| 1 |
Abstract Algebra |
Study of algebraic structures such as groups, rings, and fields. |
Cryptography, Coding Theory |
Emmy Noether |
| 2 |
Linear Algebra |
Study of vectors, vector spaces, and linear mappings. |
Computer Graphics, Data Science |
John von Neumann |
| 3 |
Algebraic Geometry |
Study of geometric properties using algebraic techniques. |
Robotics, Computer Vision |
David Hilbert |
| 4 |
Homotopy Theory |
Study of topological spaces with respect to homotopic relations. |
Algebraic Topology, Physics |
Henri Poincaré |
| 5 |
Commutative Algebra |
Study of commutative rings and their ideals. |
Algebraic Geometry, Number Theory |
David Eisenbud |
| 6 |
Universal Algebra |
General study of algebraic structures and their properties. |
Computer Science, Logic |
Alfred Tarski |
| 7 |
Noncommutative Algebra |
Study of algebraic structures where multiplication is not commutative. |
Quantum Physics, Operator Theory |
Niels Bohr |
| 8 |
Representation Theory |
Study of algebraic structures through linear transformations. |
Physics, Chemistry |
William Burnside |
| 9 |
Algebras over a Field |
Study of vector spaces equipped with a multiplication. |
Quantum Mechanics, Signal Processing |
George W. Mackey |
| 10 |
Lie Algebra |
Study of algebraic structures capturing the essence of symmetry. |
Theoretical Physics, Differential Equations |
Sophus Lie |
| 11 |
Rings and Fields |
Basic structures in modern algebra dealing with operations. |
Cryptography, Coding Theory |
Karl Weierstrass |
| 12 |
Category Theory |
Study of mathematical structures and relationships between them. |
Abstract Algebra, Topology |
Samuel Eilenberg |
| 13 |
Algebraic K-Theory |
Study of vector bundles and projective modules. |
Number Theory, Algebraic Geometry |
Michael Atiyah |
| 14 |
Graded Algebra |
Study of algebras decomposed into direct sums related by degree. |
Combinatorics, Representation Theory |
David Brion |
| 15 |
Quantum Algebra |
Study of algebraic structures in quantum mechanics. |
Theoretical Physics, Quantum Computing |
Vladimir Drinfeld |
| 16 |
Discrete Mathematics |
Study of discrete elements that uses algebraic techniques. |
Computer Science, Cryptography |
László Lovász |
| 17 |
Boolean Algebra |
Study of algebraic structures that capture the logic of true/false values. |
Computer Science, Digital Logic |
George Boole |
| 18 |
Multilinear Algebra |
Study of algebra involving multi-dimensional arrays (tensors). |
Physics, Engineering |
Hermann Grassmann |
| 19 |
Functional Algebra |
Study of functions and their algebraic properties. |
Analysis, Approximation Theory |
Fréchet and Banach |
| 20 |
Nonlinear Algebra |
Study of algebraic structures with nonlinear operations. |
Complex Systems, Dynamics |
Alfredo B. P. B. B. D. Dehghani |
| 21 |
Fuzzy Algebra |
Study of algebra based on fuzzy logic concepts. |
Artificial Intelligence, Control Systems |
Lotfi Zadeh |
| 22 |
Algebraic Dynamics |
Study of algebraic structures over the field of dynamics. |
Cryptography, Theoretical Computer Science |
N. Koblitz |
| 23 |
Real Algebraic Geometry |
Study of real-valued functions defined algebraically. |
Optimization, Control Theory |
C. A. Lloyd |
| 24 |
Algebraic Number Theory |
Study of algebraic structures related to the integers. |
Cryptography, Diophantine Equations |
Kurt Gödel |
| 25 |
Matrix Algebra |
Study of algebra involving matrices. |
Statistics, Computer Graphics |
Julius von Neumann |
| 26 |
Polynomial Algebra |
Study of polynomials and their algebraic properties. |
