I will be grading problems on neatness and clarity in addition to correctness. You may want to read this handout on Mathematical Writing. You might also find these examples of good and bad mathematical writing helpful.
The first homework assignment included several inductive proofs. Please see this example of how to write an inductive proof. You do not need to be as verbose as I was, but you should include the 3 parts that I labeled: the base case, the inductive hypothesis, and the algebra to finish the proof.
The above example was typset in LaTeX. Most CS textbooks, conference papers, and journal articles are also typeset using LaTeX. I strongly encourage (but do not require) students to do the same with their homework.
If you are interested in seeing how I typeset the example above, you can download the source. If you want to compile the example .tex file into a .pdf, You will also need to get the hmcpset.cls file which enables some shortcuts that format everything nicely. You can include that file in the same directory as the .tex file and everything will work fine.
There is a short learning curve when first starting out with LaTeX, but I think it's well worth the effort. There are lots of resources on the web. Google is your friend.
To install LaTex on a windows machine, see this guide to setting up LaTeX on Windows.
On a linux machine, you need to get the texlive package using your package manager. In Ubuntu, you could type this command at the command line:
$ sudo apt-get install texlive-fullSimilarly in fedora:
$ sudo yum install texliveYou can use any text editor to edit latex files, but my personal favorite is TexMakerX (for linux).