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If you're motivated / curious enough / have enough time, I recommend Spivak's Calculus as a way of learning calculus the, as you say, 'proper (whatever that mea
by wfn 13y ago
If you're motivated / curious enough / have enough time, I recommend Spivak's Calculus as a way of learning calculus the, as you say, 'proper (whatever that means) way.' It's basically a treatment of calculus from the perspective of real analysis, having the 'no ad-hoc rule teaching' policy at its foundation. You prove things, build up a non-fragmented edifice slowly, and end up being introduced to analysis such that you can then pick up other things (it's a rather extensive treatment of calculus indeed.) Or so goes my narrative in the midst of frustrations regarding self-motivating to continue individually progressing through the book. :)
The 3rd and maybe the 4th editions can be found online by doing an internet search for pdf/djvu files.
- enen 13y agoThanks. I'll definitely check it out.
- jfarmer 13y agoI majored in mathematics at the University of Chicago and Spivak's Calculus was my first-year calculus textbook. It confirmed what I had long believed: what I was being taught in high school wasn't really mathematics. The book might seem very alien at first, though.
- akuma73 13y agoCan anyone recommend a similar book for the theory of probability?
- eru 13y agoFor learning probability the hard way, I recommend you start with measure and integration theory. (Something like http://www.amazon.com/Probability-Measure-Theory-Second-Edition/dp/0120652021/ref=sr_1_21?ie=UTF8&qid=1377758073&sr=8-21&keywords=measure+integration+theory http://www.amazon.com/Probability-Measure-Theory-Second-Edit... might work.)