Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. It’s a branch of mathematics that deals with networks of points (vertices or nodes) connected by lines (edges). Key Characteristics / Core Concepts Vertices (Nodes): Represent objects or entities. Edges: Represent the connections or relationships between vertices. … Read more
Geometry is the branch of mathematics that deals with the size, shape, and position of two-dimensional shapes and three-dimensional objects. It explores concepts like points, lines, angles, surfaces, and solids, and the relationships between them. Geometry forms the basis of many fields including architecture and engineering. Key Characteristics / Core Concepts Points: Locations in space … Read more
Functional analysis is a branch of mathematical analysis that studies vector spaces endowed with some kind of limit-related structure (e.g., inner product, norm, topology), along with linear functions defined on these spaces. It’s a powerful tool that connects abstract algebra, topology, and analysis, with applications throughout mathematics, engineering, and computer science. Key Characteristics / Core … Read more
Differential equations are mathematical equations that relate a function with its derivatives. They describe how a quantity changes over time or in relation to other variables. Key Characteristics / Core Concepts They involve derivatives (rates of change) of a function. They can be ordinary differential equations (ODEs), involving only one independent variable, or partial differential … Read more
Complex analysis is the branch of mathematics that deals with the study of complex numbers and functions of a complex variable. It extends the techniques of calculus to the complex plane, revealing powerful tools for solving problems in various fields. Key Characteristics / Core Concepts Complex Numbers: Numbers of the form a + bi, where … Read more
Calculus is a branch of mathematics focused on continuous change. It’s built upon the fundamental concepts of limits, derivatives, and integrals. Key Characteristics / Core Concepts Limits: The foundation of calculus; exploring the behavior of a function as its input approaches a certain value. Derivatives: Measure the instantaneous rate of change of a function, often … Read more
Applied mathematics is the application of mathematical methods and techniques to solve problems in other fields. It bridges the gap between abstract mathematical theories and real-world applications. Key Characteristics / Core Concepts Problem-solving focus: Applied math prioritizes finding solutions to practical problems. Interdisciplinary nature: It draws upon various mathematical disciplines (calculus, statistics, etc.) and applies … Read more
Abstract algebra is the study of algebraic structures, which are sets equipped with operations that satisfy certain axioms. It moves beyond the concrete numbers and variables of elementary algebra to explore more general concepts and relationships. Key Characteristics / Core Concepts Groups: Sets with a single binary operation satisfying closure, associativity, identity, and inverse properties. … Read more
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols to solve equations. It provides a framework for representing and solving problems involving unknown quantities. Key Characteristics / Core Concepts Variables: Symbols (usually letters) representing unknown values. Equations: Statements showing the equality of two expressions. Expressions: Combinations of variables, … Read more