Mathematical Methods for Economic Theory 1

<B>Set Theory and Properties of Rn.-</B> Set-Theoretic Notation and Concepts.- Properties of The Real Numbers.- Binary Relations.- Euclidean Norm and Metric.- Open and Closed Sets in Rn.- Relatively Open and Closed Sets.- Some Linear Space Properties of Rn.- <B>Sequences and Infinite Series.-</B> Sequences of Real Numbers.- Subsequences and Cauchy Sequences.- Infinite Series.- Efficient Intertemporal Allocation.- Sequences and Series in Rn.- <B>Continuity.-</B> Continuous Vector-Valued Functions.- Continuity and Compactness.- Semi-Continuous Functions.- Limits Inferior and Superior of a Function.- Transformation Functions.- Production and Cost Functions.- Sequences of Functions and Limits.- <B>Linear </B> <B>Spaces.-</B> Introduction.- Linear Combinations and Subspaces.- Linear Transformations and Functionals.- Normed Linear Spaces.- Inner Product Spaces.- Product Spaces and Direct Sums.- Affine Sets.- <B>Convex Sets and Functions.-</B> Convex Sets.- Relative Interiors of Convex Sets.- Extreme Points of a Convex Set.- Minimum Distance and Projection Theorems.- Basic Separation Theorems in Rn.- Convex and Concave Functions.- Continuity of Convex Functions.- Quasi-Concave Functions.- <B>Applications of Convexity.-</B> Introduction.- Basic Production and Cost Theory.- Distance and Support Functions.- Duality of Cost and Production.- Homotheticity.- Welfare Economics.- Constrained Extrema and Saddle Points.