• Mathematics

Advanced Mathematical Methods


Author: Adam Ostaszewski
Publisher: Cambridge University Press
ISBN: 9780521289641
Category: Mathematics
Page: 545
View: 6451
Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

    • Business & Economics

Mathematics in Economics

Models and Methods
Author: Adam Ostaszewski
Publisher: Wiley-Blackwell
ISBN: 9780631180562
Category: Business & Economics
Page: 532
View: 6459
A valuable guide to the mathematical apparatus that underlies so much of modern economics. The approach to mathematics is rigorous and the mathematical techniques are always presented in the context of the economics problem they are used to solve. Students can gain insight into, and familiarity with, the mathematical models and methods involved in the transition from 'phenomenon' to quantitative statement.

    • Business & Economics

A First Course in Optimization Theory


Author: Rangarajan K. Sundaram
Publisher: Cambridge University Press
ISBN: 1139643150
Category: Business & Economics
Page: N.A
View: 2312
This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

    • Business & Economics

Mathematical Methods and Models for Economists


Author: Angel de la Fuente
Publisher: Cambridge University Press
ISBN: 9780521585293
Category: Business & Economics
Page: 835
View: 4443
A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.

    • Elections

Mathematics of Social Choice

Voting, Compensation, and Division
Author: Christoph Bo”rgers
Publisher: SIAM
ISBN: 0898717620
Category: Elections
Page: 245
View: 650
Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

    • Business & Economics

How Economics Became a Mathematical Science


Author: E. Roy Weintraub
Publisher: Duke University Press
ISBN: 0822383802
Category: Business & Economics
Page: 328
View: 3172
In How Economics Became a Mathematical Science E. Roy Weintraub traces the history of economics through the prism of the history of mathematics in the twentieth century. As mathematics has evolved, so has the image of mathematics, explains Weintraub, such as ideas about the standards for accepting proof, the meaning of rigor, and the nature of the mathematical enterprise itself. He also shows how economics itself has been shaped by economists’ changing images of mathematics. Whereas others have viewed economics as autonomous, Weintraub presents a different picture, one in which changes in mathematics—both within the body of knowledge that constitutes mathematics and in how it is thought of as a discipline and as a type of knowledge—have been intertwined with the evolution of economic thought. Weintraub begins his account with Cambridge University, the intellectual birthplace of modern economics, and examines specifically Alfred Marshall and the Mathematical Tripos examinations—tests in mathematics that were required of all who wished to study economics at Cambridge. He proceeds to interrogate the idea of a rigorous mathematical economics through the connections between particular mathematical economists and mathematicians in each of the decades of the first half of the twentieth century, and thus describes how the mathematical issues of formalism and axiomatization have shaped economics. Finally, How Economics Became a Mathematical Science reconstructs the career of the economist Sidney Weintraub, whose relationship to mathematics is viewed through his relationships with his mathematician brother, Hal, and his mathematician-economist son, the book’s author.

    • Business & Economics

Mathematics for Economics


Author: Michael Hoy,John Livernois,Chris McKenna,Ray Rees,Thanasis Stengos
Publisher: MIT Press
ISBN: 026229480X
Category: Business & Economics
Page: 976
View: 9027
This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analyses. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. The only prerequisite is high school algebra, but the book goes on to cover all the mathematics needed for undergraduate economics. It is also a useful reference for graduate students. After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. To develop the student's problem-solving skills, the book works through a large number of examples and economic applications. This streamlined third edition offers an array of new and updated examples. Additionally, lengthier proofs and examples are provided on the book's website. The book and the web material are cross-referenced in the text. A student solutions manual is available, and instructors can access online instructor's material that includes solutions and PowerPoint slides. Visit http://mitpress.mit.edu/math_econ3 for complete details.

    • Mathematics

Calculus: Concepts and Methods


Author: Ken Binmore,Joan Davies
Publisher: Cambridge University Press
ISBN: 1139643622
Category: Mathematics
Page: N.A
View: 8198
The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

