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Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.
Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials,...
In 1994, Democrats were reeling from losing control of the House of Representatives for the first time in 40 years. Returning members entered the new, 104th Congress powerless but the persona of the architect of that Republican takeover offered hope that their time in the wilderness would be brief. Speaker Newt Gingrich was a visionary but often accompanied that quality with brazen legislative initiatives and instinctive remarks that often brought turbulence to his caucus. Many of his “majority makers” had extreme views which they often expressed in eyebrow raising terms. The approval of the new Congress tanked and a 1996 government shutdown was fuel to the fire. Minority Leader Richard Gephardt made a ferocious drive to recapture the chamber for his Democrats that November and Gingrich became a leading, involuntary character in many of the candidates’ campaigns. While the effort to regain control fell short, the many contests profiled in this book offer a fascinating look at overreach and rhetoric out of touch with much of America.
Historically, when sweeping policy changes or legislation of indelible consequence are signed into law, Presidents receive the credit. There is a good reason for that. Without the Chief Executive putting his pen to paper, these advancements would have nary a chance of becoming reality. In most cases, though, a President’s signature is simply the culmination of a long fight to make an idea or actual proposal a reality. In fact, quite often it is members of Congress who nurture proposals from inception to the President’s desk. Like a train leaving its first station, the legislative process often starts with a handful of people on board until slowly, a few more passengers hop on at each stop and before long, there is a full car with people standing in the aisles. Often times, a bill becoming a law is no different.
Barack Obama made history when he became president in 2008, but his election was made possible partially by the hard work of the many African American politicians who came before him. Even before the abolition of slavery, African Americans held political office, although they have not had an easy time of it. This historical overview of black politicians in the United States enhances classroom learning by bringing to light little-known facts, supported by primary sources and a timeline of important events.
Accomplishments, associations and anecdotes - that is what this book encompasses. Previous volumes of Statesmen and Mischief Makers have portrayed members of Congress from the eras of John F. Kennedy through Ronald Reagan whose stories were the subject of fantastic tidbits. This volume is no exception but the emphasis is on the unknown men - and a few women – who were either at the center of now famous laws or had high-profile roles in historic events. It depicts those with close proximity to those who appeared on a national ticket, either as Congressional friends or opponents. These individuals never achieved the fame or only had a mere 15 minutes of it, which suited them fine. Yet their ...
Experimental Mathematics is a recently structured field of Mathematics that uses a computer and advanced computing technology as tools to perform experiments such as analysis of examples, testing of new ideas, and the search of patterns.
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