Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory, algebra, geometry, analysis, and set theory.
Glossary Collection: A Guide to Mathematical Jargon
Mathematics is a discipline that uncovers and organizes methods, theories, and theorems—developed both in service of empirical sciences and for its own advancement. It spans a vast range of interconnected fields, including number theory, algebra, geometry, analysis, and set theory.
This guide is a curated glossary collection designed for students, enthusiasts, and anyone curious about the language of mathematics. Whether you’re reviewing foundational principles or exploring advanced topics, this alphabetical reference list provides a helpful overview of key areas in the mathematical sciences.
A – Algebra and Beyond
- Linear Algebra – Vectors, matrices, transformations, and linear mappings.
- Algebraic Geometry – The intersection of algebra and geometry through polynomial equations.
- Algebraic Topology – The use of algebraic tools to study topological spaces.
- Areas of Mathematics – A high-level view of the many branches within mathematics.
C – Calculus, Categories, and Cryptography
- Calculus – The study of change through limits, derivatives, and integrals.
- Category Theory – A high-level framework connecting various mathematical structures.
- Commutative Algebra – A study of commutative rings and their properties.
- Cryptographic Keys – Mathematical terms used in securing information.
E – Experimental Methods
- Experimental Design – Planning and analyzing experiments using statistical principles.
F – Fields and Functional Spaces
- Field Theory – The theory of fields and their algebraic extensions.
- Functional Analysis – Focused on infinite-dimensional vector spaces and linear operators.
G – Games, Geometry, Graphs, and Groups
- Game Theory – Mathematical models of strategic interaction and decision-making.
- Arithmetic and Diophantine Geometry – Equations and solutions in the realm of integers.
- Classical Algebraic Geometry – Traditional studies of algebraic curves and surfaces.
- Differential Geometry and Topology – Geometry through differential and topological methods.
- Riemannian and Metric Geometry – Structures defined by distance and curvature.
- Graph Theory – The mathematics of networks, nodes, and connections.
- Group Theory – The study of symmetry and algebraic structures.
I – Invariant Concepts
- Invariant Theory – The study of properties that remain unchanged under transformations.
L – Lie Structures
- Lie Groups and Lie Algebras – Continuous symmetries and their algebraic representations.
M – Modules and Their Applications
- Module Theory – An extension of linear algebra to general rings.
N – Numbers and Their Properties
- Number Theory – The study of integers and their relationships.
O – Order and Structure
- Order Theory – Mathematical frameworks for ordering and comparison.
P – Principia and Probability
- Principia Mathematica – Key terminology from one of mathematics’ foundational texts.
- Probability and Statistics – Analyzing randomness, uncertainty, and data.
R – Real and Complex Systems
- Real and Complex Analysis – Understanding functions, limits, and continuity in various number systems.
- Representation Theory – How algebraic structures can be represented by matrices and linear transformations.
- Ring Theory – A study of algebraic structures involving rings and ideals.
S – Sets, Symbols, and Systems
- Set Theory – The fundamental language of mathematics, dealing with collections of objects.
- Shapes with Metaphorical Names – Playful and descriptive terms for geometric structures.
- Mathematical Symbols – A glossary of the symbols that define mathematical language.
- Symplectic Geometry – Mathematical structures used in classical mechanics.
- Systems Theory – The study of complex, interacting components in mathematical models.
T – Tensors and Topological Spaces
- Tensor Theory – Generalizations of vectors and matrices to higher dimensions.
- General Topology – The study of space, continuity, and convergence in abstract settings.