Numerical Methods for Pythons with Applications

Introduction

Please note that this is a preliminary course description. The final version will be published in June 2026.

The course will teach students basic numerical methods, and show how to solve problems that arise in business economics. The aim of the course is to teach basic numerical tools in Python often used in solving and analysing models in economics, finance, industrial organization, marketing and related fields.

We divide the course in two parts. In the first part of the course, we cover the basic of Python programming and with the relevant scientific packages. We also discuss basic techniques in numerical methods, simulation methods and numerical mathematical programming. The second part of the course is on applications. We will use numerical methods to solve and analyse questions related to climate change, portfolio optimization and insurance markets, savings behaviour, transportation choice, demand for products, planning problem etc.

The course will be applied. We cover basic theory related to different economic problems, but the emphasis is on how to solve and analyse a variety of models commonly used in economics and finance. We will solve, simulate and visualize models and explore alternative assumptions and extensions.

This is a course aimed at master students with some basic knowledge in programming and microeconomics/business economics at the master level. 

Course content

1.  Mathematical background: Optimization, Difference and Differential Equations.

2. Python Programming I. Loops, Conditionals, Functions.

3. Python Programming II. Numpy, Lists, Dictionaries.

4. Scientific Packages. Scipy, Numba, JAX,  and Object Oriented Programming.

5. Basic Numerical Methods I. Nonlinear Equations, Integration, and Function Minimization. 

6. Basic Numerical Methods II. Function Approximation.  Random Variables, Sampling from Distributions,

7. Simulation Techniques. Simulation of Stochastic Processes.

8. Mathematical Programming. Gurobi Package. Models with Constraints.

9. Solving Equilibrium Models. Applications: Climate Change, International Trade.

10. Topics in Finance and Risk Management. Applications: Portfolio Optimization, Insurance Markets

11. Dynamic Programming. Applications: Saving Behavior, Non-Renewable Resources, Real Options Models.

12. Continuous Time Methods. Method to solve Differential Equations, Optimization Problems.

13. Methods for Machine Learning. Neural Networks, Machine Learning as a Constrained Optimization Problem.

14. Introduction to Deep Learning

15. Applications to Business, Finance and Economics.