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I am a beginning graduate student in Mathematics soon and I am planning to self-study Numerical Analysis and Numerical Linear Algebra. I know there are already reference-request questions about this, but I am looking for some more specific books.

I am looking for books in the following categories:

  1. Books with difficult problems, and solutions in the back (ideal)
  2. Books with difficult problems
  3. Books with solutions in the back
  4. Books with separate solution manuals
  5. Problem books (ideally with solutions in the back, or solution manuals)

Could you please recommend me some textbooks, and tell me in which category they are? Thank you very much, any recommendations are immensely appreciated!

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    $\begingroup$ One book which deals with difficult problems which intersects a lot with Numerical Linear Algebra is Matrix Analysis by Horn and Jhonson. $\endgroup$
    – Ovi
    Nov 23, 2020 at 16:29
  • $\begingroup$ Stoer and Bulirsch is a good book, definitely worth a look: amazon.com/Introduction-Numerical-Analysis-Applied-Mathematics/… $\endgroup$
    – littleO
    Nov 27, 2020 at 5:04

4 Answers 4

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I would recommend this book:

Burden, Richard L., and J. Douglas Faires. Numerical Analysis. 9th ed. 2010. ISBN-13: 978-0538733519.

Since difficulty is necessarily subjective, I wouldn't attempt to answer what category it is in. However, here's a free PDF version in case you want to check out what it's like.

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    $\begingroup$ Good, solid undergrad numerical analysis book. $\endgroup$
    – littleO
    Nov 27, 2020 at 5:07
  • $\begingroup$ @littleO thanks. $\endgroup$
    – KingLogic
    Nov 27, 2020 at 5:13
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For a more proof-heavy treatment, I'd suggest

Isaacson, E., & Keller, H. B. Analysis of numerical methods.

A comprehensive treatment of several methods, with emphasis on proofs and theory. No solutions in the back, though.

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Schaum's Outline of Numerical Analysis.

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I was an algebra major student and later a postgraduate student in topological algebra. We had two main books with linear algebra problems (but, as far as I remember, non-Numerical). The books contained a lot of problems and, in the back, hints for some of (I guess, harder) problems. Maybe there are separate books containing full solutions for these problems.

[Kos] This is an English translation of the second edition of [Kos2]. This books contains relatively hard problems. One of its three chapters (about a hundred pages) is devoted to linear algebra and geometry. Unfortunately, the second edition of the book contains sufficiently many misprints, which are hopefully fixed in [Kos2].

[Pro] This books has about 350 pages and two thousands linear algebra problems.

References

[Kos] Exercises in algebra: a collection of exercises in algebra, linear algebra and geometry, ed. Kostrikin A.I., Gordon and Breach Publ., 1996.

[Kos2] A collection of linear algebra problems, 3-edn, corrected and extended, ed. Kostrikin A.I., Moscow, Phys.-mat. lit, 2001, in Russian (Сборник задач по линейной алгебре, под редакцией А.И. Кострикина, издание третье, исправленное и дополненное, Москва, Физико-математическая литература, 2001). I did not find an English translation.

[Pro] Proskuryakov I.V., A collection of linear algebra problems, in Russian (Проскуряков И.В. Сборник задач по линейной алгебре). I did not find an English translation.

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  • $\begingroup$ To be honest, I am not too sure if OP understands Russian. $\endgroup$
    – KingLogic
    Nov 27, 2020 at 5:48

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