I - Paretian Mathematics

(1) Homogeneity and Euler's Theorem

(2) Review of Linear Algebra

(A) Matrices

(B) Linear Systems of Equations

(C) Eigenvalues and Eigenvectors

(D) Complex Conjugates

(E) Some Useful Theorems

(F) Quadratic Forms

(3) Classical Optimization

II - Dynamical Systems

(1) Differential Equations

(A) General Differential Equations

(B) Dynamical Systems of Differential
Equations

(2) Stable Matrices

(3) Lyapunov's Method

(4) Solving Dynamical Systems of Differential Equations

(5) Solving Dynamical Systems of Difference Equations

III - Neo-Walrasian Mathematics

(1) Convex Structures

(2) Non-Linear Programming

(3) Linear Programming and Duality Theorems

(4) Continuity and All That

(5) Fixed Point Theorems

(6) Measures and Integration

(7) Vector Spaces

(8) Non-Standard Analysis

IV - Dynamic Optimization

(1) Introduction

(2) Calculus of Variations

(3) Optimal Control Theory

(4) Dynamic Programming

(5) Stochastic Dynamic Programming

**Extra**: How
to do mathematical proofs