mathematical proofs: a transition to advanced mathematics, third edition, prepares students for the more abstract mathematics courses that follow calculus. appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. it is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.