The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton Lifesaver Study Guides) - Tapa dura

"This well-written book prepares readers to take a real analysis course by carefully defining and proving all concepts one needs for this type of course. . . . Throughout the book, the style is incredibly reader friendly, and the author's enthusiasm for the subject is very clear."--Choice "I can imagine this book proving useful to a motivated student who is finding the transition into analysis challenging through traditional textbooks."---Dominic Yeo, Mathematical Gazette "Grinberg's accessible book gives beginning real analysis students the leg up they need."--Mark McConnell, Princeton University "This book is a great resource that every real analysis student should have. Grinberg writes like a professor would speak to a student during office hours: free of jargon, with a sense of humor, yet still in an authoritative and informative manner."--Oscar E. Fernandez, author of Everyday Calculus: Discovering the Hidden Math All around Us

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 math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide 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 math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs. * The essential "lifesaver" companion for any course in real analysis* Clear, humorous, and easy-to-read style* Teaches students not just what the proofs are, but how to do them--in more than 40 worked-out examples* Every new definition is accompanied by examples and important clarifications* Features more than 20 "fill in the blanks" exercises to help internalize proof techniques* Tried and tested in the classroom