Is everything
Our universe is not described by mathematics.
It is mathematics. - Max Tegmark
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The ontological graph organizes core mathematical concepts to build understanding and reveal their underlying connections.
A formal ontology of Algebrica’s content is currently under development and will be released using OWL, while progressively refining the underlying RDF schema and SKOS conceptual structures.
Sets and Numbers
Begin with the essential math concepts that form the basis for everything else.
Algebraic Structures
Algebraic structures organize mathematical objects and operations into systems such as groups, rings, and fields, providing a unified framework to study their properties and relationships.
Powers, Radicals and Logarithms
Explore powers, radicals, and logarithms as interconnected structures, emphasizing their formal definitions, algebraic properties, and underlying relationships within a unified framework.
Complex Numbers
The field of complex numbers constitutes a fundamental extension of the real number system, obtained by adjoining a unit whose square is negative, thereby enabling the representation of quantities not contained in the real domain.
Trigonometry
Trigonometry establishes quantitative relationships between angles and side lengths in right triangles through the introduction of trigonometric functions, providing a formal framework for analyzing geometric and analytic properties of angular measures.
Polynomials
Polynomials are algebraic expressions formed by variables, coefficients, and non-negative integer powers, combined through basic arithmetic operations and organized by degree.
Equations
Equations express equalities between mathematical quantities and constitute a fundamental tool for formulating and solving problems across all areas of mathematics.
Inequalities
Inequalities express order relations between quantities, using comparison symbols to define admissible ranges and constraints.
Lines, Planes and Conic Sections
Conic sections are curves obtained from the intersection of a plane with a cone, studied through the geometric relationships between lines, planes, and quadratic forms.
Vectors and Matrices
Matrices are arrays of numbers arranged in rows and columns, used in linear algebra to represent linear transformations and systems of equations.
Linear Systems
A linear system consists of multiple linear equations considered simultaneously, whose solution corresponds to the set of values satisfying all equations.
Sequences
Sequences are ordered collections of numbers defined by a rule or formula, where each term is associated with an index, typically taken from the natural numbers.
Series
Series are infinite sums associated with sequences, formed by adding their terms in order and typically indexed by the natural numbers.
Functions
A function is a mapping that assigns a unique output to each input, constituting a fundamental concept in mathematics.
Limits
Limits describe the behavior of a function in the vicinity of a point and constitute a foundational concept in calculus and mathematical analysis.
Derivatives
The derivative describes the rate of change of a function and constitutes a central concept in differential calculus for the analysis of variation and optimization.
Differential Calculus Theorems
Core theorems characterize the behavior of differentiable functions, including results concerning limits, tangents, and mean value properties.
Integrals
An integral represents the accumulation of a function over an interval, often interpreted as the area under a curve.
Differential Equations
A differential equation relates a function to its derivatives and serves as a model for dynamic systems and continuous change.
Probability and Statistics
Probability and statistics provide a framework for analyzing uncertainty, modeling random phenomena.
Kinematics
Kinematics is the study of motion, focusing on trajectories, velocities, and accelerations, and describing how objects move through space and time.
Other Topics
Topics that warrant a complete treatment but do not yet belong to a defined category.