Portal through Mathematics: Journey to Advanced Thinking By: Oleg A Ivanov

Author: Oleg a Ivanov

A collection of interesting, and frequently surprising, puzzles and problems on topics mostly related to secondary school mathematics. The book is organised into 29 themes, each a topic from algebra, geometry, or calculus, and each launched from an opening puzzle or problem. Excursions are provided into number theory, solid geometry, physics, and combinatorics. Requiring minimum background knowledge, the book can be followed by readers at all levels. Part I combines intriguing mathematical facts with the most striking, yet accessible, proofs. The other two parts are dedicated to problem solving: Part II involving only concepts and facts found in the high school curriculum, and Part III introducing new concepts and ideas of proof. In total, 150 problems and solutions are provided in the text. With this book, readers are introduced to the rich world between secondary school and university mathematics through a wonderful collection of mathematical titbits designed to intrigue, propel, and delight.

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