Which Classical Mathematics Textbooks Should a Mathematician Possess?

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Classical mathematics textbooks essential for advanced and undergraduate mathematicians include Richard Courant's "Differential and Integral Calculus" (volumes 1 and 2) and the two-volume "Methods of Mathematical Physics" by Courant and Hilbert. These texts are highly recommended for their foundational content and affordability, with prices around $15 each for the Courant volumes. Additionally, Segre Lang's extensive series covering various mathematical fields and levels is noted as valuable. Texts by Walter Rudin are also mentioned as significant contributions to the field. The discussion emphasizes the importance of these works for anyone serious about pursuing mathematics.
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What are the classical mathematics textbooks for advanced and undergraduate level that a mathematician should possess?
 
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have you looked at the thread "should i become a mathematician" in the academic advising forum? (post #1?)
 
Courant and Hilbert, Methods of mathematical physics (the original two-volume version)
 
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I strongly recommend Differential and Integral Calculus, vols 1 and 2, by Richard Courant, epecially given the current price: of about $15 each:

Notice the 2 volume set offered for $32, about half way down the page, formerly belonging to, and signed by, my friend the famous mathematician and author Ray Kunze, (now deceased).

I offer this as evidence that a mathematician would want these books.

https://www.abebooks.com/servlet/SearchResults?sts=t&cm_sp=SearchF-_-home-_-Results&tn=differential and integral calculus&an=courant
 
Segre Lang's large series of volumes in different fields of math and of different level

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some books by Rudin: (some items are repeated sorry)

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Thread 'A rigorous approach to learn Mathematics'

Hello Intellectuals! So far it seems to be reasonable to learn mathematics in a rigorous way by not solely considering the techniques of problem solving or the applications of a particular subject or concept. Also to truly appreciate the beauty of mathematical endeavor one need to learn the reasoning behind the origination of concepts in mathematics, so as a beginner it appears to be worthwhile to learn the highly abstract aspects of mathematics like proofs, logic, and topics in pure...
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