The quadrivium—the classical curriculum—comprises the four liberal arts of number, geometry, music, and cosmology. It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the...(展开全部)

The quadrivium—the classical curriculum—comprises the four liberal arts of number, geometry, music, and cosmology. It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the...(展开全部)

For two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right approach? Or was the right approach still something else, perhaps transformation gr...(展开全部)

This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of thi...(展开全部)

This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of thi...(展开全部)

Each of the seven liberal arts -grammar, rhetoric, dialectic, arithmetic, music, geometry and astronomy arts is discussed in an individual essay written by a specialist in the field. These essays examine the establishment of the medieval concept of the arts in the post-classical writings of the Latin encyclopedists, briefly treat their history from the eighth through the Twelft...(展开全部)

Each of the seven liberal arts -grammar, rhetoric, dialectic, arithmetic, music, geometry and astronomy arts is discussed in an individual essay written by a specialist in the field. These essays examine the establishment of the medieval concept of the arts in the post-classical writings of the Latin encyclopedists, briefly treat their history from the eighth through the Twelft...(展开全部)

The purpose of this book is to describe the classical problems in additive number theory, and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools to attack these problems. This book is intended for students who want to learn additive number theory, not for experts who already know it. The prerequisites for this book are un...(展开全部)