Multiple mysterious compilation errors

Question

I cannot compile the following files. I get multiple errors that I can't explain. Can anyone help me?

 \documentclass{article}
 \usepackage{graphicx}

 \begin{document}
 \title{Project 1}
 \author{[email protected]}

 \section{Tools}
 Text
 \section{Algorithm}

 Text. \newline
 Text:

 \[ min_{\textbf{w}} \sum_{i=1}^n (y_i - \textbf{w}^T \textbf{x_i})^2 + \lambda \|\textbf{w}\|_2^2 \]

 \newline
 Text:

 Text

\section{Features}
\section{Parameters}
\end{document}

Answer 1

You want the variable denoting a vector to be boldface, not its subscript. For making bold a letter in math mode the best way is to use \mathbf; however it's even better to hide this in a personal command:

\newcommand{\vect}[1]{\mathbf{#1}}

so that your document becomes

\documentclass{article}
\usepackage{amsmath} % necessary for math intensive documents

\newcommand{\vect}[1]{\mathbf{#1}}

\begin{document}

\title{Project 1}
\author{[email protected]}

\maketitle

\section{Tools}

Text.

\section{Algorithm}

Text. Text:
\[
\min_{\vect{w}} \sum_{i=1}^n (y_i - \vect{w}^T \vect{x}_i)^2 + 
  \lambda \lVert\vect{w}\rVert_2^2
\]
Text.

\end{document}

Why doing it indirectly? There are several reasons to. Let's see the two main ones:

1. You're marking up your document; when you want to find vectors in the typescript, you'll look for \vect rather than \mathbf that might have been used also for other purposes.

2. If you decide that, after all, boldface italic is better (the ISO regulations prescribe this for vectors, for instance), you can simply change one line in your document (and add the call to a package):

   \usepackage{bm}
   \newcommand{\vect}[1]{\bm{#1}}
   

---

Notes on the typing style.

1. Don't use \newline; paragraphs should be simply separated by a blank line in the typescript.

2. Never leave blank lines before a displayed equation in the typescript.

3. The most common operators have already a definition: use \min for the “minimum” operator.

4. Note that it's \vect{x}_i and not \vect{x_i}, because the subscript is appended to the variable name and it shouldn't be specially formatted.

5. With amsmath (that's recommended for documents using mathematics), instead of \| for representing a double bar, it's better to use the specific delimiters \lVert and \rVert. Look at the documentation of mathtools for even better ways to mark up a document (a \norm command is explained).

Answer 2

Use \mathbf in formulas, \textbf is not allowed there.

 \documentclass{article}
    \usepackage{graphicx}

    \begin{document}
    \title{Project 1}
    \author{[email protected]}
    \section{Tools}
    Text

    \section{Algorithm}

    Text. 

    Text: %if you don't want the next line to be indented, use \noindent at the beginning of the line.

    \[ \min_{\mathbf{w}}\sum_{i=1}^n (y_i - \mathbf{w}^T \mathbf{x}_i)^2 + \lambda \|\mathbf{w}\|_2^2 \]


    Text:

    Text
    \section{Features}

    \section{Parameters}

    \end{document}

Answer 3

\documentclass[preview,border=12pt,12pt]{standalone}% change this line with your own document class below
%\documentclass{article}
%\usepackage{graphicx} <=== do you really need this graphicx package when you don't import any images?

% I move this setting to the preamble
\title{The Joy of \TeX}
\author{[email protected]}
\date{\today}

% you don't need the following two lines in your production
\newlength\buffer
\buffer=\parindent\relax

\usepackage{lipsum}% disable this package in your production. I use here just to produce dummy text.
\usepackage{amsmath}% use this package if you want to get more andvanced mathematics macros.

\begin{document}
\parindent=\buffer\relax% you don't need this line in your production

\maketitle


\section{Tools}
\lipsum[1] 

\section{Algorithm}
\lipsum[2]

The following equation is fun, (by the way, you don't need to give a newline before a displayed equation)
\[ 
    \min_{\mathbf{w}} 
        \sum_{i=1}^n \left(y_i - \mathbf{w}^T \mathbf{x}_i\right)^2 
        + \lambda \lvert\mathbf{w}\rvert_2^2 
\]
Isn't it? You don't need to add a newline after the displayed equation.

\lipsum[3]
\section{Features}
\section{Parameters}
\end{document}