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Kevin Buzzard
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I am not so sure of the US system but one of the books we recommend at our university is Martin Liebeck's "A concise introduction to pure mathematics".

http://www.amazon.co.uk/Concise-Introduction-Pure-Mathematics/dp/1584881933

At least in the UK that book is pretty darn cheap.

Kevin Buzzard
  • 41.4k
  • 13
  • 166
  • 245