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