# How to align group of mathematical expressions to the left?

Here are a group of mathematical expressions:

$$arg\ \underset{\theta}{max} \underset{n}{\prod}P(Y_n|\theta)$$
$$=arg\ \underset{\theta}{max} \underset{n}{\prod}\theta^{Y_n}(1-\theta)^{1-Y_n}$$
$$=arg\ \underset{\theta}{max} \sum log\theta^{Y_n}(1-\theta)^{1-Y_n}$$
$$=arg\ \underset{\theta}{max} \sum[Y_n log\theta + (1-Y_n)log(1-\theta)]$$
Optimizing problem:
$$=-arg\ \underset{\theta}{min} \sum[Y_n log\theta + (1-Y_n)log(1-\theta)]$$


I am trying to align them to the left. I tried putting them inside %\begin{align*} ... % \end{align*} without  signs. But no luck.

• @Troy I've tried it but it does not serve my purpose. Jun 3, 2017 at 17:54
• Please describe your problem better, which code (MWE) did you tried, and what is still the problem, for example mark it in the screenshot added to your question ... Jun 3, 2017 at 18:08

Without a complete MWE, it's difficult to know what you're after, but I assume it's something like this:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\arg\ \underset{\theta}{\max} \underset{n}{\prod}P(Y_n|\theta) & =\arg\ \underset{\theta}{\max} \underset{n}{\prod}\theta^{Y_n}(1-\theta)^{1-Y_n} \\
& =\arg\ \underset{\theta}{\max} \sum \log\theta^{Y_n}(1-\theta)^{1-Y_n}           \\
& =\arg\ \underset{\theta}{\max} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]      \\
\intertext{Optimizing problem:}
& =-\arg\ \underset{\theta}{\min} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]     \\
\end{align*}
alternatively:
\begin{flalign*}
& \arg\ \underset{\theta}{\max} \underset{n}{\prod}P(Y_n|\theta) \\
& =\arg\ \underset{\theta}{\max} \underset{n}{\prod}\theta^{Y_n}(1-\theta)^{1-Y_n} \\
& =\arg\ \underset{\theta}{\max} \sum \log\theta^{Y_n}(1-\theta)^{1-Y_n}          \\
& =\arg\ \underset{\theta}{\max} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]     \\
\intertext{Optimizing problem:}
& =-\arg\ \underset{\theta}{\min} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]    \\
\end{flalign*}
\end{document}


alternatively, perhaps you'd like flalign:

• I do not want the first line to contain a = sign. Jun 3, 2017 at 17:41
• @Dipto_Das if you provide a screenshot of your desired output, it'd be most helpful Jun 3, 2017 at 18:05
• @Dipto_Das see my update Jun 4, 2017 at 8:31

The following may be what you're looking for. Note the use of \arg, \max, \min, and \log to generate upright math-operator expressions. I've also replaced the two instances of \underset{n}{\prod} with \prod_n.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
& \arg\max_\theta \prod_n P(Y_n\mid\theta)\\
&=\arg\max_\theta \prod_n \theta^{Y_n}(1-\theta)^{1-Y_n}\\
&=\arg\max_\theta \sum \log\bigl(\theta^{Y_n}(1-\theta)^{1-Y_n}\bigr)\\
&=\arg\max_\theta \sum [Y_n \log\theta + (1-Y_n)\log(1-\theta)]\\
\intertext{Optimizing problem:}
&-\arg\min_\theta \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]
\end{align*}
\end{document}

• Your code does what I want, but it places everything in the center of the page. I want them all to start from the left margin. How can I do that? Jun 3, 2017 at 18:44
• @Dipto_Das - You could (a) switch from an align* environment to an flalign* environment and (b) add a & marker at the end of one of the math lines (but before the double line-break directive). E.g., change \prod_n P(Y_n\mid\theta) to \prod_n P(Y_n\mid\theta)&.
– Mico
Jun 3, 2017 at 19:07