I’m an ME major and like studying certain math topics outside my curriculum in my spare time. I’m having a hard time deciding what books to get and I’m guessing that a good start would be finding a good book on writing proofs. I've bought one but there are no solutions for the exercises. This wouldn’t be a problem if I had a teacher to get feedback from but since this is self taught, I need some feedback. I have looked around on the forums and have not found opinions on books covering this while other topics there are so many recommendations that its difficult to decide since some cost so much $$$. I’m also interested in finding good books on PDE’s, analysis, complex analysis, and any other great book any of you would recommend :). I've had the typical college courses up to and including ODEs. Thanks for any replies.