Overview
The series is split into how many different arcs?
Pretty Little Liars
The Wonderful Wizard of Oz (1986 TV series) Story arc Hardy–Littlewood circle method Mobile Suit Gundam AGE Yu-Gi-Oh! Duel Monsters
The_Wonderful_Wizard_of_Oz_(1986_TV_series)-The_plot Story_arc-Story_arcs_in_television Hardy–Littlewood_circle_method-Outline Mobile_Suit_Gundam_AGE-Plot Yu-Gi-Oh!_Duel_Monsters-Plot
"The Wonderful Wizard of Oz" is split into four distinct parts, or story arcs, each loosely based on different Oz books originally written by L. Frank Baum. 
s in television. Story arcs on television have existed for decades, and are common in many countries where multi-episode storylines are the norm (an example being the UK's "Doctor Who"), as well as most anime series. Many arc-based series in past decades, such as "V", were often short-lived and found it difficult to attract new viewers; they also rarely appear in traditional syndication. However, the rise of DVD retail and DVR of television series has worked in arc-based productions' favor as the standard season collection format allows the viewer to have easy access to the relevant episodes. One area of television where story arcs have always thrived, however, is in the realm of the soap opera, and often episodic series have been derisively referred to as "soap operas" when they have adopted story arcs. Arc-based series draw and reward dedicated viewers, and fans of a particular show follow and discuss different story arcs independently from particular episodes. Story arcs are sometimes split into subarcs if deemed significant by fans, making it easy to refer to certain episodes if their production order titles are unknown. Episodes not relevant to story arcs are sometimes dismissed as filler by fans, but might be referred to as self-contained or stand-alone episodes by producers. 
The goal is to prove asymptotic behavior of a series: to show that "a""n" ~ "F"("n") for some function. This is done by taking the generating function of the series, then computing the residues about zero (essentially the Fourier coefficients). Technically, the generating function is scaled to have radius of convergence 1, so it has singularities on the unit circle – thus one cannot take the contour integral over the unit circle. The circle method is specifically how to compute these residues, by partitioning the circle into minor arcs (the bulk of the circle) and major arcs (small arcs containing the most significant singularities), and then bounding the behavior on the minor arcs. The key insight is that, in many cases of interest (such as theta functions), the singularities occur at the roots of unity, and the significance of the singularities is in the order of the Farey sequence. Thus one can investigate the most significant singularities, and, if fortunate, compute the integrals. 
The story of "Gundam AGE" is separated into three arcs, each revolving around a different protagonist. 
Like the earlier series, "Duel Monsters" is mainly about the various battles of a high school freshman named Yugi Mutou. However, now it's through a card game known as "Duel Monsters" ("Magic and Wizards" in the original manga, although "Duel Monsters" is also used) instead of games in general. "Duel Monsters" features major differences to the manga's storyline, including some original story arcs. The plot of "Duel Monsters" is split up into several different storylines, or arcs. 