數學
微分几何讲义
Douban
陈省身
/
陈维桓
publishing house:
北京大学出版社
2001
- 10
《微分几何讲义》系统地论述了微分几何的基本知识。全书共八章并两个附录。作者以较大的篇幅,即前三章和第六章介绍了流形、多重线性函数、向量场、外微分、李群和活动标架法等基本知识和工具。在有了上述宽广而坚实的基础之后,论述微分几何的核心问题,即联络、黎曼几何以及曲面论等。第七章复流形,既是当前十分活跃的研究领域,也是第一作者研究成果卓著的领域之一,包含有作者独到的见解和简捷的方法。第八章Finsler几何是本书第二版新增的一章,它是第一作者近来提倡的研究课题,其中Chefn联络具有突出的性质,使得黎曼几何成为Finsler几何的特殊情形。最后两个附录,介绍了大范围曲线论和曲面论,以及对微分几何与理论物理关系的论述,为这两个活跃的前沿领域提出了不少进一步的研究课题。
Mathematical Mysteries
Douban
Calvin C. Clawson
publishing house:
Basic Books
1999
An eloquent, utterly charming guide to discovering the interconnectedness of mathematics Why seemingly unrelated mathematical truths are connected in simple and beautiful equations continues to stump even mathematicians. This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line. While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.