The Magic or Madness series by Justine Larbalestier
Magic or Madness, Magic Lessons, and Magic's Child
Any book reviewer knows that talking about trilogies is tricky... How much does it matter if you've read the other books? What will you lose if you treat them as one enormous narrative rather than three distinct books? So the short answer is, you could read these separately, but you won't want to once you start the first.
Reason is the child of Sarafina, who has kept them on the run all of their lives from Reason's grandmother, Esmerelda. Esmerelda is magic, uses magic, and drained young Sarafina of her magic as a child. This is a world where people who are born magic but die young, and the choice is this: either they use their magic and live to maybe 30 (unless they feed off the young) or they don't use it and go insane. The story begins when Sarafina has finally succumbed to all her years of resisting magic by losing her mind. Reason, who was raised to believe in science, logic, and above all math, has landed at Esmerelda's house, thanks to the Australian child welfare system.
But Reason doesn't plan to stay, not even after she meets Tom, a boy her age, whom her grandmother has taken in along with his family. Reason is guarded, and Esmerelda told Tom not to tell Reason about magic, and so much of the tension in the first book is watching how little these characters actually say to one another about what is happening.
The entire trilogy takes place over the course of a few weeks, as Reason's plans to leave are complicated when she discovers a magic door in the back of her grandmother's house that transports her instantly from Sydney to New York City and from summer to winter. The combination of Aussie teen slang and New York misunderstandings is amusing but never slapstick. Larbalestier has created a robust and contemporary fantasy setting that is entrancing without being flighty or etherial and well worth the 3-book reading.