Error correcting codes are one of the coolest things you can do with math. In general learning math is important for the knowledge buzz moments and the general "tooling for thought" but all of these are a little abstract and hard to "sell." With coding theory, we have much more practical selling points: learn math so you can understant GSM, 3G, LTE, 5G, 6G,... Wifi, ..., satellite comms, storage like CDs, DVDs, BlueRay, HDs, etc.

The linked book is pretty good with lots of nice explanations and good examples.

For a short, blog-post-like intro to the subject check out this 9-page PDF: https://minireference.com/static/excerpts/error_correcting_c... Read the linked book for the full details.