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Differential Geometry
This book is an introduction to modern differential geometry. The authors begin with the necessary tools from analysis and topology, including Sard's theorem, de Rham cohomology, calculus on manifolds, and a degree theory. The general theory is illustrated and expanded using the examples of curves and surfaces. In particular, the book contains the classical local and global theory of surfaces, including the fundamental forms, curvature, the Gauss-Bonnet formula, geodesics, and minimal surfaces. -
Convex Optimization Theory
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虚数i的奥秘
本书系统全面地介绍了虚数i的有关知识,循序渐进地讲述了数的诞生到复数的应用。叙述浅显易懂,可读性强,适合于一般数学爱好者,尤其是中学生阅读。 -
Probability and Statistics (3rd Edition)
Probability & Statistics was written for a one or two semester probability and statistics course offered primarily at four-year institutions and taken mostly by sophomore and junior level students, majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus. The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a new chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), expanded coverage of residual analysis in linear models, and more examples using real data. -
进位制与数学游戏
李友耕所著的《进位制与数学游戏(普及版)》在较系统、全面论述进位制知识的基础上,分别介绍了涂色游戏、猜测游戏、演变游戏、火柴游戏、配对游戏、戥秤称珠游戏、天平称珠游戏以及砝码、链条、链环等游戏的玩法及进位制知识在其中的应用原理。本书集趣味性、知识性与科学性于一体,奇妙严密,通而不俗,充分展示数学思维之美妙与深刻。 《进位制与数学游戏(普及版)》读者主要为数学研究人员、数学专业的大学生、爱好数学的中学生以及对数学感兴趣的大众读者。 -
D-Modules, Perverse Sheaves, and Representation Theory
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.