You will likely notice that, in some exercises, I use what’s called the enharmonic equivalent of certain notes. An enharmonic equivalent is the same sound written a different way. For example, A# and Bb are the same sound but they are written as a different note. I use enharmonic equivalents to avoid writing double flats and double sharps when possible – you will find double sharps occasionally but only when I felt it necessary.
Personally, I much prefer to see an E rather than an Fb written. Same with seeing a B rather than a Cb, and so on. I made decisions on certain exercises that could be argued for or against what I decided to write in the end. It was a judgment call on my part.
Regarding the mixing of sharps and flats in the same bar – I come across flats and sharps in the same bar frequently on sessions or when I’m reading someone else’s material (sometimes even my own) and I think seeing those here from time to time will help prepare you for those occasions when you do come across them. In the end, it’s good to know about enharmonic equivalents and their application and use.
Here are a few things to ponder.
Do you consider an Eb to be the same note as a D#? Is an A# the same note as a Bb?
Is Gb the same note as F#?
It’s the same sound but is it the same note?!?