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The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
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Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloaneās Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Describes the arithmetic of modular forms and elliptic curves; self-contained and ideal for both graduate students and professional number theorists.
Set includes revised editions of some issues.
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This publication is intended to be both a directory of secondary schools in the United States and roster or high schools which are accredited by state and regional accrediting agencies. It is the first comprehensive list of secondary schools the Office has issued. From the standpoint of accrediting it is a continuation or the Office's practice of issuing periodically a list or those schools which have been accredited by state and regional accrediting agencies.