math-for-macro
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Source files of the course "Mathematics for Macroeconomics"
Mathematical Methods for Macroeconomics
This repository contains material for a one-week graduate course on mathematical methods for macroeconomics.
Instructor
The course material was developed by Pascal Michaillat for EC400 at the London School of Economics & Political Science.
Course Webpage
The course is hosted at https://www.pascalmichaillat.org/t3.html.
Course overview
The course covers basic mathematical methods to study dynamical systems, in discrete time and in continuous time. Dynamical systems are systems that involve more than one time-period; they are prevalent in many areas of macroeconomics. The course covers three methods:
- Dynamic programming - to solve discrete-time optimization problems
- Optimal control - to solve continuous-time optimization problems
- Differential equations - to characterize continuous-time systems
Course material
The repository contains all the material for the course.
-
lectures
folder - 3 sets of lecture notes -
homework
folder - 13 exercises and their solutions -
exam
folder - a one-hour exam and its solutions
The material is available both as LaTeX files and as PDF files. The PDF files are produced by compiling the LaTeX files using pdfTeX and the MacTeX-2021 distribution.
Lectures
The lectures
folder contains the following material:
-
dynamicprogramming.pdf
- lecture notes covering dynamic programming -
dynamicprogramming.tex
- LaTeX file producingdynamicprogramming.pdf
-
optimalcontrol.pdf
- lecture notes covering optimal control -
optimalcontrol.tex
- LaTeX file producingoptimalcontrol.pdf
-
differentialequations.pdf
- lecture notes covering differential equations -
differentialequations.tex
- LaTeX file producingdifferentialequations.pdf
-
phasediagrams.key
- Keynote file containing phase diagrams included in the lecture notes -
phasediagrams.pdf
- PDF version ofphasediagrams.key
-
paper.sty
- LaTeX style file for scientific papers -
notes.sty
- LaTeX style file for lecture notes -
math.sty
- LaTeX style file containing mathematical formatting and shortcuts
Homework
The homework
folder contains the following material:
-
exercises.pdf
- 13 exercises covering all three topics -
exercises.tex
- LaTeX file producingexercises.pdf
-
exercises_solutions.pdf
- solutions to the exercises -
exercises_solutions.tex
- LaTeX file producingexercises_solutions.pdf
-
paper.sty
- LaTeX style file for scientific papers -
notes.sty
- LaTeX style file for lecture notes -
math.sty
- LaTeX style file containing mathematical formatting and shortcuts
Exam
The exam
folder contains the following material:
-
exam.pdf
- one-hour exam covering all three topics -
exam.tex
- LaTeX file producingexam.pdf
-
exam_solutions.pdf
- solutions to the exam -
exam_solutions.tex
- LaTeX file producingexam_solutions.pdf
-
paper.sty
- LaTeX style file for scientific papers -
notes.sty
- LaTeX style file for lecture notes -
math.sty
- LaTeX style file containing mathematical formatting and shortcuts
Useful resources
No textbook is required for this short course, but the following textbooks provide useful additional material:
- Chapters 6 & 7 of Introduction to Modern Economic Growth by Daron Acemoglu
- Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris Hirsch, Stephen Smale, and Robert Devaney
License
The content of this repository is licensed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0).