Visualizing a university’s catalog can illuminate aspects of the curriculum design. These characteristics should match our understanding of the disciplines being taught at the school.
As the largest university in the U.S., the University of Central Florida (UCF) has painstakingly built a robust catalog of colleges, departments, majors, and courses to service approximately 60,000 students each semester. These resources are all related in various ways: colleges have departments which curate majors that are comprised of courses that have other courses as prerequisites.
These relationships give rise to implicit connections between the disciplines of study. In what follows, we use a method of laying out these resources called a force layout, which visually positions elements together or apart based on simulated forces that depend on the connections between the elements.
Visualizing a College
A visualization of UCF’s College of Sciences reveals patterns that match our intuitions. Large nodes are departments, medium nodes are majors, and small nodes are courses. Lines connect nodes according to the aforementioned relationships:
As you traverse the graph around the top outer edge going left, you see the manifestation of the purity spectrum of the sciences, hilariously depicted in this xkcd comic:
Another interesting facet of this graph is the central position occupied by the department of statistics. As one moves from theoretical to empirical, the language of science shifts from the mother tongue of mathematics to the dialect of statistics. This medial position corroborates the classification of statistics as the “servant of all science.”
Lastly, we can find political science almost isolated at the bottom, suggesting that it’s a science of a special breed. Indeed, political science is a primarily observational endeavor, not experimental like most of the other sciences, although this isn’t always the case.
Visualizing a Major
Using UCF’s Mathematics major as example, we can see a rich structure emerge. The intricate set of course requirements induces a format that belies the graduated nature of mathematical understanding. Certain concepts must be learned incrementally at the zone of proximal development to ensure that the student can digest higher level materials.
In the graph above, the radius of a course corresponds the the number of courses that have it as a prerequisite. From this we can quickly identify the seminal courses in a math degree at UCF: Logic and Proof, Linear Algebra, and Calculus with Analytic Geometry III.
According to Alex Wissner-Gross, intelligence is characterized by the maximization of future freedom of action. To ensure that you have the most freedom of choice in what you can take in following semesters, it makes sense to take these foundational courses early.
By contrast, a psychology degree at UCF has a less rigid structure:
From this graph it’s apparent that once we’ve taken General Psychology, we’ve unlocked access to mostly all the courses necessary for a Psychology degree at UCF.
Possible Extensions with Data
If we had data on student grades and course choices semester after semester, we could identify the choke-points of a degree, i.e. where students are failing in their progression. We can use this information along with machine learning to improve advising services that assist students in choosing optimal paths through a degree, based on the data of other students like them who have succeeded. This data-driven advising could augment or replace curricular suggestions that have historically been based on faulty human insight, to the benefit of all students.