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The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton Lifesaver Study Guides), by Raffi Grinberg
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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
- Sales Rank: #177405 in Books
- Published on: 2017-01-10
- Original language: English
- Dimensions: 9.90" h x .60" w x 6.90" l, .0 pounds
- Binding: Paperback
- 200 pages
From the Back Cover
"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
"Grinberg's accessible book gives beginning real analysis students the leg up they need."--Mark McConnell, Princeton University
About the Author
Raffi Grinberg is an entrepreneur and former management consultant. He graduated with honors from Princeton University with a degree in mathematics in 2012.
Most helpful customer reviews
8 of 8 people found the following review helpful.
The most intuitive and friendly approach to analysis I have ever seen.
By Amazon Customer
I simply cannot recommend this book highly enough. The material is presented in a friendly, approachable manner that illustrates the concepts very lucidly with examples and engaging dialogue between the author and reader. One of the main difficulties that math students have with proofs is that proofs are often given as a final draft; the thought process and reasoning that went into tying the assumption(s) and conclusion(s) together are often omitted and this leaves the student perplexed on how to approach proofs. This book gives you a firm grounding in proof analysis as well as propositional and quantificational logic to become proficient in developing your own proofs. I genuinely feel that after using this book, a student will have a much easier time approaching proofs in other math classes. Using this book as a prerequisite to, or concurrently with, a real analysis course will be beneficial to you if you are struggling or just need a little extra intuitive help. Either way, you will not regret purchasing this book.
3 of 3 people found the following review helpful.
Not enough content
By A. Ali
There's no discussion of differentiation or the Riemann integral in this book -- staples of any real analysis course. The exposition is not superior to those of any number of introductory analysis texts. My advice would be to stick to texts like Ross, Bartle and Sherbert, Hpwie, or Zorn. Of these three probably Zorn is the most elementary -- but even it has a chapter on differentiation and a chapter on the Riemann integral.
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