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Real Analysis Lifesaver.

By: Grinberg, Raffi, 1990-.
Material type: materialTypeLabelBookSeries: Princeton lifesaver study guide: Publisher: [Princeton, New Jersey] : Princeton University Press, 2017Description: 1 online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 140088313X; 9781400883134.Other title: All the tools you need to understand proofs [Subtitle from resource:].Subject(s): Mathematical analysis | Functions of real variables | Numbers, Real | Analyse math�ematique | Fonctions de variables r�eelles | Nombres r�eels | MATHEMATICS -- Calculus | MATHEMATICS -- Mathematical Analysis | EDUCATION / Teaching Methods & Materials / Mathematics | Functions of real variables | Mathematical analysis | Numbers, RealGenre/Form: Electronic books.Additional physical formats: Print version:: Real Analysis Lifesaver.DDC classification: 515/.8 Online resources: Click here to access online
Contents:
Preliminaries. Introduction ; Basic math and logic ; Set theory -- Real numbers. Least upper bounds ; The real field ; Complex numbers and Euclidean spaces -- Topology. Bijections ; Countability ; Topological definitions ; Closed and open sets ; Compact sets ; The Heine-Borel Theorem ; Perfect and connected sets -- Sequences. Convergence ; Limits and subsequences ; Cauchy and monotonic sequences ; Subsequential limits ; Special sequences ; Series.
Summary: 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 (3z(Blifesaver(3y (Bcompanion 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 (3z(Bfill in the blanks(3y (Bexercises to help internalize proof techniques Tried and tested in the classroom.
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Includes bibliographical references and index.

Preliminaries. Introduction ; Basic math and logic ; Set theory -- Real numbers. Least upper bounds ; The real field ; Complex numbers and Euclidean spaces -- Topology. Bijections ; Countability ; Topological definitions ; Closed and open sets ; Compact sets ; The Heine-Borel Theorem ; Perfect and connected sets -- Sequences. Convergence ; Limits and subsequences ; Cauchy and monotonic sequences ; Subsequential limits ; Special sequences ; Series.

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 (3z(Blifesaver(3y (Bcompanion 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 (3z(Bfill in the blanks(3y (Bexercises to help internalize proof techniques Tried and tested in the classroom.

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