# PhD Math Bootcamp 2019

### Lecture Notes

1 - Lecture 1 - Linear Algebra
- Lecture 2 - Linear Algebra
- Lecture 3 - Linear Spaces
- Lecture 4 - Set Theory
- Lecture 5 - Logic
- Old Linear Algebra Notes
- Latex Tutorial pdf and Latex Zip Folder (containing tex and other necessary files)
2 - Lecture 6 - Proofs
- Lecture 7 - Proofs and Real Analysis
- Lecture 8 - Real Analysis
- Lecture 9 - Real Analysis
- Lecture 10 - Real Analysis
- Old Proof Notes
- Old Real Analysis Notes
- Old Real Analysis Solutions
- Columbia Real Analysis Notes
3 - Lecture 11 - Real Analysis and Calculus
- Lecture 12 - Calculus
- Lecture 13 - Calculus and Optimization
- Lecture 14 - Optimization
- Python Tutorial Notebook
- Old Optimization and Multivariate Calculus Notes
- Columbia Convexity Notes
- Columbia Multivariate Calculus Notes

### Assignments

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, Matrix Algebra and Set Theory July 29 Assignment 1 Assignment 1 Key
Set Theory, Proofs and Real Analysis August 5 Assignment 2 Assignment 2 selected solutions
Optimization and Multivariate Calculus August 12 Assignment 3 Assignment 3 Key
Mathcamp Final given Summer 2018   Final Exam 2018 Final Exam 2018 Key
Mathcamp Final given Summer 2019 August 13 Final Exam 2019 Final Exam 2019 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 22nd.

### 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.

\begin{problem}{?}
\end{problem}


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

\begin{problem}{23}
\end{problem}


### 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.

#### Before coming to mathcamp:

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

#### Week 1 (July 22-July 26)

22 Linear Systems and Matrix Algebra S&B 6-9; Notes
23 Linear Systems and Matrix Algebra S&B 6-9; Notes
24 Linear Spaces S&B 10, 11
25 Set Theory Provided Notes
26 Logic & Weekly Review Appendix A1; Provided Notes

#### Week 2 (July 29-August 2)

29 Proofs Appendix A1; Provided Notes Assignment 1 due
30 Proofs and Real Analysis S&B 12; Appendix A1; Provided Notes
31 Real Analysis S&Provided Notes
1 Real Analysis Provided Notes
2 Real Analysis & Weekly Review Provided Notes

#### Week 3 (August 5-August 9)

5 Real Analysis and Multivariate Calculus S&B 13-15, 30 Assignment 2 due
6 Multivariate Calculus S&B 13-15, 30
7 Multivariate Calculus and Optimization S&B 13-15, 30
8 Optimization S&B 20-21
9 Envelope Theorem & Weekly Review S&B 20-21