"Mathematics in Economics" is 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 therefore gain insight into, and familiarity with, the mathematical models and methods involved in the transition from "phenomenon" to quantitative statement.

Topics covered include: Sets and NumbersMatrices and VectorsModelling Consumer ChoiceDiscrete VariablesFunctionsEquilibriumEigenvalues and EigenvectorsLimits and their UsesContinuity and Its UsesPartial DifferentiationThe GradientTaylor's Theorem - An Approximation ToolEconomic Dynamics: Differential Equations.Each chapter ends with exercises designed to help students understand and practice the techniques they have learnt. The author has provided solutions to selected problems so that the book will function as an effective teaching tool on introductory courses in mathematics for economics, quantitative methods and for mathematicians taking a first course in economics. "Mathematics in Economics" has been developed from a course taught jointly by Ken Binmore (Professor of Economics) and Adam Ostaszewski (Senior Lecturer in Mathematics).

This book is devoted to modern methodologies of financial risk management of pension plans, mostly defined benefit plans. The reader is expected to know basic probability theory and mathematical analysis, while all required concepts in financial and actuarial mathematics are developed in the text. The book outlines basic actuarial valuation concepts and then presents actuarial funding and valuation methods for defined benefit plans, and discusses their relationship to other types of pension plans. Optimal funding methodologies are developed in simple deterministic and in stochastic cases. The question of measurement of rate of return of a fund is analyzed in detail, pointing out how the choice of a market index affects it. The problem of stability of the value of liabilities is analyzed as well. Modern investment theory, including equilibrium and arbitrage models, is used to discuss ways to value both marketable and non-marketable assets, as well as liabilities. All commonly used methodologies of valuation of assets are listed and analyzed. Finally, financial risk management for pension plans is presented in detail, with emphasis on applicable asset-liability management methodologies. This portion of the book starts with the basics: duration, convexity, immunization, and develops alternative immunization methodologies, as well as other risk management tools, such as value-at-risk, risk-based-capital, and shortfall constraint approach. A new optimal methodology, an alternative to classical immunization, is developed, and shown to be strikingly similar to conservative management approaches used by practitioners. Throughout the book, all concepts and methodologies are illustrated with examples and exercises, including past problems from the Society of Actuaries and Casualty Actuarial Society professional examinations (used with permission).

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.

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.