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Studying Mathematics - The Beauty, the Toil and the Method (Paperback, Softcover reprint of the original 1st ed. 2018)
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Studying Mathematics - The Beauty, the Toil and the Method (Paperback, Softcover reprint of the original 1st ed. 2018)
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This book is dedicated to preparing prospective college students
for the study of mathematics. It can be used at the end of high
school or during the first year of college, for personal study or
for introductory courses. It aims to set a meeting between two
relatives who rarely speak to each other: the Mathematics of
Beauty, which shows up in some popular books and films, and the
Mathematics of Toil, which is widely known. Toil can be overcome
through an appropriate method of work. Beauty will be found in the
achievement of a way of thinking. The first part concerns the
mathematical language: the expressions "for all", "there exists",
"implies", "is false", ...; what is a proof by contradiction; how
to use indices, sums, induction. The second part tackles specific
difficulties: to study a definition, to understand an idea and
apply it, to fix a slightly wrong argument, to discuss suggestions,
to explain a proof. The third part presents customary techniques
and points of view in college mathematics. The reader can choose
one of three difficulty levels (A, B, C).
General
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