Invitation to the Mathematics of Fermat-Wiles

"To decompose a cube into two other cubes, a fourth power, and generally an arbitrary power into two of the same powers above the second power, is an impossible thing and I have certainly found its admirable proof. This narrow margin would not contain it." Scrawled as an aside in the margin of Fermat's copy of Diophantus' Arithmetica lies the original formulation of mathematics' most famous enigma: Fermat's last theorem. For 350 years mathematicians struggled with the theorem until, on the 19th of September 1994, Andrew Wiles presented a proof. Invitation to the Mathematics of Fermat-Wiles collects and expounds diverse mathematical developments that helped lay the foundations for Wiles' proof. This book is a translation from the second edition of the French version. Key Features · Rigorously presents concepts required to get a grasp of Wiles' proof, assuming only modest undergraduate level math. · Sets the math in its historical context. · Contains several themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. · Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem. Invitation to the Mathematics of Fermat-Wiles is accessible without compromising the rigor of its mathematical exposition. It could be used as the basis for special courses on Fermat's last theorem or to provide an undergraduate or graduate level introduction to a wide range of theories (e.g. commutative algebra, field theory, representations of linear groups, algebraic geometry and functions of a complex variable). However, the book is principally aimed at the inquiring and mathematically informed reader who is intrigued by the unraveling of this fascinating puzzle. Yves Hellegouarch studied at the École Normale Supérieure in Paris. He has been teaching at the University of Caen since 1970. In 1972 he wrote a thesis on "Elliptic curves and Fermat's equation".Hellegouarch, Yves is the author of 'Invitation to the Mathematics of Fermat-Wiles' with ISBN 9780123392510 and ISBN 0123392519.