Keith (Stanford University, Stanford, California, USA) Devlin 
Sets, Functions, and Logic [PDF ebook] 
An Introduction to Abstract Mathematics, Third Edition

Keith Devlin. You know him. You»ve read his columns in MAA Online, you»ve heard him on the radio, and you»ve seen his popular mathematics books. In between all those activities and his own research, he»s been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students.
Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students» experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics–one that motivates readers and sets the stage for the challenges that lie ahead.
Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read…and enjoy…and learn from.
About the Author
Dr. Keith Devlin is Executive Director of Stanford University»s Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences, .
Dr. Devlin is also one of the world»s leading popularizers of mathematics. Known as ‘The Math Guy’ on NPR»s Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.