Note: This is my plan for the last chapter of my fic. I have no idea how long it will be yet or when I will finish it. I just want to write down the final chapter because I had the idea for it. I will tweak it slightly in the future (still not sure who Septima will marry), but this is the bones of it.
Septima, dressed in a black gown and tasseled cap, walked across the stage and held her head high proudly as she went over to Pr. Tremaine and received her PhD in math.
''Congratulations, you are now Dr. Vector,'' Pr. Tremaine said, ''Your thesis is remarkable. I myself have never heard of some of these waveform equations that might make quantum tunneling possible one day.'' (Plus you got a matching surname to boot for the discipline of math. As if by magic, is what Pr. Tremaine thought to himself).
Vector had wrote her thesis about how some forms of matter are mathematically able to quantum tunnel, despite not being proven yet in the muggle world. (The magic world, of course, has observed this phenomenon in things like platform 9 3/4.)
Vector beamed and choked up as she gave her acceptance speech.
''Thank you to everyone for your support. At one point I never thought that I would be doing arith- I mean math- again after my accident. But thanks to the support of all of you, I am standing here today with my PhD in hand,'' she said.
The crowd of both her muggle and magical (disguised as muggles, but with poor outfit choices like tutus and fedoras) family and friends applauded her.
As she stepped down from the stage, her husband kissed her on the cheek.
''I never doubted that your could do it, dear,'' he said.
With a smile greater than Gilderoy Lockhart's used to be, Septima and a few other people got caught up in the excitement of the moment and pulled out their wands to produce sparks (similar to muggle fireworks).
''Oh my god, what is that?!'' screamed Pr. Tremaine and then he promptly fainted.