1. An algorithmic trading management computer system for facilitating electronic market participation of traders, the algorithmic trading management computer system comprising: a sequence construction module for providing, using computer processing components, conditional user interface features on a computer user interface for allowing traders to construct a sequence for structuring at least one trading order, the sequence construction module automatically generating at least one trading algorithm sequence based on the constructed sequence for structuring at least one trading order; sequence modification components for allowing, using the computer processing components, traders to modify collected algorithms collected from external sources in order to customize the sequence through the computer user interface, the sequence modification components automatically modifying the at least one algorithm sequence based on the customization; and operator intervention tools for allowing, using the computer processing components, traders to manually influence sequence execution through the computer user interface wherein the at least one algorithm sequence is processed by at least one computing processing component to complete at least one trading order.