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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 third and last volume covers Counting, Generating
Functions, Graph Theory, Number Theory, Complex Numbers,
Polynomials, 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.
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 second volume covers Plane Geometry, Trigonometry,
Space Geometry, Vectors in the Plane, Solids 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.
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 third and last volume covers Counting, Generating
Functions, Graph Theory, Number Theory, Complex Numbers,
Polynomials, 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.
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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