Basic Mathematical Structures
[Video Introduction] (coming soon)
In this sequence of tutorials, we review some basic mathematical structures and concepts that provide the necessary foundation for discrete mathematics. These tutorials are compact and faster-paced than other topics in our tutorials, since most students should have seen this material well before they get to a college-level discrete mathematics class. The basic tutorials are the following.
Sets and Sequences: Sets, multisets, tuples, and sequences are basic mathematical structures used to represent collections of data. The differences really come down to whether duplicates are allowed in the collection, and whether the collection is ordered or not.
Relations: Given collections of data (for example, as a set), how can you represent relationships between items in one or more sets? Relations represent basic properties of pairs of items, such as one number being less than another (the “less than” relation).
Functions: Functions are really just a special kind of relation that meet certain requirements. If you’re a computer science student and have done some programming, you probably have an idea of a function as something that computes a value from inputs. While that’s not a bad mental model, it’s not the full mathematical concept – in particular, functions may or may not be computable!
Let’s get started.
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