Mathematical Methods in Economics and Social Choice

1: Sets, Relations and Preferences.- 1.1 Elements of Set Theory.- 1.2 Relations, Functions and Operations.- 1.3 Groups and Morphisms.- 1.4 Preferences and Choices.- 1.5 Social Choice and Arrow’s Impossibility Theorem.- 2: Linear Spaces and Transformations.- 2.1 Vector Spaces.- 2.2 Linear Transformations.- 2.3 Canonical Representation.- 2.4 Geometric Interpretation of a Linear Transformation.- 3: Topology and Convex Optimisation.- 3.1 A Topological Space.- 3.2 Continuity.- 3.3 Compactness.- 3.4 Convexity.- 3.5 Optimization in Convex Sets.- 3.6 Kuhn-Tucker Theorem.- 3.7 Choice on Compact Sets.- 3.8 Political and Economic Choice.- 3.9 References.- 4: Differential Calculus and Smooth Optimisation.- 4.1 Differential of a function.- 4.2 Cr-Differentiable Functions.- 4.3 Constrained Optimization.- 4.4 The Pareto Set and Price Equilibria.- 4.5 References.- 5: Singularity Theory and General Equilibria.- 5.1 Singularity Theory.- 5.2 Transversality.- 5.3 Generic Existence of Regular Economies.- 5.4 Economic Adjustment and Excess Demand.- 5.5 Structural Stability of a Vector Field.- 5.6 Speculations on Chaos.- 5.7 References.- Review Exercises.- Name Index.