proof based math books suggestions

<p>I'm considering learning some theoretical math just to fill up time while im bored at work but I've only had exposure up to multivariable calculus (not proof based, just normal). I'm looking at Apostol and Spivak's Calculus book, but unfortunately my library doesn't have those books (sorry im cheap). Can someone suggest other math books that are intro to proofs like spivaks/apostol? Will Rudin's "Introduction to Analysis" be a good start for me or will it be too advanced? Also looking at this book:</p>

<p><a href="http://www.amazon.com/ADVANCED-CALCULUS-WILFRED-KAPLAN/dp/032118968X/ref=pd_bbs_sr_4/104-8653705-0484753?ie=UTF8&s=books&qid=1184352138&sr=8-4%5B/url%5D"&gt;http://www.amazon.com/ADVANCED-CALCULUS-WILFRED-KAPLAN/dp/032118968X/ref=pd_bbs_sr_4/104-8653705-0484753?ie=UTF8&s=books&qid=1184352138&sr=8-4&lt;/a&gt;&lt;/p>

<p>Rudin is a bit advanced for an introduction to analysis, but you could try anyways. You can get a cheap, paperback copy of Rudin's text on half.com or something. </p>

<p>I'd recommend this book:
<a href="http://www.amazon.com/Mathematical-Analysis-Straightforward-Approach-Binmore/dp/0521288827%5B/url%5D"&gt;http://www.amazon.com/Mathematical-Analysis-Straightforward-Approach-Binmore/dp/0521288827&lt;/a&gt;&lt;/p>

<p>Rudin is boring (and might be beyond your level). Get Spivak or Apostol.</p>

<p>You can learn proof-based theoretical math that isn't analysis. I learned how to do proofs and stuff out of this book (<a href="http://www.amazon.com/Mathematical-Thinking-Problem-Solving-Proofs-2nd/dp/0130144126/ref=pd_bbs_sr_1/103-0317380-1208610?ie=UTF8&s=books&qid=1184380909&sr=1-1%5B/url%5D"&gt;http://www.amazon.com/Mathematical-Thinking-Problem-Solving-Proofs-2nd/dp/0130144126/ref=pd_bbs_sr_1/103-0317380-1208610?ie=UTF8&s=books&qid=1184380909&sr=1-1&lt;/a&gt;) at a summer program.</p>