Control Theory, Signal Processing |
Galois and Abel |
| 27 |
Iterated Algebraic Structures |
Study of composed algebraic structures. |
Fractal Geometry, Image Processing |
Benoit B. Mandelbrot |
| 28 |
Ordered Algebraic Structures |
Study of algebraic structures with a defined order. |
Lattice Theory, Data Structures |
George Birkhoff |
| 29 |
Geometry of Numbers |
Study of whole-number lattices in Euclidean spaces. |
Number Theory, Optimization |
Carl Friedrich Gauss |
| 30 |
Positive Algebra |
Study of algebraic properties of positive numbers. |
Statistics, Economics |
David B. Johnson |
| 31 |
Tropical Geometry |
Study of algebraic structures under tropical operations. |
Combinatorial Optimization, Topology |
Gian-Carlo Rota |
| 32 |
Spectral Algebra |
Study of algebraic structures related to eigenvalues and eigenvectors. |
Quantum Mechanics, Control Systems |
John von Neumann |
| 33 |
Algebraic Topology |
Study of topological spaces through algebraic methods. |
Data Analysis, Network Theory |
Henri Poincaré |
| 34 |
Complex Algebra |
Study of numbers in the complex number system. |
Electrical Engineering, Quantum Physics |
Carl Friedrich Gauss |
| 35 |
Higher Algebra |
Study of algebraic structures in higher dimensions. |
Complex Geometry, Algebraic Topology |
L. Marie V. C. G. K. J. Ellison |
| 36 |
Vector Algebra |
Study of algebra involving vectors. |
Physics, Engineering |
Isaac Newton |
| 37 |
Descriptive Set Theory |
Study of sets and functions through algebraic means. |
Real Analysis, Topology |
Paul Cohen |
| 38 |
Nonlinear Dynamics |
Study of systems that exhibit nonlinear behavior. |
Physics, Ecology |
Henri Poincaré |
| 39 |
Algebraic Combinatorics |
Study of algebraic structures in combinatorial settings. |
Graph Theory, Optimization |
László Babai |
| 40 |
Combinatorial Algebra |
Study of algebraic structures related to combinatorial objects. |
Data Science, Coding Theory |
Richard P. Stanley |
| 41 |
Symbolic Algebra |
Study of algebraic structures focusing on symbols and variables. |
Computer Algebra Systems, AI |
Jean-Pierre Serre |
| 42 |
Rational Algebra |
Study of algebraic structures that involve rational expressions. |
Number Theory, Algebraic Geometry |
Richard Dedekind |
| 43 |
Stable Homotopy Theory |
Study of homotopical features in stable categories. |
Mathematical Physics, Algebraic Topology |
M. Hovey |
| 44 |
Spectral Theory |
Study of the eigenvalues and eigenvectors of operators. |
Functional Analysis, Quantum Mechanics |
David Hilbert |
| 45 |
Hilbert Algebras |
Study of algebraic structures with a Hilbert space connection. |
Functional Analysis, Quantum Mechanics |
David Hilbert |
| 46 |
Partial Algebra |
Study of algebraic structures that are not fully defined everywhere. |
Mathematical Programming, Computer Science |
Z. L. P. V. C. A. K. C. V. C. O. N. Us |
| 47 |
Affine Algebra |
Study of algebraic structures related to affine spaces. |
Geometry, Optimization |
Julius von Neumann |
| 48 |
Action Algebra |
Study of groups acting on algebraic structures. |
Topological Dynamics, Group Theory |
Évariste Galois |
| 49 |
Form Algebra |
Study of algebraic structures based on specific forms or representations. |
Algebraic Surfaces, Model Theory |
David Hilbert |
| 50 |
Minimal Algebra |
Study of algebraic structures that avoid redundancy. |
Formal Methods, Code Optimization |
J. D. R. R. M. B. R. F. G. B. B. C. F. G. H. |
| 51 |
Geometric Algebra |
Study of algebraic structures that also incorporates geometry. |
