18.090 Introduction To Mathematical Reasoning Mit !free! Today

"Book of Proof" by Richard Hammack (free online). This is more gentle than Velleman but excellent for drilling.

No textbook required; lecture notes provided. Recommended references: 18.090 introduction to mathematical reasoning mit

Why Hammack? It is exceptionally clear, conversational, and filled with graduated exercises. Chapters progress from simple truth tables to the mind-bending proof of the irrationality of ( \sqrt2 ) to the fact that the real numbers are uncountable. Students repeatedly praise the book for its "hand-holding without being condescending." "Book of Proof" by Richard Hammack (free online)