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I'm a business/international relations person and a lot of my job is flying around. I have had a lot of downtime recently, and couldn't find a sustainable hobby to fill in that time.

Until I found Michael Spivak's Calculus and decided that it was legitimately a very fun book to read. I didn't actually do the problem sets, but I read the book carefully, and can say that while I by no means mastered the material, I'm generally conversant in it. I might actually end up doing the problem sets at some point, but that's another thing...

In a similar vein to my previous endeavors, becoming "fluent" in undergraduate biology and philosophy through self-study during my downtime, I'd like to do the same thing with mathematics and statistics.

Can someone help me plan out and structure what books I should read and in what order? Let's try to avoid popular science books. I liked the level of technicality in Spivak's book. Again, I'm not trying to reach any sort of academic mastery, just technical "conversational" fluency.

There are plenty of "what should I read" questions around, but I think mine is slightly different, by virtue of asking for a structure, and specifying what I want to achieve. Also, I like the proof-based approach used by Spivak, and would like to see something similar for statistics.

edit

To clarify, when I read Spivak's book Calculus, I didn't skip the dense parts. I read and understood the proofs. Whether I could replicate them on my own is another issue--I attribute this to the lack of problem sets completed--but I enjoyed the dense parts of Spivak's books. So, I am absolutely looking for something more technical than A Brief History of Time, etc, etc.

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    what do you mean when you say you are conversent in it?2012-08-17
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    How about, I can read and understand any equation you put in front of me, and generally know how I can manipulate them.2012-08-17
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    Or, an extension, I can understand, if not solve, whatever makes the front page of M.SE?2012-08-17
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    *Any* equation? Let's see. Here's an equation for you: $s^2=g_{\mu\nu}v^\mu v^\nu$. What does it mean, and what can you do with it?2012-08-17
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    I meant I want to learn to the point where I can understand any equation. The last comment lacked context.2012-08-17
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    It seems you've read Spivak's _Calculus_ as one might pick up and read any coffee table-type book. But to be honest, I can't imagine one can simply read such an active textbook and enculture a deep understanding of the material without truly engaging with it, i.e., completing exercises, re-producing proofs, asking questions, etc. That is, I'm not necessarily sure if one can can claim being conversant in the material and having understood all the proofs without at least a vague idea for how to reconstruct them.2012-08-17
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    I had the same reaction as Riem when I read the post initially.2012-08-17
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    The OP is not looking to "enculture a deep understanding" nor to attain "academic mastery," but simply to acquire "conversational fluency" as a hobby. Now we can argue about what being mathematically conversant actually entails, but I think it's pretty clear what the OP is after. I think it's great what the OP is doing, and wish more non-mathematicians would have a similar interest -- with exercises completed now, later, or never. Not everyone is looking to become a professional mathematician.2012-08-17
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    "I read and understood the proofs. Whether I could replicate them on my own is another issue..." Many would argue that being able to replicate a proof on your own is the truest test of understanding.2012-08-17
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    @JoelCornett Ahaha, I was exaggerating a bit. I could, of course, reconstruct the exact proofs as given by Spivak, otherwise it'd be debatable whether or not I actually read the book to begin with. I suppose what I was trying to go for with that sentence was, "Whether I could do/think of an equally difficult proof on my own."2012-08-17
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    @nanana: Hehe. No judgements here. Based on your question, I recommend looking into graph theory and combinatorics. These fields seem like ones that would be right up your alley.2012-08-18

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