Discrete Mathematics#
Discrete Mathematics is the branch of Math studying separate, countable objects rather than smooth, continuous changes. It uses distinct values, integers, and logic instead of calculus or real numbers. It serves as the core mathematical foundation for computer science, coding, and digital systems.
A function is a rule that assigns each input exactly one output.
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links, or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
A matrix is some table of numbers, symbols, or mathematical objects coming from a set. A matrix has a “height” and a “width” corresponding to the number of rows and the number of columns, respectively. We describe a matrix first by its number of rows and then by its number of columns.
Propositional logic is concerned with statements to which the truth values, true and false, can be assigend. The purpose is to analyze these statements either individually or in a composite manner.
Set theory in discrete mathematics is the foundational branch of mathematical logic that studies sets, which are unordered collections of distinct objects.