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1. 1. Advanced Problems In Mathematics

   Preparing for University

   

   A rigorous problem-based companion that develops advanced problem-solving skills through a carefully chosen collection of challenging exercises across algebra, analysis, number theory, geometry and inequalities; each topic is introduced with strategy notes and worked examples, and many problems are accompanied by hints and full solutions that explain standard and creative methods. The book emphasizes methods useful in competition and examination settings (particularly STEP-style questions), teaches how to approach unfamiliar problems, and highlights common pitfalls and useful heuristics such as invariants, extremal arguments and clever substitutions. Suitable for motivated undergraduates and students preparing for mathematical Olympiads or entrance exams, it aims both to build technique and to deepen mathematical understanding rather than just present answers.

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