Computer Graphics, Physics |
Clifford and Grassmann |
| 52 |
Cohomological Algebra |
Study of cohomology theories and their algebraic connections. |
Algebraic Geometry, Topology |
H. Cartan |
| 53 |
Differential Algebra |
Study of algebraic structures through differential operations. |
Control Theory, Dynamical Systems |
H. B. Fine |
| 54 |
Algebraic Logic |
Study of logical structures using algebraic methods. |
Mathematical Logic, Computer Science |
Larry V. H. C. J. De Jongh |
| 55 |
Parametric Algebra |
Study of algebraic structures varying with parameters. |
Control Theory, Mathematical Finance |
P. M. L. J. R. R. St. M. |
| 56 |
Homological Algebra |
Study of algebraic structures using sequences and diagrams. |
Algebraic Topology, Algebraic Geometry |
Daniel Quillen |
| 57 |
Boolean Network Algebra |
Study of states and transitions in Boolean networks. |
Systems Biology, Control Theory |
John von Neumann |
| 58 |
Algebraic Cryptography |
Application of algebraic structures in cryptographic systems. |
Secure Communications, Data Protection |
Whitfield Diffie and Martin Hellman |
| 59 |
Monoidal Algebra |
Study of monoids and their algebraic properties. |
Category Theory, Homotopy Theory |
Saunders Mac Lane |
| 60 |
Reed-Muller Algebra |
Study of polynomial functions defined over finite fields. |
Error-Correction Codes, Information Theory |
Robert W. R. Reed |
| 61 |
Algebra of Functions |
Study of functions under algebraic operations. |
Functional Analysis, Approximation Theory |
Henri Lebesgue |
| 62 |
Stochastic Algebra |
Study of algebraic structures in stochastic processes. |
Probability Theory, Statistics |
Andrey Kolmogorov |
| 63 |
Ramsey Theory |
Study of conditions under which a certain order must appear. |
Combinatorics, Graph Theory |
Frank Ramsey |
| 64 |
Geometric Probability Algebra |
Study of probabilities related to geometric figures and properties. |
Statistics, Theoretical Physics |
Georgy P. M. W. H. H. R. A. |
| 65 |
Lattice Algebra |
Study of algebraic structures based on lattice theory. |
Distributive Algebra, Combinatorics |
Birkhoff and R. L. P. R. L. N. C. C. |
| 66 |
Tropical Algebra |
Study of an algebraic system with different operations. |
Mathematics, Computer Science |
Gian-Carlo Rota |
| 67 |
Time Series Algebra |
Study of algebraic structures related to time series. |
Economics, Data Science |
P. M. B. C. A. Z. D. J. |
| 68 |
Dual Algebra |
Study of algebraic structures and their dual representations. |
Linear Algebra, Functional Analysis |
Henry J. Fréchet |
| 69 |
Fuzzy Set Algebra |
Study of algebraic operations in fuzzy set theory. |
Artificial Intelligence, Control Systems |
Lotfi A. Zadeh |
| 70 |
Vector-Valued Algebra |
Study of algebra involving vector-valued functions. |
Vector Calculus, Engineering |
David M. E. A. V. W. |
| 71 |
Design Algebra |
Study of algebraic structures in the design of experiments. |
Statistics, Engineering |
Ronald A. Fisher |
| 72 |
Error-Correcting Algebra |
Study of algebraic codes that can correct errors in data transmission. |
Information Theory, Computer Science |
Richard Hamming |
| 73 |
Noncommutative Geometry |
Study of geometry in noncommutative settings. |
Theoretical Physics, Quantum Mechanics |
Alain Connes |
| 74 |
Cryptographic Algebra |
Study of algebra applied to cryptography and secure communications. |
Cyber Security, Information Theory |
Rivest, Shamir, and Adleman |
| 75 |
Algebraic Statistics |
Study of statistical methods using algebraic structures. |
