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I remember reading a series of three books that started in some sort of slum with the female protagonist. At a certain point every kid, no matter the status, is tested for their ability to use magic. This is because magic can be extremely problematic when left alone. Mages normally explode quite violently when they die and their remaining magical energy gets out of control. Therefore everyone with an aptitude for magic gets recruited and trained in a special school to learn how to use magic.
The school also has a room where mages are supposed to die without hurting anyone. But strangely for most people, there is also some sort of old graveyard and nobody understands why - after all there is no body to bury if a mage dies.
The protagonist learns a lot of simple magic - little shields to be safe from physical attacks and methods to raise the core temperature when it's cold outside. Raising the core temperature was mentioned as something students starting in winter would learn really fast - they were only allowed certain clothes in the school.
The problem comes later in the books. The reader learns that there are other kinds of mages who were banned a long time ago and lived in the desert. They still knew how to raise their magical energy, which normal mages of the current time forgot. By cutting someone and touching their blood a mage could siphon their energy and increase their own pool of energy. The normal process was that there was one master and one student. The master taught the student and in turn got to take their magical energy. This also allowed to take all of the energy of a mage in their last moments, which means there was no energy to go wild after death and therefore no explosion.
By constantly increasing their magical energy their spells were extremely powerful. Once these people learned that others forgot about extracting magical energy from others they decided to start a war. They could easily kill most of the normal mages. Those were extremely weak compared with the bad guys and didn't expect such power.
Luckily the protagonist and one of her teachers(?) were different. He knew about this kind of magic and taught her about it. So they started fighting back and I think in the end they were able to defend themselves against the invaders by showing them, that the old knowledge was not lost and killing a handful of the enemies. Their numbers were really low and explosions from mage deaths were extremely devastating after all.
The magic system was really fascinating and I would love to read them again, but I only borrowed them from a friend around 2010 or so. I've read the books in German and each one had the female protagonists name in the title.
Can you help me remember what the name of the series was