PREPARATION FOR MATHEMATICS OLYMPIADS FOR UNIVERSITY STUDENTS
Keywords:
Cauchy-Buniakowski inequality, fixed point, idempotent matrices, Sylvester rank inequality, sequence, Darboux sum, Bolzano-Weierstrass theorem, limit point, prime number, field, invertible, pigeonhole principle, Cayley-Hamilton theorem, characteristic polynomial, eigenvalues, algebraic closure, continuous function, Euclidean plane, uncountable set, neighbourhood, injective, surjective, bijective, simple graph, planar graph, subgraph, Kuratowski’s Theorem, Euler’s formula, metric space.Abstract
This article presents a sample mock exam to prepare for Mathematical Olympiads. It presents complex problems and their solutions from fields such as algebra, mathematical analysis, topology, combinatorics, number theory. Necessary for solving given problems, important theorems and affirmations are given. Modern and unusual methods for solving mathematical problems are described. For each problem, a marking scheme is also given that complies with the requirements of International Mathematical Olympiads.
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