Now I have many LaTeX-files on my computer and a memory stick. Is it wise to show at least some of them like thesis on Internet if employers wants to see my ways to write solutions?
If you are well-versed in writing LaTex files, consider including that or mentioning it on your Resume, pointing your level of knowledge and perhaps mention some example documents you've done.
Sending samples of those files with your applications is something I would not suggest, unless they ask you to see some of the LaTex files you've done.
You mention you are seeking job in the software industry. You also mentioned GitHub.
Yes, GitHub is a good place (repository) where you can put your code that you wish to show others. There you can put some sample software you've coded that you feel comfortable showing and link it to your other media, etc..