A Concrete Introduction to Real Analysis
A Concrete Introduction to Real Analysis (Pure and Applied Mathematics) Robert Carlson,
Publisher: Chapman & Hall/CRC
ISBN: 1584886544
DDC: 515
Edition: Hardcover; 2006-05-30
Summary:
Most volumes in analysis plunge students into a challenging new
mathematical environment, replete with axioms, powerful abstractions,
and an overriding emphasis on formal proofs. This can lead even
students with a solid mathematical aptitude to often feel bewildered
and discouraged by the theoretical treatment. Avoiding unnecessary
abstractions to provide an accessible presentation of the material, A
Concrete Introduction to Real Analysis supplies the crucial
transition from a calculations-focused treatment of mathematics to a
proof-centered approach. Drawing from the history of mathematics and
practical applications, this volume uses problems emerging from
calculus to introduce themes of estimation, approximation, and
convergence. The book covers discrete calculus, selected area
computations, Taylor's theorem, infinite sequences and series,
limits, continuity and differentiability of functions, the Riemann
integral, and much more. It contains a large collection of examples
and exercises, ranging from simple problems that allow students to
check their understanding of the concepts to challenging problems
that develop new material. Providing a solid foundation in analysis,
A Concrete Introduction to Real Analysis demonstrates that the
mathematical treatments described in the text will be valuable both
for students planning to study more analysis and for those who are
less inclined to take another analysis class.
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