Pre-Calculus is the academic step before the incorporation of Calculus principles applied to real and imagined universal problems. A student entering a Pre-Calculus environment should be familiar with mathematics as a language and skill useful in both defined and imagined spaces. Pre-Calculus introduces mathematicians to a compendium of symbols and universal concepts including line tangentials, maximums and minimums, logarithmic line equations, the Karp Reduction, norms and lengths, symmetric differences and the occurrence of projected spaces. Pre-Calculus courses dedicate considerable amounts of time and resources to help students become familiar with the language and standard nomenclature of advanced Calculus and its applications.