  The structure of knowledge is commonly described as a network of key concepts
and semantic relations between them. A learner of a particular domain can
discover this network by navigating the nodes and edges presented by
instructional material, such as a textbook, workbook, or other text. While over
a long temporal period such exploration processes are certain to discover the
whole connected network, little is known about how the learning is affected by
the dual pressures of finite study time and human mental errors. Here we model
the learning of linear algebra textbooks with finite length random walks over
the corresponding semantic networks. We show that if a learner does not keep up
with the pace of material presentation, the learning can be an order of
magnitude worse than it is in the asymptotic limit. Further, we find that this
loss is compounded by three types of mental errors: forgetting, shuffling, and
reinforcement. Broadly, our study informs the design of teaching materials from
both structural and temporal perspectives.
