For the math(s), most yacht-master examiners are happy with the candidate using a calculator. It's only a few of the RYA fossils who remember teaching Nelson who insist on the longhand version. I used my wife's old Texas TI82 with a celestial navigation programme at first, but then I loaded the AstroNav app onto my iPhone. When I did my yacht-master, the examiner was happy with it. Astro Nav will allow you to input your chosen celestial bodies and does everything for you. Although it does give you the option of inputing your assumed position from the GPS! . Furthermore, in extremis you can use your iPhone as the sextant utilizing the accelerometers. It's not going to be as accurate as a real sextant, but I have achieved a fix within 15 miles of my actual position on it. Asto Nav also has a very good tutorial. For identifying the celestial bodies, the Nightsky app is useful.
I write for a sailing magazine and have always pointed out the potential for satellite navigation systems to be unreliable and have advocated that yachties do need to keep up with their celestial navigation.