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"Mathematical olympiads" as a book category covers collections and guides focused on high-level problem solving for math competitions (IMO, national and regional olympiads, and preparatory contests). These books present challenging problems across algebra, number theory, combinatorics, and geometry together with detailed solutions, strategies, heuristics, and proof techniques; many include past contest papers, annotated solutions, training plans, and topic primers to build the necessary theory and intuition. Aimed at motivated students, coaches, and hobbyists, they balance rigorous exposition with problem-based learning, often emphasizing creative reasoning, common solution patterns, and methods for constructing and writing clear proofs. Titles range from elementary introductions for beginners to advanced compilations and research-style treatments for experienced competitors.

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