Begun in Hungary in the nineteenth century, Mathematical Olympiads are now held for high school students throughout the world. They feature problems which, though they require only high school mathematics, seem very difficult because they are unpredictable and have no obvious starting point. This book introduces readers to these delightful and challenging problems and aims to convince them that Olympiads are not just for a select minority. The book contains problems from the British Mathematical Olympiad (BMO) competitions between 1965 and 1996. It includes hints and solutions for each...

Conceived by the author as an introduction to -why the calculus works- (otherwise known as -analysis-), this volume represents a critical reexamination of the infinite processes encountered in elementary mathematics. Part I presents a broad description of the coming parts, and Part II offers a detailed examination of the infinite processes arising in the realm of number--rational and irrational numbers and their representation as infinite decimals. Most of the text is devoted to analysis of specific examples. Part III explores the extent to which the familiar geometric notions of length,...

What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways:...