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...

A book for the eternally curious, Coincidences fuses a professor s understanding of the hidden mathematical skeleton of the universe with the sensibility of a stand-up comedian, making life s big questions accessible and compelling. Each chapter opens with a surprising insight not a mathematic formula, but a common observation. From there, the authors leapfrog over math and anecdote toward profound ideas about nature, art, and music. Coincidences is a book for lovers of puzzles and posers of outlandish questions, lapsed math aficionados and the formula-phobic alike."

Mathematicians do not know in advance if their assertions are true, so they need to verify assertions with rigorous proofs or produce counterexamples, then attempt to salvage the assertions by transforming them into theorems. Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation invites readers to experience this progression of mathematical discovery. Burger's informal, humorous writing style and intriguing puzzles engage readers throughout the learning process. The innovative text offers a discovery-based approach that is ideal.

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.