Math Exploration Difficulty Level

[SC2Player]

I'm trying to figure out an appropriate difficulty level for my math exploration (i.e. what can be assumed knowledge).  I know that anything in the HL core is fine, but will I need to define ideas from the option/further math topics, especially if my math HL class isn't doing that option (We're only doing the calculus option in class)?  The IB just took out the matrices section from the core, and I really don't want to define what a matrix is again...  Same goes for stuff like bijective functions, homomorphisms, and basic set theory (or anything in the options besides the calculus one).  

If it helps, my topic is on the relationship between complex numbers and 2x2 matrices.  

Edited December 21, 2016 by SC2Player

[kw0573]

Since there are no penalties for going outside of 6-12 pages, you should be clear with all terminology. Usually one-sentence definitions are enough. For example you can give an example of a one-to-one mapping and say "A one-to-one mapping is also called bijection." You definitely want to define terms that you will mention and use often, with the exception of "matrix" or "row operations" because they could be taught alongside intersection of 3 planes in vectors. A key is to use varied sentence structures so not all are in the form "the definition of ___ is ___________".