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I am a programmer, and I want to become a machine learning researcher and a good software engineer. I dabbled with calculus, linear algebra, and real analysis for a few months when I was enrolled in a university. I majored in biology in the university, by the way. About $7$ years have passed since I dabbled with them, and I seem to have forgotten $99.9\%$.

I need to start math from scratch again. I've finished all but $3$ sections of Andrew Ng's machine learning class on coursera. I am going to read 'how to prove it' by velleman and then a discrete mathematics book. After then, I'll learn calculus, linear algebra, probability and statistics.

The problem is which discrete mathematics material to use after 'how to prove it'.

Amazon reviews say that Epp's book explains the concepts the best but that Rosen's book covers more subjects. According to amazon reviews, 'Concrete mathematics' by Knuth seems to be for students who already know calculus and linear algebra which I have to learn from scratch again.

Which learning material do you think is appropriate for a clueless self-learner like me?

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The Amazon reviews are correct about the relative strengths of the books by Rosen and Epp. Concrete Mathematics is a different kind of book altogether and doesn't really belong in the discussion. I recommend the book Mathematics: A Discrete Introduction by Edward Scheinerman: it's better written than the Rosen and has better coverage than the Epp.

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  • $\begingroup$ An amazon review says "There are COUNTLESS times in the book where there will be a large proof about a major concept that will take you hours to wrap your head around, only to discover that afterwards it tells you that it is incorrect and suggests that you try to figure it out for yourself!!". If the book's author enjoys to tantalize the readers and prompt them to figure out what's wrong in proofs on purpose, I'm not sure if it's a good book to read. $\endgroup$ – crocket Apr 25 '15 at 4:58
  • $\begingroup$ @Minsky: The three one-star reviews of Scheinerman at Amazon were quite clearly written by students who would in all likelihood have had problems with any book that actually required them to think. Exercises requiring you to work out what’s wrong with a supposed proof are very instructive: they’re a good intermediate step between just reading someone else’s correct proof and constructing your own from scratch. $\endgroup$ – Brian M. Scott Apr 25 '15 at 5:02
  • $\begingroup$ I'm not sure if fixing incorrect proofs is a good way to learn for someone who learns math alone at his room. $\endgroup$ – crocket Apr 25 '15 at 6:16
  • $\begingroup$ @Minsky: If you can’t do that, you can’t count on coming up with correct proofs on your own, and that’s something that you will eventually need to be able to do. What book you eventually choose is of course up to you; I’ve given you my considered opinion, as someone who has taught this material many, many times. Others may well have other opinions, though there aren’t many with much more experience than I at teaching the material to a wide range of students. $\endgroup$ – Brian M. Scott Apr 25 '15 at 6:17
  • $\begingroup$ I second this recommendation. Great book. $\endgroup$ – Nick Alger Jan 8 '18 at 2:21

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