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I'm a first year graduate student. I had an engineering background so my knowledge in analysis is not much deeper than what covered in regular calculus series. Would it be viable/beneficial to study Rudin's complex and real analysis directly to build up mathematical maturity? Thank you.

Daniel Li
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    NOOOOOOO! Jump into Baby Rudin or work exercises in Spivak's Calculus (the analysis exercises, not the "rote computations"). Or even look at my multivariable mathematics book (which has the multivariable analysis material, plus computational stuff). – Ted Shifrin Feb 08 '18 at 00:38
  • That's a hard book to read. I would read something easier first, like Rudin's Principles of Mathematics Analysis or Royden. – D_S Feb 08 '18 at 00:39
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    I concur in principle with @TedShifrin s NOOO... But you could keep it open, try to read it, and work backward through prerequisites as you encounter things you can't fathom yet. That's often a good way to learn a new subject, as long as the gap between what you're reading and what you know isn't too large. – Ethan Bolker Feb 08 '18 at 00:44
  • Seconding (thirding?) the comments of Ted Shifrin and Ethan Bolker, you don't want to jump straight into the deep end. Rudin's books are works of beauty, but they are very, very hard to learn from. They are lovely references, and if you understand the material well, they are tremendously useful to have on your shelf, but they are hard books. This is particularly true of Papa Rudin (i.e. Real & Cplx Anal), but also (in my opinion) true of Baby Rudin (i.e. Principles of Real Anal). Spivak might be a better choice, and I like Apostol. Maybe even Courant (for a slightly heterodox treatment). – Xander Henderson Feb 08 '18 at 01:01

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