CS 173 homeworks are submitted on-line, using moodle type-in boxes. Many simple proofs can be submitted using plain text. Others, however, require latex equation mode and/or jpg diagrams.
In moodle type-in boxes, latex mode equations are surrounded by double dollar signs ($$). The following quick-start guides show a variety of commands that you can use within the equation.
Many tools are available for creating jpg (aka jpeg) diagrams. Look for one that makes it easy to draw geometrical regions (e.g. circles) and arrows (including curvy ones). Some suggestions are
It is also possible to make nice figures using paint packages, tablet-based presentation tools, and with paper and a scanner. However, this works well only for folks who draw neatly and are practiced with their tools. In the hands of most people, these methods result in pictures that are sloppy, low contrast, and/or too large to fit nicely on a normal screen. In particular, use a real flatbed scanner rather than improvising with (say) the camera on your cell phone. It is your responsibility to ensure that the output looks neat and is easy to grade. If the solution can not be understood as it is handed in you will lose points.
In some cases, it may be helpful to grab a figure from the posted homework (e.g. by screen capture) and annotate it. You are not required to start from scratch.
If you are already familiar with more sophisticated diagram-drawing packages such as gastex, tikz, or ipe, by all means use them.