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In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the author’s concern for the student audience through emphasis upon motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles; this text provides a foundation for the comprehension and exploration of modern work on singularities.   ---   In the first chapter one finds many special curves with very attractive geometric presentations – the wealth of illustrations is a distinctive characteristic of this book – and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book – and how else could it be with the first author – is the chapter on the resolution of singularities (always over the complex numbers).  (…) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews).

Curves, Algebraic. --- Curves, Plane. --- Geometry, Projective. --- Curves, Algebraic --- Curves, Plane --- Geometry, Projective --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Projective geometry --- Higher plane curves --- Plane curves --- Algebraic curves --- Mathematics. --- Algebraic geometry. --- Commutative algebra. --- Commutative rings. --- Algebraic topology. --- Algebraic Geometry. --- Commutative Rings and Algebras. --- Algebraic Topology. --- Geometry, Modern --- Algebraic varieties --- Geometry, algebraic. --- Algebra. --- Topology --- Mathematical analysis --- Algebraic geometry --- Rings (Algebra) --- Algebra

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Algebra --- Geometry --- Analytical spaces --- 512.64 --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear and multilinear algebra. Matrix theory

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Algebraic geometry --- Curves, Algebraic --- Curves, Plane --- Geometry, projective

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Felix Hausdorff is a singular phenomenon in the history of science. As a mathematician, he played a major role in shaping the development of modern mathematics in the 20th century. He founded general topology as an independent mathematical discipline, while enriching set theory with a number of fundamental concepts and results. His general approach to measure and dimension led to profound developments in numerous mathematical disciplines, and today Hausdorff dimension plays a central role in fractal theory with its many fascinating applications by means of computer graphics. Hausdorff ’s remarkable mathematical versatility is reflected in his published work: today, no fewer than thirteen concepts, theorems and procedures carry his name. Yet he was not only a creative mathematician – Hausdorff was also an original philosophical thinker, a poet, essayist and man of letters. Under the pseudonym Paul Mongré, he published a volume of aphorisms, an epistemological study, a book of poetry, an oft-performed play, and a number of notable essays in leading literary journals. As a Jew, Felix Hausdorff was increasingly persecuted and humiliated under the National Socialist dictatorship. When deportation to a concentration camp was imminent, he, along with his wife and sister-in law, decided to take their own lives. This book will be of interest to historians and mathematicians already fascinated by the rich life of Felix Hausdorff, as well as to those readers who wish to immerse themselves in the intricate web of intellectual and political transformations during this pivotal period in European history.

Mathematics. --- History. --- Science --- Sociology --- History of Mathematical Sciences. --- History of Science. --- Biographical Research. --- Biographical methods.

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