  Traffic jams on roadways, echo chambers on social media, crowds of moving
pedestrians, and opinion dynamics during elections are all complex social
systems. These applications may seem disparate, but some of the questions that
they motivate are similar from a mathematical perspective. Across these
examples, researchers seek to uncover how individual agents -- whether drivers,
Twitter accounts, pedestrians, or voters -- are interacting. By better
understanding these interactions, mathematical modelers can make predictions
about the group-level features that will emerge when agents alter their
behavior. In this tutorial, which is based on the lecture that I gave at the
2021 American Mathematical Society Short Course, I introduce some of the terms,
methods, and choices that arise when building such data-driven models. I
discuss the differences between models that are statistical or mathematical,
static or dynamic, spatial or non-spatial, discrete or continuous, and
phenomenological or mechanistic. For concreteness, I also describe models of
two complex systems, election dynamics and pedestrian-crowd movement, in more
detail. With a conceptual approach, I broadly highlight some of the challenges
that arise when building and calibrating models, choosing complexity, and
working with quantitative and qualitative data.
