\documentclass[twoside,11pt]{homework}
\coursename{COMS 4771 Machine Learning (**add semester here**)}
\studname{Name Surname} % YOUR NAME GOES HERE
\studmail{uni@columbia.edu}% YOUR UNI GOES HERE
\hwNo{1} % THE HOMEWORK NUMBER GOES HERE
\date{**add date here**} % DATE GOES HERE
% Uncomment the next line if you want to use \includegraphics.
%\usepackage{graphicx}
\begin{document}
\maketitle
\section*{Problem 1}
% YOUR SOLUTION GOES HERE
% SOME EXAMPLE LATEX CODE BELOW (DON’T INCLUDE IN YOUR ACTUAL SUBMISSION!)
Examples of blackboard and calligraphic letters: $\bbR^d \supset
\bbS^{d-1}$, $\cC \subset \cB$.
Examples of bold-faced letters (perhaps suitable for matrix and
vectors):
\begin{equation}
L(\vx,\vlambda) = f(\vx) – \innerprod{\vlambda,\vA\vx-\vb} .
\label{eq:lagrangian}
\end{equation}
\newcommand\var{\ensuremath{\operatorname{var}}}%
Example of a custom-defined math operator:
\[
\var(X) = \bbE X^2 – (\bbE X)^2 .
\]
Example of references: the Lagrangian is given in
Eq.~\eqref{eq:lagrangian}, and Theorem~\ref{thm:euclid} is
interesting.
Example of adaptively-sized parentheses:
\[
\left(\prod_{i=1}^n x_i\right)^{1/n}
+ \left(\prod_{i=1}^n y_i\right)^{1/n}
\leq
\left(\prod_{i=1}^n (x_i + y_i)\right)^{1/n}
.
\]
Example of aligned equations:
\begin{align}
\Pr(X = 1 \,|\, Y = 1)
& = \frac{\Pr(X = 1 \,\wedge\, Y = 1)}{\Pr(Y = 1)}
\notag \\
& =
\underbrace{
\frac{\Pr(Y = 1 \,|\, X = 1) \cdot \Pr(X = 1)}{\Pr(Y = 1)}
}_{\text{Usual expression for Bayes’ rule}}
.
\label{eq:bayes-rule}
\end{align}
Example of a theorem:
\begin{theorem}[Euclid]
\label{thm:euclid}
There are infinitely many primes.
\end{theorem}
\begin{proof}[Euclid’s proof]
There is at least one prime, namely $2$.
Now pick any finite list of primes $p_1, p_2, \dotsc, p_n$.
It suffices to show that there is another prime not on the list.
Let $p := \prod_{i=1}^n p_i + 1$, which is not any of the primes on
the list.
If $p$ is prime, then we’re done.
So suppose instead that $p$ is not prime.
Then there is prime $q$ which divides $p$.
If $q$ is one of the primes on the list, then it would divide $p –
\prod_{i=1}^n p_i = 1$, which is impossible.
Therefore $q$ is not one of the $n$ primes in the list, so we’re
done.
\end{proof}
Here is a centered table.
\begin{center}
\begin{tabular}{c||c|c|c|c}
& A
& B
& C
& D \\
\hline
\hline
$1$
& entries
& in
& a
& table
\\
\hline
$2$
& more
& entries
& more
& entries
\end{tabular}
\end{center}
%Here is a centered figure. You’ll need hw0.pdf in the same path.
%\begin{center}
% \includegraphics[height=0.3\textheight]{hw0.pdf}
%\end{center}
\section*{Problem 2}
% YOUR SOLUTION GOES HERE
\section*{Problem 3}
% YOUR SOLUTION GOES HERE
\section*{Problem 4}
% YOUR SOLUTION GOES HERE
\section*{Problem 5}
% YOUR SOLUTION GOES HERE
\end{document}