Foundations of Mathematical Economics Book

	Introduction
	A Note to the Reader
1	Sets and Spaces	1
1.1	Sets	1
1.2	Ordered Sets	9
1.3	Metric Spaces	45
1.4	Linear Spaces	66
1.5	Normed Linear Spaces	114
1.6	Preference Relations	130
2	Functions	145
2.1	Functions as Mappings	145
2.2	Monotone Functions	186
2.3	Continuous Functions	210
2.4	Fixed Point Theorems	232
3	Linear Functions	263
3.1	Properties of Linear Functions	269
3.2	Affine Functions	276
3.3	Linear Functionals	277
3.4	Bilinear Functions	287
3.5	Linear Operators	295
3.6	Systems of Linear Equations and Inequalities	306
3.7	Convex Functions	323
3.8	Homogeneous Functions	351
3.9	Separation Theorems	358
4	Smooth Functions	417
4.1	Linear Approximation and the Derivative	417
4.2	Partial Derivatives and the Jacobian	429
4.3	Properties of Differentiable Functions	441
4.4	Polynomial Approximation	457
4.5	Systems of Nonlinear Equations	467
4.6	Convex and Homogeneous Functions	483
5	Optimization	497
5.1	Introduction	497
5.2	Unconstrained Optimization	503
5.3	Equality Constraints	516
5.4	Inequality Constraints	549
6	Comparative Statics	601
6.1	The Envelope Theorem	603
6.2	Optimization Models	609
6.3	Equilibrium Models	622
	References	635
	Index of Symbols	641
	General Index	643