Discrete Mathematics - An Open Introduction, 4th Edition

 The new edition brings many improvements and a new organization of content. In particular, the book now starts with logic and proofs, then practices those proofs with graph theory. The second half of the book contains material on counting (with a new "application to probability" section) and sequences. Over the last few years, I have found that students have more success with this arrangement. There is also a stronger emphasis on discrte structures, which should make the book more useful for students in computer science, while still focusing on understanding mathematical concepts essential for math majors and future math teachers.
There is more interactivity as well. More interactive exercises (which you can give students credit for if you create a course with the book on Runestone Academy; it is completely free for you and your students) and some interactive Sage and Python code to explore some topics.