Suppose we have some topological spaces lying around. How can we build new topological spaces using the old ones? There are four fundamental constructions: subspaces, disjoint unions, products, and quotients. Defining the topologies on each can be done in two ways. One way is through ad hoc definitions. These definitions make some intuitive sense, but look very different from one construction to the next. The other way uses canonical maps. Canonical maps provide a single framework in which all constructions obey the same unifying principle.
A clean and easy to use LaTeX template for homework / assignments. Applicable at the university level for math and computer science courses. Problems and solutions are neatly organized, can be renamed, and referenced in a brief table of contents. Customizeable author, course, title information. Custom footers highlight sections that span pages.
This is the template, originally written by Dr. Tom Heinzl, which we use for group projects in the final year of Mathematical Science degrees at the University of Plymouth. I have modified the example to use BibTeX.