Data Analysis, Econometrics |
David R. Cox |
| 76 |
Complex Systems Algebra |
Study of algebraic structures in complex systems and networks. |
Physics, Ecology |
D. U. E. C. |
| 77 |
Sparse Algebra |
Study of algebraic objects with many zero entries or low dimensionality. |
Data Compression, Machine Learning |
Anonymous |
| 78 |
Modular Algebra |
Study of algebraic structures under modular constraints. |
Number Theory, Cryptography |
Augustin-Louis Cauchy |
| 79 |
Stochastic Process Algebra |
Study of algebraic structures in stochastic modeling. |
Finance, Risk Management |
K. J. M. D. |
| 80 |
Probabilistic Algebra |
Study of algebra involving probability and expectation. |
Statistics, Data Science |
Andrey Kolmogorov |
| 81 |
Interactive Algebra |
Study of algebraic structures applied in interactive systems. |
Human-Computer Interaction, AI |
Jacques Chabanol |
| 82 |
Structural Algebra |
Study of the underlying structures of algebraic theories. |
Abstract Algebra, Model Theory |
F. W. Lawvere |
| 83 |
Finite Algebra |
Study of algebraic structures over finite sets or fields. |
Combinatorics, Group Theory |
Jean-Pierre Serre |
| 84 |
Influential Algebra |
Study of how algebraic properties can influence systems. |
Complexity Theory, Systems Analysis |
Alfredo. M. H. S. H. |
| 85 |
Algebraic Entropy |
Study of measures of complexity in algebraic systems. |
Information Theory, Complexity Science |
Samir K. M. H. C. N. B. |
| 86 |
Braid Algebra |
Study of algebraic structures that encapsulate braiding operations. |
Topological Studies, Physics |
Emmy Noether |
| 87 |
Self-Dual Algebra |
Study of algebraic structures that are self-dual in nature. |
Mathematical Logic, Quantum Physics |
Josse C. C. De E. |
| 88 |
Comprehensive Algebra |
A broad study of various algebraic structures and their interrelations. |
Mathematics, Engineering |
C. A. B. R. |
| 89 |
Exponential Algebra |
Study of properties involving exponential functions in algebra. |
Mathematics, Economics |
Anonymous |
| 90 |
Polynomial Time Algebra |
Study of polynomial-time algorithms in algebraic computations. |
Computer Science, Algorithm Theory |
Anonymous |
| 91 |
Linear Time Algebra |
Study of linear-time complexity in algebraic algorithms. |
Computer Science, Complexity Theory |
Anonymous |
| 92 |
Constructive Algebra |
Study of algebraic systems that can be constructed effectively. |
Computer Science, Logic |
Ernst Zermelo |
| 93 |
Temporal Algebra |
Study of algebraic structures with respect to time variables. |
Computing, AI |
Anonymous |
| 94 |
Polynomial Function Algebra |
Study of algebraic functions expressed as polynomials. |
Mathematics, Computer Science |
George B. R. H. |
| 95 |
Invariant Theory |
Study of algebraic structures invariant under group actions. |
Classical Geometry, Algebraic Geometry |
W. H. Abel |
| 96 |
Quasi-Algebraic Structures |
Study of structures that are partially algebraic. |
Nonlinear Systems, Numerical Methods |
Anonymous |
| 97 |
Normed Algebra |
Study of algebraic systems with a norm defined on them. |
Functional Analysis, Banach Spaces |
Stefan Banach |
| 98 |
Hybrid Algebra |
Study of algebraic structures combining different types of algebra. |
Economics, Engineering |
Anonymous |
| 99 |
Quantum Field Theory Algebra |
Study of algebraic properties in quantum field theory. |
Physics, Quantum Computing |
Richard Feynman |
| 100 |
Algorithmic Algebra |
Study of algebraic methods in solving computational problems. |
Computer Science, Data Structures |
Anonymous |