Definitive math books for a physics major

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SUMMARY

This discussion focuses on essential mathematics textbooks for physics majors, highlighting key works such as "Calculus" by Stewart, "Mathematical Methods" by Boas, and "Mathematical Methods for Physicists" by Riley. Participants recommend the "Princeton Companion to Mathematics" for its high-quality articles and broad coverage of mathematical concepts relevant to physics. Additionally, the book "Applied Mathematical Methods for Theoretical Physics" is suggested for its treatment of calculus of variations in physics applications. These resources are crucial for deepening mathematical understanding in the context of physics.

PREREQUISITES
  • Familiarity with calculus concepts from Stewart's "Calculus"
  • Understanding of mathematical methods as presented in Boas' "Methods"
  • Knowledge of advanced mathematical techniques from Riley's "Methods"
  • Basic exposure to physics principles relevant to mathematical applications
NEXT STEPS
  • Explore "Applied Mathematical Methods for Theoretical Physics" for advanced applications of calculus in physics
  • Read "Princeton Companion to Mathematics" for a comprehensive overview of mathematical concepts
  • Investigate additional mathematical methods textbooks suitable for graduate-level physics
  • Research calculus of variations and its applications in theoretical physics
USEFUL FOR

Physics undergraduates, graduate students in physics, and anyone seeking to enhance their mathematical foundation for advanced studies in physics.

zheng89120
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So as a physics undergrad, I have been studying extensively into the popular (and useful) textbooks books by Stewart (Calc), Boas (Methods), and Riley (Methods). Any ways, I was just wondering, is there another book on mathematics for that a physics major should probably like to look, say after after spending a good amount of time with Riley's book? (Though if such a book would be on mathematical methods, it may be at a graduate school level.) thanks
 
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I think this book has a rather nice high level treatments of some applications of the calculus of variations to physics: https://www.amazon.com/Applied-Mathematical-Methods-Theoretical-Physics/dp/3527405348#reader_3527405348

Maybe you would like the Princeton companion to mathematics. The quality of the articles is very high on average. It has introduction to many areas of mathematics and often their applications to physics. It is a very good sampler of high level mathematics. https://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809
 

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