Introduction to Relations: A relation is a set of ordered pairs, where each element from one set is associated with one or more elements of another set. It is an important concept in mathematics, particularly in algebra and set theory,…
Introduction to Algorithms: An algorithm is a step-by-step set of instructions or rules designed to solve a specific problem or perform a computation. Algorithms are fundamental to computer science, helping in tasks like data processing, calculation, and automated reasoning. Definition…
Introduction to Recurrence Relations: Recurrence relations provide a mathematical framework for defining sequences and functions based on previous terms. They are widely used in various fields, including computer science, combinatorics, and number theory. Definition of Recurrence Relations: A recurrence relation…
Introduction to Number Theory Number theory is a branch of pure mathematics devoted primarily to the study of integers and integer-valued functions. Historically, number theory is one of the oldest branches of mathematics, as it has its origins in the…
Introduction to Graph Theory Graph theory is a branch of mathematics that deals with the study of graphs. A graph is a collection of points (called vertices or nodes) connected by lines (called edges or links). Graph theory has applications…
Introduction to Combinatorics Combinatorics is a branch of mathematics focused on counting, arranging, and combining objects. It has applications in numerous fields, including computer science, cryptography, probability theory, and optimization. It involves a variety of concepts such as permutations, combinations,…
Introduction to Logic Logic is the foundation of mathematical reasoning and philosophy. It is the study of principles of valid inference and demonstration. Logic allows us to construct and analyze arguments, test their validity, and deduce conclusions from premises. There…
Introduction to Set Theory Set theory is a branch of mathematical logic that studies collections of objects, called sets. Set theory is fundamental to nearly every other part of mathematics and is used to define and analyze mathematical concepts, from…