As a mathematics undergraduate at a British university, perhaps I'm in a position to make some recommendations. At school I read a couple of books which really spurred my interest in mathematics and motivated me to take it as a major at university.
My first recommendation, "How to Solve It, Polya", is a cult classic. It introduces new methods of thinking about mathematical problems and is accessible for someone with just basic high school mathematics. A strikingly powerful piece of literature.
"The Art and Craft of Problem Solving, Zeitz" is a more modern book. Zeitz has trained several American IMO (International Mathematical Olympiad) teams. It introduces both approaches to solving difficult mathematical problems and the machinery required to do so. Aside from that, it lists several techniques of improving your mathematical ability from a variety of angles (word games and so forth...)
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As a mathematics undergraduate at a British university, perhaps I'm in a position to make some recommendations. At school I read a couple of books which really spurred my interest in mathematics and motivated me to take it as a major at university.
My first recommendation, "How to Solve It, Polya", is a cult classic. It introduces new methods of thinking about mathematical problems and is accessible for someone with just basic high school mathematics. A strikingly powerful piece of literature.
"The Art and Craft of Problem Solving, Zeitz" is a more modern book. Zeitz has trained several American IMO (International Mathematical Olympiad) teams. It introduces both approaches to solving difficult mathematical problems and the machinery required to do so. Aside from that, it lists several techniques of improving your mathematical ability from a variety of angles (word games and so forth...)
Hope you enjoy. Best of luck!