This is the expanded notes of a course intended to introduce students specializing in mathematics to some of the central ideas of traditional economics. The book should be readily accessible to anyone with some training in university mathematics; more advanced mathematical tools are explained in the appendices. Thus this text could be used for undergraduate mathematics courses or as supplementary reading for students of mathematical economics.
This text offers a presentation of the mathematics required to tackle problems in economic analysis. After a review of the fundamentals of sets, numbers, and functions, it covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics.
Mathematics for Economists with Applications provides detailed coverage of the mathematical techniques essential for undergraduate and introductory graduate work in economics, business and finance. Beginning with linear algebra and matrix theory, the book develops the techniques of univariate and multivariate calculus used in economics, proceeding to discuss the theory of optimization in detail. Integration, differential and difference equations are considered in subsequent chapters. Uniquely, the book also features a discussion of statistics and probability, including a study of the key distributions and their role in hypothesis testing. Throughout the text, large numbers of new and insightful examples and an extensive use of graphs explain and motivate the material. Each chapter develops from an elementary level and builds to more advanced topics, providing logical progression for the student, and enabling instructors to prescribe material to the required level of the course. With coverage substantial in depth as well as breadth, and including a companion website at www.routledge.com/cw/bergin, containing exercises related to the worked examples from each chapter of the book, Mathematics for Economists with Applications contains everything needed to understand and apply the mathematical methods and practices fundamental to the study of economics.
This textbook provides a one-semester introduction to mathematical economics for first year graduate and senior undergraduate students. Intended to fill the gap between typical liberal arts curriculum and the rigorous mathematical modeling of graduate study in economics, this text provides a concise introduction to the mathematics needed for core microeconomics, macroeconomics, and econometrics courses. Chapters 1 through 5 builds students’ skills in formal proof, axiomatic treatment of linear algebra, and elementary vector differentiation. Chapters 6 and 7 present the basic tools needed for microeconomic analysis. Chapter 8 provides a quick introduction to (or review of) probability theory. Chapter 9 introduces dynamic modeling, applicable in advanced macroeconomics courses. The materials assume prerequisites in undergraduate calculus and linear algebra. Each chapter includes in-text exercises and a solutions manual, making this text ideal for self-study.
An early but still useful and frequently cited contribution to the science of mathematical economics, this volume is geared toward graduate students in the field. Prerequisites include familiarity with the basic theory of matrices and linear transformations and with elementary calculus. Author Jacob T. Schwartz begins his treatment with an exploration of the Leontief input-output model, which forms a general framework for subsequent material. An introductory treatment of price theory in the Leontief model is followed by an examination of the business-cycle theory, following ideas pioneered by Lloyd Metzler and John Maynard Keynes. In the final section, Schwartz applies the teachings of previous chapters to a critique of the general equilibrium approach devised by Léon Walras as the theory of supply and demand, and he synthesizes the notions of Walras and Keynes. 1961 edition.
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.
With the failure of economics to predict the recent economic crisis, the image of economics as a rigorous mathematical science has been subjected to increasing interrogation. One explanation for this failure is that the subject took a wrong turn in its historical trajectory, becoming too mathematical. Using the philosophy of mathematics, this unique book re-examines this trajectory. Philosophy of Mathematics and Economics re-analyses the divergent rationales for mathematical economics by some of its principal architects. Yet, it is not limited to simply enhancing our understanding of how economics became an applied mathematical science. The authors also critically evaluate developments in the philosophy of mathematics to expose the inadequacy of aspects of mainstream mathematical economics, as well as exploiting the same philosophy to suggest alternative ways of rigorously formulating economic theory for our digital age. This book represents an innovative attempt to more fully understand the complexity of the interaction between developments in the philosophy of mathematics and the process of formalisation in economics. Assuming no expert knowledge in the philosophy of mathematics, this work is relevant to historians of economic thought and professional philosophers of economics. In addition, it will be of great interest to those who wish to deepen their appreciation of the economic contours of contemporary society. It is also hoped that mathematical economists will find this work informative and engaging.
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. 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 Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
