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When you finish a problem—or finally look at the answer—do not just check if you were right. Analyze Geoff Smith’s elegant solutions. Note how he starts his proofs and look for ways to optimize your own mathematical handwriting. Maintain a Problem Journal
Applying the AM-GM (Arithmetic Mean-Geometric Mean) inequality and the Cauchy-Schwarz inequality.
Even if you solve a problem correctly, read Geoff Smith’s solution. You will often discover a more elegant method, a shortcut, or a broader generalization that enhances your mathematical toolkit.
: Divisibility, modular arithmetic, and Diophantine equations.
Solving polynomial equations where the solutions must be integers. 2. Geometry
Geoff Smith’s is a foundational text in the UK Mathematics Trust (UKMT) Handbooks series , specifically designed to transition students from standard school curricula to the rigorous proofs required for competition mathematics. Core Purpose and Audience
To succeed in the Mathematical Olympiad, students should:
Whether you are a student dreaming of an IMO medal, a teacher looking for a structured course, or a self‑learner who enjoys a good mathematical challenge, deserves a place on your bookshelf. As its author has shown through decades of service to mathematics outreach, the journey from struggling with a problem to discovering an elegant solution is one of the most rewarding experiences in education – and this book is an ideal guide for that journey.
