The Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen- tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task. Thus transcendental numbers are an enigmatic species of number: We know they are all around us and yet it requires enormous effort to catch one. More often than not, they slip through our fingers and dissappear back into the dense jungle of numbers. Here we will venture to tame a few of these incredible creatures. In the pages ahead we offer an approach to transcendence that...

Diophantine analysis, an area of number theory that helps to discover hidden treasures and truths within the numbers by exploring rational numbers, comprises two different but interconnected domains - diophantine approximation and diophantine equations. This book presents the fundamental ideas and theorems from diophantine approximation.

The Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen- tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task. Thus transcendental numbers are an enigmatic species of number: We know they are all around us and yet it requires enormous effort to catch one. More often than not, they slip through our fingers and dissappear back into the dense jungle of numbers. Here we will venture to tame a few of these incredible creatures. In the pages ahead we offer an approach to transcendence that...

'The Heart of Mathematics' succeeds at reaching non-math, non-science-oriented majors and encouraging them to discover the mathematics inherent in the world around them.