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Disciplines are academic groupings based on areas of aptitude within Brakebills College. Professor Sunderland describes them as follows: "everybody at Brakebills has an aptitude for magic, but there are individual variations--people tend to have affinity for some specific strain."
Despite the fact that affinities are innate Professor Sunderland says "[it] has to do with where you were born, and where the moon was, and what the weather was like, and what kind of person you are, plus all kinds of technical stuff that's not worth getting into".  At the end of a Brakebills student's second year, various "inductive" tests are performed by the student to determine which of the Discipline Groups they should be sorted into.
Horomancy: Also known as clock magic, it's an obscure discipline deals with the creation of magical clocks for various effects. Horomancy functions as a sort of magical programming, which the starting spotand most obvious effect is manipulation of time, but further study may lead to weather, optics, probabilities and field effects. Stoppard's discipline was this, and he describes it as the "best of both worlds" when it comes to magic and computers. He showed versatility when he used a clock device to create a force field, shaped like a bubble, around him and the rest of the thief squad . Jane Chatwin was also very gifted in this discipline, but only used it for temporal manipulation, through the use of a pocketwatch given her by the Dwarves of Fillory. 
Probability Magic: Just as Horomancy allows you to manipulate probabilities, the study is also a discipline of its own. Lionel was an expert in this kind of magic. The discipline deals with altering probability fields, which themselves are inherently invisible, but their secondary effects are observed as chance occurrences that are highly unlikely in normal situations. An example of such are Lionel's effect over it in a cards deck, where a card tossed on the side might land on its edge and balance there, or spin on one corner.
Sense Magic: This fields of magic is used by talent scouts of Brakebills, and possibly the other magical institutions, to locate acts of magic being performed by potential students. It is typically cast upon globes, allowing for international recruitment, and isn't very reliable for discerning an exact location, but directs the scouts to a magician's general vicinity.
In the TV series, students are tested upon acceptance to the school, and allowed to move into a Discipline specific house at the end of the first year. Once their Discipline is determined students have the opportunity to congregate in a Discipline-specific location with other members of their Discipline.