PhD Math Bootcamp 2018

Note: This is not the current Mathcamp. Click here for the 2019 Math Bootcamp


Click here for syllabus

Lecture Notes

Week Lecture Notes Readings
1 - Linear Algebra Notes - Link to advice for incoming Economics PhD students
- Latex Tutorial pdf and Latex Zip Folder (containing tex and other necessary files)
- Sets and Logic Reading
2 - Proof Notes
- Real Analysis Notes
- Real Analysis Solutions
- Cauchy Sequence Example
- Columbia Real Analysis Notes
3 - Optimization and Multivariate Calculus Notes
- Python Tutorial Notebook
- Columbia Convexity Notes
- Columbia Multivariate Calculus Notes


Assignments will be posted here on Tuesday evening of each week. I will also post solutions.

Description Due Date Assignment Key
Univariate calculus Assignment 0 Assignment 0 Key
Linear Systems and Matrix Algebra July 27 Assignment 1 Assignment 1 Key
Set Theory and Proofs and Real Analysis August 3 Assignment 2 Assignment 2 Key
Multivariate Calculus and Miscellaneous Topics August 10 Assignment 3 Assignment 3 Key
Mathcamp Final given Summer 2018 August 15 Final Exam 2018 Final Exam 2018 Key

Note: The material in assignment 0 is fair game for the final exam. You should complete these problems to refresh old topics and learn some new ones. However, you do not need to turn this assignment in to me. I will assume your understanding and familiarity with the material during the mathcamp, so please complete your study no later than July 23rd

Assignment LaTeX Template

The template file is hw_template.tex (thanks to my colleague Brett Devine). The template is marked with some commented code to know where you type the assignment name, your name and where your answers go.

First, enter the assignment name and your name in the designated fields.

\title{Assignment ?}
\author{Jon Doe}

Next, for each problem, you can use the custom {problem} environment created in the file. Simply type the following every time start an answer for a new problem.

    Type your answer here.

In the above code, you need to replace the ? with the number of the problem. For example, if you are typing your answer to Problem 23, you would type

    Your answer here.

Course Outline

Below I have provided a tentative schedule. Dates as well as topics are subject to change depending on the pace of the course, as well as what I think should be covered. Also, I will be introducing programming (specifically using Python) on August 9th. That day will be optional, although I strongly recommend you attend.

Before coming to mathcamp:

Date Topics Readings Assignments
Prereqs Univariate Calculus S&B 2-5 Prerequisite assignment to be completed early in the course.

Week 1 (July 23-July 27)

Date Topics Readings Assignments
23 Linear Systems and Matrix Algebra S&B 6-9; Notes  
24 Linear Systems and Matrix Algebra S&B 6-9; Notes  
25 Linear Spaces S&B 10, 11  
26 Linear Spaces and Set Theory S&B 10, 11; Provided Notes  
27 Weekly Review   Assignment 1 due

Week 2 (July 30-August 3)

Date Topics Readings Assignments
30 Set Theory S&B 10, 11; Provided Notes  
31 Proofs and Real Analysis S&B 12; Appendix A1; Provided Notes  
1 Proofs and Real Analysis S&B 12; Appendix A1; Provided Notes  
2 Proofs and Multivariate Calculus S&B 13-15, 30  
3 Weekly Review   Assignment 2 due

Week 3 (August 6-August 10)

Date Topics Readings Assignments
6 Optimization S&B 20-21  
7 Multivariate Calculus S&B 13-15  
8 Multivariate Calculus S&B 13-15, 30  
9 Introduction to Programming Optional  
10 Weekly Review    

Week 4 (August 13-14)

Date Topics Readings Assignments
13     Assignment 3 due
13-15 Final Exam No Notes See Below

There will be multiple times for the Final Exam (since orientation week will be so hectic). Here is a list of those days and times. Note that you only have to attend one. If any of the three don’t work, let me know and we will figure out a different time that works for you.

Date Time
Monday August 13 3-5
Tuesday August 14 10-12
Wednesday August 15 3-5

S&B ~ Simon & Blume text