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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
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
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