Mathematics Equivalent to Landau & Lifshitz

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SUMMARY

The discussion centers on identifying mathematical resources equivalent to the Landau & Lifshitz series for graduate-level mathematics. Key recommendations include Serge Lang's comprehensive texts, Spivak's calculus books, and the Stein and Shakarchi series focused on analysis. Participants emphasize the need for a separate set theory text addressing ZFC to complete mathematical education. For those interested in mathematics for physics, the conversation suggests exploring differential topology, modern differential geometry, fiber bundles, and algebraic topology.

PREREQUISITES
  • Familiarity with graduate-level mathematics concepts
  • Understanding of calculus and analysis
  • Knowledge of set theory, particularly Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC)
  • Basic concepts in theoretical physics and mathematical physics
NEXT STEPS
  • Research Serge Lang's complete works on algebra
  • Study Michael Spivak's calculus books for a deeper understanding of calculus
  • Explore the Stein and Shakarchi series for advanced analysis techniques
  • Investigate differential topology and modern differential geometry for applications in theoretical physics
USEFUL FOR

Graduate students in mathematics, theoretical physicists, and anyone seeking to deepen their understanding of advanced mathematical concepts relevant to physics.

Snow-Leopard
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Can one tell me about the Mathematical Equivalent to Landau & Lifgarbagez. or any other set that deal with all Graduate Level Mathematics.

There is a Series by Springer, Springer Graduate Texts in Mathematics but they contains too many books. It would be great if they contain Max. 20 books. If any series exist then give me Link to Amazon.

If one Already completed his Graduate Studies in Mathematics (having main focus on Calculus & Analysis) then they also give List of all book they used.(the complete set)
 
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There is no such series today, except maybe Springer's GTM series...

Of course, if you are feeling machocistic, there's always Bourbaki...

 
You always have Lang's books. He has books on about everything of mathematics.

You might also check out Stein and Shakarchi's series. But that's on analysis only.
 
micromass said:
You always have Lang's books. He has books on about everything of mathematics.

You might also check out Stein and Shakarchi's series. But that's on analysis only.
Although, correct me if I'm wrong, lang is missing a proper book on set theory so if you want to complete your math education make sure to get a separate set theory text that deals with ZFC and the brilliance of Cantor in all its glory.
 
WannabeNewton said:
Although, correct me if I'm wrong, lang is missing a proper book on set theory so if you want to complete your math education make sure to get a separate set theory text that deals with ZFC and the brilliance of Cantor in all its glory.
Although, to be fair, it's not as if L&L is complete either.
 
How about this series,(topic-wise)
1.Algebra: All books by Serge Lang.
2.Calculus: All books by Spivak.
3.Analysis: All books by Stein and Shakarchi.

If any topics in Graduate course not in that then I go to Library. I want to do Mathematics just for Physics.
 
Snow-Leopard said:
How about this series,(topic-wise)
1.Algebra: All books by Serge Lang.
2.Calculus: All books by Spivak.
3.Analysis: All books by Stein and Shakarchi.

If any topics in Graduate course not in that then I go to Library. I want to do Mathematics just for Physics.

If you want to mathematics just for physics, then you really don't need to read those books. Those books are pure mathematics and don't really care for physics very much.

Just get some methods book and work through that. On the other hand, if you're into very theoretical physics or mathematical physics, then pure math books are useful. But only do it if it interests you.
 
thank you micromass, I mean after completing my Undergradute, I go Physics Graduate Course but not taking Maths its just be a side subject (which I prepare through self-study)
 
If you want math for theoretical physics, then you should study differential topology and modern differential geometry.

If you want to get into stuff like modern field theories etc., then fiber bundles, geometric topology, algebraic topology and quantum algebra should also be interesting.
 
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Smirnov, a course of higher mathematics
 

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