The Rithmatist is a book (first in a planned series by the same name) by Sanderson. Who exactly is "the" Rithmatist referred to by the title? The school that is the main setting for the book has a dedicated program for Rithmatists, which most of the characters are connected to, so it's not as if there's a clear choice for "the" Rithmatist.
Coming at this after another re-read, I think that there's something clever going on with this title: when it says "The Rithmatist", it's actually referring to two people together (Joel and Melody). This answer will lack nice direct quotes because I only managed to get my hands on an audiobook.
Joel and Melody are arguably the two most major characters in the novel. As we are introduced to them at the beginning, he's an ordinary non-Rithmatist (just a student attending the general school who is obsessed with Rithmatics) and she's a failing Rithmatist (struggling with the basics and wishing she could drop out). Alone, neither could be called a fully competent Rithmatist, even on the level expected of a student. However by the end, they can work in harmony to be more than the sum of their parts and act as a capable Rithmatist.
The book traces their growing friendship and trust, leading up to the twin climaxes: the dorm fight and the melee.
The dorm fight makes it clear that neither alone is enough. Joel can't defend himself without Rithmatic powers, and Melody panics, unsure what to do with the powers she has. What they end up doing requires both of them, as she draws the maze he tells her to, while he waits and times when to get the Scribbler's attention. They work together to trap enemy chalklings inside said maze. Crucially, Melody doesn't understand what's happening at first. She questions Joel using his chalk, possessed of no magic, for part of the maze. However she trusts him enough to not ask too many questions.
But it's the melee, which serves as a climax for the internal arcs of each character and their friendship arc, where them working as one is really hammered in. They fight from the same circle, something which we are informed is technically legal - but a regular Rithmatist would want their own circle, to take their own chances instead of relying entirely on a circlemate. Joel takes the role of planning, again, drawing their defense to precise geometric specification. Melody is the Rithmatic hand and creative spirit, tracing Joel's lines and drawing pretty unicorn chalklings (which Joel objects to on the grounds of not being "manly", then concedes). Joel understands the bookish theory. Melody understands the chalklings, which work on a level beyond dry book theories. Together they work side-by-side in trust, with the book emphasizing their easy communication, eventually winning the melee against all odds.
They are the winning Rithmatist.
 Specifically "The Rithmatist, a Macmillian Audio Production from Tor Books" and "read by Michael Kramer"
 Joel more so than Melody (he's the point-of-view character for nearly all the book), but she crashes into his storyline and gets her own intertwined arc.
 It's more fitting to be here instead of the dorm fight, anyways - the dorm fight is a climax for the main external arc, which Joel is much more involved in than Melody. Thus his talents are rightfully emphasized more in it.