This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

Some of the most interesting problems set to solid state physicists, often on the borderline of other disciplines (mechanical engineering, chemistry, biology, hydrodynamics, computer science), have their origin in the interplay of matter and randomness. This field has seen the emergence of the most remarkable successes of the last few years which have sometimes opened unexpected new avenues - for example the theory of spin-glasses with its impact on various domains such as computer assisted design, the model for brain and the development of simulations on special purpose computers. This last success has been one of the main motivations for organizing another summer school devoted to the problems which result from the interplay of matter and randomness. All the courses were given by specialists in their particular field and the subjects covered included percolation and random media, aggregation, localization (electrons and waves), pattern selection, spin-glasses, and macroscopic quantum effects. Emphasis was placed on novel methods and the controversial open questions that continue to make the field lively and competitive.

This unique book addresses trends such as vitalism, neo-Kantianism, existentialism, Marxism and feminism, and provides concise biographies of the influential philosophers who shaped these movements, including entries on over ninety thinkers. Offers discussion and cross-referencing of ideas and figures Provides Appendix on the distinctive nature of French academic culture

In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.