The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs

Description

The essential "lifesaver" that every student of real analysis needs 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 Review: Entertaining hard work to try to understand analysis - Quite demanding for someone who used Analysis 40+ years ago. Not the solution but the thoughts I have to make are the real fun for me. Review: Ojalá lo hubiese descubierto antes - Hay algunas personas a las que nos gustan las matemáticas. Toda la vida pudimos haber sido buenos en ellas, y llega un punto en el que descubrimos que existen las matemáticas avanzadas, las de demostraciones. Notamos que estas siguen unas reglas del juego para las que el puro conocimiento anterior no es suficiente. Es otro mundo, al que es difícil acceder. Este libro está escrito tan amenamente y con una comprensión pedagógica de que el lector se enfrenta ante el desafío de aprender a demostrar, que siento por fin que alguien entendió mis necesidades académicas. Altamente recomendable. Me tomé la libertad de anexar dos hojas. Ahí uno puede vislumbrar la calidad pedagógica del autor. Ojalá lo hubiese descubierto antes.