What is Pre-algebra and why is it needed?
Pre-algebra forms he foundation of maths of a middle school student. The objective of it is to prepare students for the study basic arithmetic, and then starting to work with variables and slowly growing to work with complex problems.
Why set-theory is required?
Set theory is the common language to speak about mathematics, so learning set theory means learning the common language. It allows us to better understand infinite objects, and the assumptions needed to better control their behavior.
Why do we need algebra?
Algebra makes it easy to state a mathematical relationship and its equation by using letters of the alphabet or other symbols to represent entities as a form of shorthand. Algebra then allows you to substitute values in order to solve the equations for the unknown quantities.