The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the...

This self-contained text offers an elementary introduction to partial differential equations (pdes), primarily focusing on linear equations, but also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of pdes...

In the first part, the book investigates the current features of...

The Great Depression of the 1930s gave birth to a branch of economics that in 1933 Ragnar Frisch christened macroeconomics. Over the decades that followed up to the present, the interactions of economic events, economic policy, and macroeconomic theory have created a fascinating story integral to the life and politics of national economies...

This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal...

Content preparation is an integral part of the usability equation: it answers the question of what information is needed for effective decision making. Once content preparation has been established, the question "how to present what" can be answered. Content Preparation Guidelines for the Web and Information Appliances:...

Weapons, vehicles, tools, buildings, trees, plants, walls, ceilings, and floors-these items may seem secondary to the game environment, but they are integral parts of the game and they all need to be created. Maya Studio Projects: Game Environments and...

There is no question that the Web has become an integral part of modern life for people around the world, connecting us to each other and to seemingly infinite portals of information in real time. In the era of Web 2.0, barriers to participation have been lowered further and further, and we’ve seen the birth of myriad new people to...