# Introduction to Dynamic Programming¶

We have studied the theory of dynamic programming in discrete time under certainty. Let's review what we know so far, so that we can start thinking about how to take to the computer.

## The Problem¶

We want to find a sequence $\{x_t\}_{t=0}^\infty$ and a function $V^*:X\to\mathbb{R}$ such that

$$V^{\ast}\left(x_{0}\right)=\sup\limits _{\left\{ x_{t}\right\} _{t=0}^{\infty}}\sum\limits _{t=0}^{\infty}\beta^{t}U(x_{t},x_{t+1})$$

# Faster Computations with Numba¶

## Some notes mostly for myself¶

Altough Python is fast compared to other high-level languages, it still is noat as fast as C, C++ or Fortran. Luckily, two open source projects Numba and Cython can be used to speed-up computations. Numba is sponsored by the producer of Anaconda, Continuum Analytics

# Working with Economic data in Python¶

This notebook will introduce you to working with data in Python. You can use packages like Numpy to work with arrays, matrices, and such, and anipulate data (see my Introduction to Python). But given the needs of economists it is better to use Pandas. Pandas

# Using Geographic Information Systems (GIS) in GIS and ¶

## Geographic Information Systems (GIS)¶

GIS refers to methods of storing, displaying and analyzing geogaphical information. These methods have become essential in economic analysis (as you have noticed from the reading list for our Ph.D. course on economic growth). For this reason, it is good that you acquaint yourself with these methods. They will prove very useful when doing research, especially to show the spatial distribution of your variables of interest, contructing new measures, or doing spatial analysis.