This is amazing! I have a background in physics and electronics, but I have never been involved in amateur radio. However, I would love to and would like to ask if one could point me to resources for delving into it? When it comes to math and e.g. electrodynamics and practical filters, I wouldn't need an introduction. Thanks!
Getting a license is your first step if you want to transmit. If you are in the US, the ARRL produces the training material for the various tests. There are free apps that go over the test questions but I like having a little more context to the answers.
With your background you'd probably need to devote time mostly to learning the rules and regulations. You can take all 3 tests in one sitting for a $15 fee and be done with it. Each test gets you more privileges (power, frequencies).
Even without a license you can receive with a cheap SDR and home brew antenna. This blog has many examples of that: https://www.rtl-sdr.com/
Finally, you may want to find a local club. Usually visiting during a "contest" will enable you to get on the air. In the US you don't need a license to use the radio if you are with a properly licensed operator.
There is lots of cool science to be done with radio, being done by amateurs. Starting with the Society for Radio Astronomy mentioned already, but also see:
What I did was to find the local club, go there, learn about the next course & exam, and focus solely on learning morse code (because I wanted the full license). Because I had an electronics&radio background I didn't have to spend any time on that part, I could focus all my time on the specific amateur radio regulations (not difficult) and learning morse (although IIRC I still had to take a written exam about radio transmission theory - not sure though, it's been a long time. I remember though that professional "telegraph" operators from ships didn't have to take any exams at all, but I don't think that kind of ship operators exist anymore. No morse code there, for sure..).
I only want to do HF.. but that's outside the point, I did write that this was a long time ago, and at that time you did need CW to get the full license.
The Society for Amateur Radio Astronomy (SARA) mailing list and website (http://www.radio-astronomy.org/) should be your first stop. There's also a decently active (daily) radio astronomy news feeds/forum over at http://notabug.io/t/radioastronomy . Like others have said, cheap SDR receivers like RTL-SDR based devices have made it easy to get involved.
I've been a ham radio operator in the US for a couple years now, and its a really interesting hobby that will put you on contact with very smart inviting people. Its a great way to learn more about electricity too.
You can get all the books to really learn the material (the ones by KB6NU are the best) but if you already have the background you can just study the test. I use an app called Ham Test Prep on android to take quizzes that basically amount to flashcards. Once you learn most of the questions and answers, you can pass pretty easily.
