Most of the course is based on this book:

Sets, Logic, and Maths for Computing, 2nd edition
David Makinson

The book is available electronically for free. (If you are inside the LTH network.)

Some errata are listed here.

Mathematics relevant to Computer Science

• Richard Hammack, Book of Proof, as PDF
  
  Nice script that covers roughly the same ground as the first four lectures in this course as well as the one on proofs, which uses material from parts II and III of this book. Highly recommended if you are interested in a different presentation from that in SLAM.

• Eric Lehman, F Thomson Leighton, Albert R Meyer, Mathematics for Computer Science, as PDF
  
  Very comprehensive book on a wide range of math topics relevant to Computer Science, including everything we discuss in this course. Recommended if you are interested in deeper and more thorough treatment of some topic.

Set theory

• Abraham A. Fraenkel, Abstract Set Theory, 3rd ed., North Holland, 1966
  
  This is an excellent book on, well, set theory, written by one of the masters himself (Fraenkel is the "F" in "ZF set theory"). It stands out from many other books on mathematics in that it is very readable, largely because it avoids formal notation when it is not required, while still remaining very precise. It's proof that it is possible achieve mathematical precision without the typical salad of symbols and greek letters.

• Paul R. Halmos, Naive Set Theory, Springer, 1974
  
  "Naive" is to be understood in a technical sense here, of course.

Various

The Cantor-Schröder-Bernstein theorem is one of those things that seem pretty obvious, but can be quite tricky to prove. Here are some proofs: one proof, six more proofs.

Charles Sanders Peirce, Logical Machines, American Journal of Psychology, vol. I (1887), pp. 165-170, PDF

Lennart Salling, Algoritmik : related material of some interest, the book is in Swedish