Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable". His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fa...(展开全部)

'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' - "The Guardian". In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics wa...(展开全部)

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detaile...(展开全部)

Praise for William Dunham s Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments." Ivars Peterson Author, The Mathematical Tourist Mathemat...(展开全部)

Praise for William Dunhams Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments." —Ivars Peterson Author, The Mathematical Tourist Mathemat...(展开全部)

This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance ...(展开全部)

雷蒙德•斯穆里安生于1919年，至今年届九旬。他是世界著名的数学家、逻辑学家、哲学家，还是一个钢琴演奏师，和舞台魔术师。他先后在芝加哥大学的罗斯福学院教授钢琴，在达特茅斯大学教授数学，在普林斯顿大学，在印第安那大学，在纽约城市大学的雷曼学院和研究生中心教授哲学和逻辑，后来又回到印第安那大学，应聘为奥斯卡•尤因哲学教授，最后在那里荣誉退休。他分别以数理逻辑、集合论、可计算函数、数学游戏和逻辑谜题以及东方哲学为题撰写了大量的研究文章，他还撰写了二十三本书，其中六本是学术专著，十七本是通俗著作。