A collection of expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held at Boston University. The purpose of the conference, and indeed of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to show, at long last, that Fermats Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermats Last Theorem, the volume concludes by reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Indispensable for students and professional mathematicians alike.

In "Programming VB .NET: A Guide for Experienced Programmers," authors Gary Cornell and Jonathan Morrison carefully explain the exciting features of Visual Basic .NET. Since VB .NET is, for all practical purposes, a whole new language even for the most experienced Visual Basic programmers, developers need to think differently about many familiar topics. Cornell and Morrison are there to help you with careful discussions of each topic.

Cornell and Morrison write from the point of view of the experienced programmer, with constant references to the changes from earlier versions of VB. Developers learn how to use VB .NET for database programming through ADO.NET and web programming through ASP.NET. After reading "Programming VB .NET: A Guide for Experienced Programmers," developers will have a firm grasp of the exciting VB .NET language and its uses in creating powerful .NET applications. What you'll learn Who this book is for

All experienced programmers wishing to take advantage of the amazing powers of VB .NET will benefit from this book's careful treatment of fundamental topics, including inheritance, interfaces, and exception handling, as well as all the powerful newer features, such as stream-based I/O and true multithreading.

This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

Build Bulletproof Programs for Windows and the Internet!

Visual Basic 6 has a lot to offer, from its new file handling objects and advanced Internet programming capabilities to its new database features. Learn to build your own commercial-quality application -- not just toy apps -- using this comprehensive, hands-on tutorial from expert author Gary Cornell, winner of the prestigious Readers Choice Award from Visual Basic Programmers journal. This best-selling guide for the beginning and intermediate programmer has been thoroughly revised and updated to cover the newest version of the worlds #1 visual programming tool.

Using modular, step-by-step instructions, you will:

• Progress from elementary programming skills to marketable expertise.
• Learn object-oriented programming.
• Create VB Forms for use in Internet Explorer.
• Discover Visual Basics newest database features.
• Create sophisticated event-driven programs.
• Build you own special-purpose Internet Browser.
• Use the Visual Basic environment to develop programs.
• Discover how to distribute your programs.
• Unleash the power of graphics programming , OLE, and ActiveX.