Essential Textbooks thread

I've decided I'm gonna start building up a small collection of physical textbooks, as opposed to just using PDFs. What are some must haves? I'm thinking to start with baby rudin.
Also, is hardback really much better than soft back to justify the extra price?

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math.stackexchange.com/questions/185607/problem-books-in-higher-mathematics
springer.com/series/714?detailsPage=titles
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rudin is (literally) a meme

Give a suggestion then. Are there any texts that are either:
Good to keep around as a reference
Considered the authoritative text in the field
Books I will pass down to my kids

>Give a suggestion then.
How am I supposed to do that without knowing your background and motivations?

I want to learn about quantum computing and in general about math and physics

I'm undergrad with highest math being linear and cal III and highest physics EMT I and modern

Forgot to mention, I'm not OP but suggestions would be nice

Bump

For undergraduate analysis
>Good to keep around as a reference
Tao
>Considered the authoritative text in the field
Rudin
>Books I will pass down to my kids
Simon's volumes in analysis

Nice picks. Hard cover or soft?

Rule of thumb is to buy older edition hard covers. If you're buying something from Springer (yellow books), paperback is the choice, their hardcovers are cheap mass market deals and will fall apart fast, especially if you're like me and flip from page to page nonstop. Springer also has editions of books in English intended for distribution in Asia, and those are the cheapest. My Eisenbud is one of those, and it's a very sturdy paperback.

Papa Rudin has an iconic green hardcover edition, get that though.

My picks for undergrad:
Velleman's proofs book
Munkres topo
Zorich or Tao (really cheap to get) anal (Rudin is great for course, but terrible for reference or self-study)
Demidovich excercise book for anal
Lay or Axler for lingebra if you're engineer, Shilov if you're mathematician
Lang's algebra in paperback (says grad, but it's undergrad really)

>Lang
gross

>(says grad, but it's undergrad really)
there is an undergrad algebra by lang, it's as poorly written as his grad algebra though.

There's no point in getting the undergrad one. The grad one is comfortably readable to undergrad.
50 years and there is no superior book to Lang for algebra. Do you suggest not learning it? Rowen is terrible because it's not abstract enough. There might be some russian textbook on algebra though.

>_undergrad_ picks
>lang
ev-RY bo-DY wants to rule the woorrrld

Don't blame for american education being so shit they have to take calc in uni. Lang is comfortable for undergrads.

>50 years and there is no superior book to Lang for algebra.
catch-all algebra books are a literal waste of ink, get a proper book on group theory, a proper book on homological algebra, etc.

Artin's book for Algebra is excellent

Lang is a good reference, thus it's a good candidate for personal library, which is what OP asked for. Though for learning it's definitely better, even mandatory, to get a book on each topic.

Name me, please, higher (further) math textbooks with good exercise sets (from simple to relatively difficult) and complete solution manuals, like generic calculus books (Stewart, Larson, Anton) or generic diff-equations books (Zill, etc). A book from any brach of higher math, just available on libgen or torrents with full solutions.

>higher (further) math textbooks with good exercise sets (from simple to relatively difficult) and complete solution manuals
Murty - Algebraic Number Theory
Murty - Analytic Number Theory
Murty - Modular Forms
math.stackexchange.com/questions/185607/problem-books-in-higher-mathematics
springer.com/series/714?detailsPage=titles

Yes, I know about this Springer series, but thanks. Maybe something more generic? For recreational exercising after a work day, prefferably computational. With little enlightening chapters.

Too shallow, doesn't cover what Lang does, excercises are on the easier side.
Again, i don't know what is expected of undergrads in america, but where i come from we use Lang's graduate textbook for freshman algebra course (2 semesters) and around 70% of students pass it each year. I regularly come back to it even in grad.