Reddit mentions of Fat Back

Looks like you're going to the U of Iowa next year. There are some great jazz trombone people in the state - I recommend looking up Dr. Anthony Williams. He's the trombone professor up at UNI and he is a great Classical/Jazz trombone player. More importantly, he's a great teacher. I graduated the year before he started working at UNI, but I've taken a couple lessons with him and found them well worth the money.

In the meantime, transcribe, transcribe, transcribe! The first solo I have all of my students transcribe is Chris Buckholz's Fat Back. It's a medium swing tune in F minor, the solo remains mostly diatonic and it swings its ass off. Chris has a fantastic time feel, especially for a trombone player.

Finally, start digging into jazz theory. Knowing how to read chord symbols is ESSENTIAL. I recommend learning some basic jazz piano skills, as well as composing your own tunes. Improvisation is nothing more than spontaneous composition. Once I started writing tunes, I became much better at recognizing the sounds I was hearing inside my own head.

Good luck! Have fun in Iowa City! It has a great jazz scene, you will not be hurting for things to see or do in that town.