The first three editions of H．］．Royden’S Real Analysis have contributed to the education of generation so fm a them atical analysis students．This four the dition of Real Analysispreservesthe goal and general structure of its venerable predecessors——to present the measure theory．integration theory．and functional analysis that a modem analyst needs to know． The book is divided the three parts：Part I treats Lebesgue measure and Lebesgueintegration for functions of a single real variable；Part II treats abstract spaces topological spaces，metric spaces，Banach spaces，and Hilbert spaces；Part III treats integration over general measure spaces．together with the enrichments possessed by the general theory in the presence of topological，algebraic，or dynamical structure． The material in Parts II and III does not formally depend on Part I．However．a careful treatment of Part I provides the student with the opportunity to encounter new concepts in afamiliar setting，which provides a foundation and motivation for the more abstract conceptsdeveloped in the second and third parts．Moreover．the Banach spaces created in Part I．theLp spaces，are one of the most important dasses of Banach spaces．The principal reason forestablishing the completeness of the Lp spaces and the characterization of their dual spacesiS to be able to apply the standard tools of functional analysis in the study of functionals andoperators on these spaces．The creation of these tools is the goal of Part II．

Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

《实变函数论与泛函分析:下册•第2版修订本》第一版在1978年出版。此次修订，是编者在经过两次教学实践的基础上，结合一些学校使用第一版所提出的意见进行的。《实变函数论与泛函分析:下册•第2版修订本》第二版仍分上、下两册出版。上册实变函数，下册泛函分析。本版对初版具体内容处理的技术方面进行了较全面的细致修订。下册内容的变动有：在第六章新增了算子的扩张与膨胀理论一节，对其他一些章节也补充了材料。各章均补充了大量具有一定特色的习题。 《实变函数论与泛函分析:下册•第2版修订本》可作理科数学专业，计算数学专业学生教材和研究生的参考书。 《实变函数论与泛函分析:下册•第2版修订本》下册经王建午副教授初审，江泽坚教授复审，在初审过程中，陈杰教授给予甚大关注。

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.