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Before the internet people who wanted to be mathematicians had to read books, so books were extremely important. I was reading Littlewood's "A Mathematician's Miscellany" where he gives the sequence of books he read before university (see pg.67 here: https://archive.org/stream/mathematiciansmi033496mbp#page/n77/mode/2up )

In that spirit, which sequence of books would you recommend to someone having only a high school background of math but who is willing to learn?

Also what do you think of the following sequence? :

Apostol's Calculus volumes

Artin's Algebra

Rudin's Principles of Analysis

Axler's Linear Algebra Done Right

Marsden/Hoffman's Complex Analysis

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    $\begingroup$ In my experience, questions like this get put on hold. But I'm not against them so I'll just leave this here. $\endgroup$ – got it--thanks Sep 26 '15 at 13:16
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You're list is fine. Only thing is that using several books to cover different topics can sometimes be difficult, as you sort of get used to a particular Author's technique and notation. But at some point you will have to read from different authors so I guess it's up to you.

How about finding a book that covers all topics at undergraduate level. I recommend the one I used: Mary L Boas. Mathematical Methods in the Physical Sciences 3rd Edition. This book covers everything you mentioned from Linear Algebra to Complex Analysis, Calculus of Variations and much more, in nice detail might I add.

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