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A Readable Introduction to Real Mathematics (Paperback, 2nd ed. 2018)
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A Readable Introduction to Real Mathematics (Paperback, 2nd ed. 2018)
Series: Undergraduate Texts in Mathematics
Expected to ship within 10 - 15 working days
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Designed for an undergraduate course or for independent study, this
text presents sophisticated mathematical ideas in an elementary and
friendly fashion. The fundamental purpose of this book is to teach
mathematical thinking while conveying the beauty and elegance of
mathematics. The book contains a large number of exercises of
varying difficulty, some of which are designed to help reinforce
basic concepts and others of which will challenge virtually all
readers. The sole prerequisite for reading this text is high school
algebra. Topics covered include: * mathematical induction * modular
arithmetic * the Fundamental Theorem of Arithmetic * Fermat's
Little Theorem * RSA encryption * the Euclidean algorithm *
rational and irrational numbers * complex numbers * cardinality *
Euclidean plane geometry * constructibility (including a proof that
an angle of 60 degrees cannot be trisected with a straightedge and
compass)* infinite series * higher dimensional spaces. This
textbook is suitable for a wide variety of courses and for a broad
range of students of mathematics and other subjects. Mathematically
inclined senior high school students will also be able to read this
book. From the reviews of the first edition: "It is carefully
written in a precise but readable and engaging style... I
thoroughly enjoyed reading this recent addition to the Springer
Undergraduate Texts in Mathematics series and commend this clear,
well-organised, unfussy text to its target audiences." (Nick Lord,
The Mathematical Gazette, Vol. 100 (547), 2016) "The book is an
introduction to real mathematics and is very readable. ... The book
is indeed a joy to read, and would be an excellent text for an
'appreciation of mathematics' course, among other possibilities."
(G.A. Heuer, Mathematical Reviews, February, 2015) "Many a
benighted book misguidedly addresses the need [to teach
mathematical thinking] by framing reasoning, or narrowly, proof,
not as pervasive modality but somehow as itself an autonomous
mathematical subject. Fortunately, the present book gets it
right.... [presenting] well-chosen, basic, conceptual mathematics,
suitably accessible after a K-12 education, in a detailed,
self-conscious way that emphasizes methodology alongside content
and crucially leads to an ultimate clear payoff. ... Summing Up:
Recommended. Lower-division undergraduates and two-year technical
program students; general readers." (D.V. Feldman, Choice, Vol. 52
(6), February, 2015)
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