Mathematical Methods in Economics
Mathematical Methods in Economics by Norman Schofield, published by Taylor & Francis Group on March 6, 2018, is a comprehensive exploration of mathematical concepts applied to economic theory. This edition spans 298 pages and is presented in English. The book covers a range of topics including set theory, linear systems, topology, and differential calculus, providing a structured approach to understanding the mathematical foundations essential for economic analysis.
Readers will find detailed discussions on various mathematical methods relevant to economics, such as preference relations, linear transformations, and convex optimization. The text delves into the intricacies of mathematical concepts like eigenvalues and eigenvectors, as well as the principles of constrained optimization. With its focus on the intersection of mathematics and economics, this book serves as a valuable resource for those looking to deepen their understanding of the quantitative aspects of economic theory.
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Cover — Half Title — Title Page — Copyright Page — Contents — Foreword — 1. SETS, RELATIONS AND PREFERENCES — 1.1. ELEMENTS OF SET THEORY — 1.1.1. A Set Theory — 1.1.2. A Propositional Calculus — 1.1.3. Partitions and Covers — 1.1.4. The Universal and Existential Quantifiers — 1.2. RELATIONS, FUNCTIONS AND OPERATIONS — 1.2.1. Relations — 1.2.2. Mappings — 1.2.3. Functions — 1. 3. PREFERENCES — 1.3.1. Preference Relations — 1.3.2. Rationality — 1.3.3. Choices — 1. 4. GROUPS AND MORPHISMS — 2. LINEAR SYSTEMS — 2 .1. VECTOR SPACES — The Exchange Theorem — 2.2. LINEAR TRANSFORMATIONS — 2.2.1. Matrices — 2.2.2. The Dimension Theorem — 2.2.3. The General Linear Group — 2.2.4. Change of Basis — Basis Change Theorem — Isomorphism Theorem — 2.2.5. Examples — 2.3. CANONICAL REPRESENTATION — 2.3.1. Eigenvectors and Eigenvalues — 2.3.2. Examples — 2.3.3. Symmetric Matrices and Quadratic Forms — 2.3.4. Examples — 2. 4. GEOMETRIC INTERPRETATION OF A LINEAR TRANSFORMATION — 3. TOPOLOGY AND CONVEX OPTIMISATION — 3.1. A TOPOLOGICAL SPACE — 3.1.1. Scalar Product and Norm — 3.1.2. A Topology on a Set — 3.2. CONTINUITY — 3.3. COMPACTNESS — Weierstrass Theorem — Heine Borel Theorem — Tychonoff’s Theorem — 3. 4. CONVEXITY — 3.4.1. A Convex Set — 3.4.2. Examples — 3.4.3. Separation Properties of Convex Sets — Separating Hyperplane Theorem — 3.5. OPTIMISATION ON COMPACT SETS — 3.5.1. Optimisation of a Convex Preference — 3.5.2. Kuhn Tucker Theorem — 4. DIFFERENTIAL CALCULUS AND SMOOTH OPTIMISATION — 4.1. DIFFERENTIAL OF A FUNCTION — 4. 2. cr-DIFFERENTIABLE FUNCTIONS — 4.2.1. The Hessian — 4.2.2. Taylor’s Theorem — Mean Value Theorem — Taylor’s Theorem — 4.2.3. Critical Points of a Function — 4.3. CONSTRAINED OPTIMISATION — 4.3.1. Concave and Quasi-Concave Functions
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