Basics of optimization theory with applications in MATLAB and R

This document is the result of a reorganization of lecture notes used by the author during the Teaching Assistantship of the Optimization course at the M.Sc. in Economics program at the University of Venice. It collects a series of results in Static and Dynamic Optimization, Differential and Difference Equations useful as a background for the main courses in Mathematics, Finance and Economics both at the M.Sc. and at the Ph.D. level. In addition, it offers a brief critical summary of the power of programming and computational tools for applied mathematics, with an overview of some useful functions of the softwares MATLAB and R. All the codes used are available upon request to the author.