Information and Course Material for the 2021 Math Camp of the MA in Economics at Columbia University
View the Course Material on GitHub CesarBarilla/Columbia-MA-Math-Camp-2021
Welcome ! This page hosts the course material of the August 2021 Math Camp for Columbia’s Economics Masters program.
Graders : Utkarsh Kumar and Akanksha Vardani
Office Hours : TBA
The course will cover the mathematical tools and concepts required for the first year sequence of the Master’s in Economics. The main goal of the course is to prepare for first year classes by reviewing or introducing fundamental concepts in various domains of mathematics – analysis, linear algebra, calculus, probability, optimization. A strong emphasis will be put on proof-writing skills and proper mathematical rigor, as well as problem-solving and application of the tools. Students are expected to have taken courses in elementary analysis and unidimensional calculus, as well as have some familiarity with concepts in probability and linear algebra.
The class will be taught in a hybrid format from Monday August 16th to Thursday September 2nd. Lectures will be held in person (room TBA) every weekday from 9.30am to 12pm EST ; they will simultaneously be available on Zoom as well as recorded for asynchroneous attendance. If possible, students are strongly encouraged to attend the lectures in real time.
The course is largely self-contained. Lecture notes will be posted on the website ; teaching itself will mostly take place on the blackboard but additional notes or slides might be provided. Some additional notes and textbook references are provided below.
Problem sets will be assigned weekly. They are important practice and will be graded for feedback, although no grade will be given for the class. Problem sets will have to be submitted online (modalities to be specified) and will have to be typed – LaTeX is very strongly encouraged as it is an extremely valuable skill that students should acquire as soon as possible. There will be a final exam – the date and modality of the exam will be announced later.
Here is a tentative course outline (each main section is a link to the corresponding lecture notes) :
Lectures notes are susceptible to being continuously updated (be sure to check the date of last update, which is always mentioned at the top of the pdf).
Problem sets will be posted here. Below is a tentative schedule.
Final Exam and Solutions
Two very useful short introductions to mathematical proofs :
Lecture notes from last year’s math camp are available here.
Below is a list of useful references and textbooks sorted by theme. Within each theme, references are listed in (approximately) increasing complexity. References marked with a (!) are more advanced and are included either for future references or very motivated students.
The problem sets will have to be typed and students are encouraged to use LaTeX. LaTeX is a powerful tool for seamless and systematic typesetting that produces clean and readable documents. It is arguably the best practical options to typeset mathematical notations and it is the standard tool in the academic world in Economics. For those that are not familiar with LaTeX, here are a few references to get started :
You can find Past Exams and Solutions Here and Past Problem Sets and Solutions here.