    • Mathematics

Mathematical Analysis for Economists


Author: R. G. D. Allen
Publisher: READ BOOKS
ISBN: 9781443725224
Category: Mathematics
Page: 572
View: 2742
MATHEMATICAL ANALYSIS FOR ECONOMISTS by R. G. D. ALLEN. Originally published in 1937. FOREWORD; THIS book, which is based on a series of lectures given at the London School of Economics annually since 1931, aims at providing a course of pure mathematics developed in the directions most useful to students of economics. At each stage the mathematical methods described are used in the elucidation of problems of economic theory. Illustrative examples are added to all chapters and it is hoped that the reader, in solving them, will become familiar with the mathematical tools and with their applications to concrete economic problems. The method of treatment rules out any attempt at a systematic development of mathematical economic theory but the essentials of such a theory are to be found either in the text or in the examples. I hope that the book will be useful to readers of different types. The earlier chapters are intended primarily for the student with no mathematical equipment other than that obtained, possibly many years ago, from a matriculation course. Such a student may need to accustom himself to the application of the elementary methods before proceeding to the more powerful processes described in the later chapters. The more advanced reader may use the early sections for purposes of revision and pass on quickly to the later work. The experienced mathematical economist may find the book as a whole of service for reference and discover new points in some of the chapters. I have received helpful advice and criticism from many mathe maticians and economists. I am particularly indebted to Professor A. L. Bowley and to Dr. J. Marschak and the book includes numerous modifications made as a result of their suggestions on reading the original manuscript. I am also indebted to Mr. G. J. Nash who has read the proofs and has detected a number of slips in my construction of the examples. R. G. D. ALLEN THE LONDON SCHOOL OF ECONOMICS October, 1937. Contents include: FOREWORD ----------v A SHORT BIBLIOGRAPHY - ..... xiv THE USE OF GREEK LETTERS IN MATHEMATICAL ANALYSIS - - ...... xvi I. NUMBERS AND VARIABLES -------1 1.1 Introduction ---------1 1.2 Numbers of various types ------3 1.3 The real number system -------6 1.4 Continuous and discontinuous variables ... - 7 1.5 Quantities and their measurement ..... 9 1.0 Units of measurement - - - - - - - 13 1.7 Derived quantities - - - - - - - - 14 1.8 The location of points in space - - - - - 1G 1.9 Va viable points and their co-ordinates 20 EXAMPLES 1 The measurement of quantities graphical methods ---------23 . JpOJ ACTIONS AND THEIR DIAGRAMMATIC REPRESENTATION 28 2.1 Definition and examples of functions 28 2.2 The graphs of functions - - - - - - - 32 2.3 Functions and curves - - - - - - - 3 5 2.4 Classification of functions - - - - - - 38 2.5 Function types - - - - - - - - 41 2.6 The symbolic representation of functions of any form - 45 2.7 The diagrammatic method - - - - - - 48 2.8 The solution of equations in one variable 50 2.9 Simultaneous equations in two variables 54 EXAMPLES II Functions and graphs the solutionjof equa- tions ......... 57 III. ELEMENTARY ANALYTICAL GEOMETRY 61 3.1 Introduction ......... 61 3.2 The gradient of a straight line ..... 03 3.3 The equation of a straight line - - - 66 viii CONTENTS CHAP. 3.4 The parabola 09 3.5 The rectangular hyperbola - - - - - - 72 3.6 The circle 75 3.7 Curve classes and curve systems . - ... 76 3.8 An economic problem in analytical geometry 80 EXAMPLES III--The straight line curves and curve systems 82 IV...

    • Mathematics

Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory
Author: Carl M. Bender,Steven A. Orszag
Publisher: Springer Science & Business Media
ISBN: 1475730691
Category: Mathematics
Page: 593
View: 7995
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

    • Mathematics

Linear Algebra: Concepts and Methods


Author: Martin Anthony,Michele Harvey
Publisher: Cambridge University Press
ISBN: 1107493684
Category: Mathematics
Page: 527
View: 2585
Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.

    • Mathematics

Mathematics for Economics and Finance

Methods and Modelling
Author: Martin Anthony,Norman Biggs
Publisher: Cambridge University Press
ISBN: 1139643266
Category: Mathematics
Page: N.A
View: 7029
Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.

    • Mathematics

Advanced Calculus

Revised
Author: Lynn Harold Loomis,Shlomo Sternberg
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category: Mathematics
Page: 596
View: 4178
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

    • Mathematics

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9829

    • Mathematics

Advanced Mathematical Methods for Finance


Author: Giulia Di Nunno,Bernt Øksendal
Publisher: Springer Science & Business Media
ISBN: 9783642184123
Category: Mathematics
Page: 536
View: 4952
This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

    • English literature

British Book News


Author: N.A
Publisher: N.A
ISBN: N.A
Category: English literature
Page: N.A
View: 1316

    • Econometrics

Maths for Economics


Author: Geoff Renshaw
Publisher: Oxford University Press
ISBN: 0198704372
Category: Econometrics
Page: 744
View: 9031
Drawing on his extensive experience teaching in the area, Geoff Renshaw has developed Maths for Economics to enable students to master and apply mathematical principles and methods both in their degrees and their careers. Through the use of a gradual learning gradient and the provision of examples and exercises to constantly reinforce learning, the author has created a resource which students can use to build their confidence - whether coming from a background of a GCSE or A Level course, or more generally for students who feel they need to go back to the very basics. Knowledge is built up in small steps rather than big jumps, and once confident that they have firmly grasped the foundations, the book helps students to make the progression beyond mechanical exercises and on to the development of a maths tool-kit for the analysis of economic and business problems - an invaluable skill for their course and future employment. The Online Resource Centre contains the following resources: For Students: Ask the author forum Excel tutorial Maple tutorial Further exercises Answers to further questions Expanded solutions to progress exercises For Lecturers (password protected): Test exercises Graphs from the book Answers to test exercises PowerPoint presentations Instructor manual

    • Business & Economics

PreMBA Analytical Primer

Essential Quantitative Concepts for Business Math
Author: Regina Trevino
Publisher: Springer
ISBN: 0230615783
Category: Business & Economics
Page: 201
View: 3418
The PreMBA Analytical Primer is a concise and focused review of the analytical tools and methods that are required in MBA quantitative courses.

    • Business & Economics

Real Analysis with Economic Applications


Author: Efe A. Ok
Publisher: Princeton University Press
ISBN: 1400840899
Category: Business & Economics
Page: 832
View: 7902
There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.

    • American literature

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual
Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 9763