A Transition to Proof: An Introduction to Advanced Mathematics
describes writing proofs as a creative process. There is a lot that
goes into creating a mathematical proof before writing it. Ample
discussion of how to figure out the "nuts and bolts'" of the proof
takes place: thought processes, scratch work and ways to attack
problems. Readers will learn not just how to write mathematics but
also how to do mathematics. They will then learn to communicate
mathematics effectively. The text emphasizes the creativity,
intuition, and correct mathematical exposition as it prepares
students for courses beyond the calculus sequence. The author urges
readers to work to define their mathematical voices. This is done
with style tips and strict "mathematical do's and don'ts", which
are presented in eye-catching "text-boxes" throughout the text. The
end result enables readers to fully understand the fundamentals of
proof. Features: The text is aimed at transition courses preparing
students to take analysis Promotes creativity, intuition, and
accuracy in exposition The language of proof is established in the
first two chapters, which cover logic and set theory Includes
chapters on cardinality and introductory topology
General
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