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标签:拓扑学
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拓扑学
本书作者在拓扑学领域享有盛誉。 本书分为两个独立的部分;第一部分普通拓扑学,讲述点集拓扑学的内容;前4章作为拓扑学的引论,介绍作为核心题材的集合论、拓扑空间。连通性、紧性以及可数性和分离性公理;后4章是补充题材;第二部分代数拓扑学,讲述与拓扑学核心题材相关的主题,其中包括基本群和覆盖空间及其应用。 本书最大的特点在于对理论的清晰阐述和严谨证明,力求让读者能够充分理解。对于疑难的推理证明,将其分解为简化的步骤,不给读者留下疑惑。此外,书中还提供了大量练习,可以巩固加深学习的效果。严格的论证,清晰的条理、丰富的实例,让深奥的拓扑学变得轻松易学。 -
蚁迹寻踪及其他数学探索
书中讨论了“为什么某些用分式定义的序列只产生整数”,“怎样才能让两人通过电话玩扑克,还要保证对手不受欺骗”等许多有趣的数学问题。 -
基础拓扑和几何讲义
《基础拓扑和几何讲义》内容为:At the present time, the average undergraduate mathematics major findsmathematics heavily compartmentalized. After the calculus, he takes a coursein analysis and a course in algebra. Depending upon his interests (or those ofhis department), he takes courses in special topics. If he is exposed to topology,it is usually straightforward point set topology; if he is exposed to geometry, it is usually classical differential geometry. -
微分几何与拓扑学简明教程
由A.C.米先柯和A.T.福明柯编著的《微分几何与拓扑学简明教程》是俄 罗斯数学教材选译系列之一,是微分几何教程的简明阐述,在大学数学系两 个学期中讲授。内容包含:一般拓扑,非线性坐标系,光滑流形的理论,曲 线论和曲面论,变换群,张量分析和黎曼几何,积分法和同调论,曲面的基 本群,黎曼几何中的变分原理。叙述中用大量的例子说明并附有习题,常有 补充的材料。 《微分几何与拓扑学简明教程》适合数学、物理及相关专业的高年级本 科生、研究生、高校教师和研究人员参考使用。 -
代数拓扑的微分形式
代数拓扑的微分形式,ISBN:9787506201124,作者:(美)Raoul Bott,(美)Loring W.Tu著 -
Algebraic Topology
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.
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