I recommend this book for the author's presentation of magic as a dangerous and painful thing, but a genetic gift that has madness as its only alternative. It's a gritty, more realistic presentation of magic than most YA books give (Fleishman's Fade being a horrific exception).
The main character is named Reason. She loves math. Her mother raised her to fear and hate her grandmother, who is - according to the mom - an evil woman dabbling in the trappings of witch craft. Well, no, actually, she's a practicing mage. There's a difference, as we see as the book goes on.
One of the main carriers of the plot is a door that opens from Sydney in the height of summer to New York during a snow storm. The characters that go through it suffer the equivalent of jet lag plus some disorientation about what day/time it is. Due to the combination of time and the character's name, and I found myself singing the Time song from The Phantom Tollbooth more than once.