I have Ubuntu Mate 16.04 installed on a flash drive. There are a number of pre-installed programs that I have no use for and would like to uninstall them. However, how to do that escapes me. I know how to add them, but removing them isn't as simple as Linux Mint. Ye olde software center present in conventional Ubuntu isn't there.

My first thought is to install Synaptic. It should be in the repos if it's not already present (note: I don't have 16.04 to test this. Also, Ubuntu should include Synaptic. That it does not is a failure on Ubuntu's part, if not a blunder, as Synaptic is a fundamental Debian tool).

Use Synaptic to remove them.

You could likely also use apt-get or aptitude, which are command line programs. See their respective man pages for more.

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Yeah. While I was still typing, Frankbell has modified his post. If it is sufficient, skip this message.
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Debian-based systems (using the deb package format) usually come with the apt utility. I will not say, that it is easier, better, preferable to use to any others, but it's advantage is clearly that knowing this tool you do not need to know any others. Also, apt is usually installed by default. Just check.
You uninstall software like this:
You install software:
But you need to know the packages. To still facilitate these tasks and to give you even more security (on Debian-based systems) you can use the aptitude-utility. It replaces apt and will show you the possible consequences of your actions, before you effectuate them. Aptitude comes with a semi-graphical interface and is controlled by keyboard-shortcuts or via a menu on top.

This is an example for a posting which can become very long but I force myself to terminate right h.

You are most welcome.

Second thoughts. It's what I do.