The Real Analysis Lifesaver

Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based maths.

Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach. First, it shows students how to work backwards to solve the crux of the problem, then it guides them on how to write it up formally. The book provides plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding.

Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about maths. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humour. It is the lifesaver that every drowning student needs.

The Real Analysis Lifesaver is the essential companion for any course in real analysis. It is clear, humorous, and written in an easy-to-read style. The book teaches students not just what the proofs are, but how to do them, with more than 40 worked-out examples. Every new definition is accompanied by examples and important clarifications.

Additionally, the book features more than 20 "fill in the blanks" exercises designed to help internalise proof techniques. This approach has been tried and tested in the classroom, ensuring it is an effective tool for any student.