How to add the section title to the header without changing the header formatting?

Question

Below is the code I have currently and the output which it brings, but I was wondering if there was a way to get the section title to show in the same way without having to type it in /rhead for every section?

\documentclass[a4paper, 12pt, fleqn]{article}
\usepackage{fancyhdr}
\titleformat{\section}[display]{\centering\Large\bfseries}{}{0pt}{\underline} \sectionfont{\centering}
\pagestyle{fancy}
\fancyhf{}
\rhead{Unit 1: Algebra}
\lhead{MST124}
\rfoot{Page \thepage \hspace{1pt} of \pageref{LastPage}}
\section{Unit 1: Algebra}

Answer 1

As you load titlesec, I would use \titleps via the [pagestyles] option, which has a \sectiontitle command. Here is a code for a two-sided layout:

\documentclass[a4paper, twoside, 12pt, fleqn]{article}
\usepackage{lastpage}
\usepackage[pagestyles]{titlesec} %
\titleformat{\section}[display]{\centering\Large\bfseries}{}{0pt}{\underline}
\usepackage{lipsum}

\newpagestyle{own}{\headrule%
\sethead[\sectiontitle][][MST124]{MST124}{}{\sectiontitle}
\setfoot[Page \thepage \hspace{1pt} of \pageref{LastPage}][][]{}{}{Page \thepage \hspace{1pt} of \pageref{LastPage}}
}
\pagestyle{own}

\begin{document}

\section{Unit 1: Algebra}
\lipsum[1-20]

\end{document} 

Answer 2

To get the right headers you have to use the correct marks. In your case \leftmark should respond to your need:

\documentclass[a4paper, 12pt, fleqn]{article}
\usepackage{fancyhdr}
\usepackage{titlesec}
\usepackage{lastpage}
\usepackage{lipsum}
\titleformat{\section}[display]
  {\centering\Large\bfseries}
  {Unit \thesection}
  {0pt}
  {} 

\pagestyle{fancy}
  \fancyhf{}
  \fancyhead[R]{Unit \leftmark}
  \fancyhead[L]{MST124}
  \fancyfoot[R]{Page \thepage\ of \pageref{LastPage}}

\begin{document}

\section{Algebra}
\lipsum

\section{Foo}
\lipsum

\end{document}