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An Excursion through Elementary Mathematics, Volume I - Real Numbers and Functions (Paperback, Softcover reprint of the original 1st ed. 2017)
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An Excursion through Elementary Mathematics, Volume I - Real Numbers and Functions (Paperback, Softcover reprint of the original 1st ed. 2017)
Series: Problem Books in Mathematics
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This book provides a comprehensive, in-depth overview of elementary
mathematics as explored in Mathematical Olympiads around the world.
It expands on topics usually encountered in high school and could
even be used as preparation for a first-semester undergraduate
course. This first volume covers Real Numbers, Functions, Real
Analysis, Systems of Equations, Limits and Derivatives, and much
more. As part of a collection, the book differs from other
publications in this field by not being a mere selection of
questions or a set of tips and tricks that applies to specific
problems. It starts from the most basic theoretical principles,
without being either too general or too axiomatic. Examples and
problems are discussed only if they are helpful as applications of
the theory. Propositions are proved in detail and subsequently
applied to Olympic problems or to other problems at the Olympic
level. The book also explores some of the hardest problems
presented at National and International Mathematics Olympiads, as
well as many essential theorems related to the content. An
extensive Appendix offering hints on or full solutions for all
difficult problems rounds out the book.
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