For sophomore-level and above courses in Mathematical Methods, Mathematics for Economists. An introduction to those parts of mathematical analysis and linear algebra which are most important for economists.

Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'.
Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, fourier methods and the FFT, linear programming, and computer graphics.
Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.
Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

This revised and updated fourth edition designed for upper division courses in linear algebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linear algebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves.

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete R n setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

This edition differs from the third mainly in the inclusion of additional problems, as well as a complete update of the Suggested Reading, together with some changes of exposition, mainly in Chapters 5 and 20.

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, "An Introduction to Mathematical Analysis for Economic Theory and Econometrics" takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. It begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers. It takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem. It focuses on examples from econometrics to explain topics in measure theory.

This book gives architects and designers a working knowledge of architectural acoustics. The control of sound is important not only in obvious places like concert halls, but also in offices where privacy is essential. In Architectural Acoustics , six experienced consultants present basic acoustical principles; specific materials, methods, and techniques for controlling sound in and around buildings; and some recent innovations in acoustical research.

Volume II of "Calculus", contained in this work, presents multi-variable calculus and linear algebra, with applications to differential equations and probability. Volume I, sold separately, presents one-variable calculus with an introduction to linear algebra.

《数学分析原理》(英文版)(第3版)涵盖了高等微积分学的丰富内容，最精彩的部分集中在基础拓扑结构、函数项序列与级数、多变量函数以及微分形式的积分等章节。第3版经过增删与修订，更加符合学生的阅读习惯与思考方式。《数学分析原理》(英文版)(第3版)内容相当精练，结构简单明了，这也是作者著作的一大特色。与其说这是一部教科书，不如说这是一部字典。

The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.
This text is part of the Walter Rudin Student Series in Advanced Mathematics.

"…the best book to learn matrix and related ideas…statisticians, econometricians, computer scientists, engineers, and psychometricians will find this extremely useful." (Journal of Statistical Computation and Simulation, March 2006)

This two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books.</P>
The first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor. </P>
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WINNER OF THE 2005 DEGROOT PRIZE! This book is for people who want to learn probability and statistics quickly. It brings together many of the main ideas in modern statistics in one place. The book is suitable for students and researchers in statistics, computer science, data mining and machine learning. This book covers a much wider range of topics than a typical introductory text on mathematical statistics. It includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses. The reader is assumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. The text can be used at the advanced undergraduate and graduate level.

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

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．

This book is intended as a textbook for a first-year Ph. D. course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.

Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.