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A First Course in Modular Forms
This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
Diamond Grill
None
Modular Forms and Fermat’s Last Theorem
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 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 Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermat's 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.
Number Theory, Analysis and Geometry
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.
Essentials of Artificial Intelligence
Since its publication, Essentials of Artificial Intelligence has been adopted at numerous universities and colleges offering introductory AI courses at the graduate and undergraduate levels. Based on the author's course at Stanford University, the book is an integrated, cohesive introduction to the field. The author has a fresh, entertaining writing style that combines clear presentations with humor and AI anecdotes. At the same time, as an active AI researcher, he presents the material authoritatively and with insight that reflects a contemporary, first hand understanding of the field. Pedagogically designed, this book offers a range of exercises and examples.
Biscuits of Number Theory
An anthology of articles designed to supplement a first course in number theory.
Arithmetic and Geometry
The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
The Collected Works
The Collected Works of Burt L. Standish and Gilbert Patten presents a formidable exploration into the heart of early 20th-century American literature, showcasing a diverse array of styles and themes. Rich in its depiction of heroism, adventure, and the pursuit of justice, this anthology spans the evolution of dime novels to serialized narratives that captivated readers across the nation. The collection stands out for its inclusion of some of the most memorable exploits of Frank Merriwell and the Barbour family, characters who exemplified the era's ideals of manliness and moral integrity. Each piece serves as a cultural artifact, offering insights into the American psyche during a period of r...
Selling to the Government
Learn the crucial ins and outs of the world’s largest market The U.S government market represents the largest single market—anywhere. Government contract tracking firm Onvia estimates that government business—federal, state, local, and education—represents better than 40 percent of the nation’s GDP. While anyone can play in this market, only those with the right preparation can win. Selling to the Government offers real-world advice for successful entry into the biggest market anywhere. Get proven approaches, strategies, tactics, and tools to make your business stand out, build relationships, understand procedures, and win high-stakes contracts. • Every year thousands of companie...
