This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, Euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are more demanding.This text grew out of lectures which the author gave at the N.S.F. Advanced Science Seminar on Algebraic Groups at Bowdoin College in 1968.

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

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.

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 & 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.

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 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.

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

《非线性泛函分析及其应用,第3卷,变分法及最优化》内容简介：自1932年，波兰数学家Banach发表第一部泛函分析专著“Theorie des operations lineaires”以来，这一学科取得了巨大的发展，它在其他领域的应用也是相当成功。如今，数学的很多领域没有了泛函分析恐怕寸步难行，不仅仅在数学方面，在理论物理方面的作用也具有同样的意义，M．Reed和B．Simon的“Methods of Modern MathematicalPhysjcs”在前言中指出：“自1926年以来，物理学的前沿已与日俱增集中于量子力学，以及奠定于量子理论的分支：原子物理、核物理固体物理、基本粒子物理等，而这些分支的中心数学框架就是泛函分析。”

This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."--MATHEMATICAL REVIEWS

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

《线性代数(第2版)(英文影印版)》是Kenneth Hoffman《线性代数》第2版。本版在第1版的基础上作了一些增加和改进,尤其是在典范式和内积空间的讲述上做了较大的改变。作者从线性代数的最基本知识开始讲述了典范型、内积空间、双线性型、复内积空间以及谱理论。书中许多定理的证明非常完整，受到广大数学学者的赞赏，并且非常适合初学者学习理解。对偶空间和张量在《线性代数(第2版)(英文影印版)》同时讲解，这也是《线性代数(第2版)(英文影印版)》的一大特色。

《非交换几何》主要内容：his book is the English version of the French “Geometrie non commutative” published by InterEditions Paris （1990）. After the excellent initial translation by S.K. Berberian, a considerable amount of rewriting was done and many additions made, multiplying by 3.8 the size of the original manuscript. In particular the present text contains several unpublished results.

简明微积分发展史，ISBN：9787535544810，作者：龚升、林立军