Abstract Algebra
Groups, rings, fields, modules.
Algebraic Geometry
Study of solutions of polynomial equations through geometric methods.
Algebraic Number Theory
Algebraic numbers, quadratic fields, zeta functions, cyclotomic fields.
Algebraic Topology
Fundamental group, homology, cohomology.
Analytic Number Theory
Prime number theorem, Dirichlet series, Sieve methods, Riemann zeta function, arithmetic functions.
Category Theory
Categories, morphisms, functors, natural transformations.
Class Field Theory
Advanced theory of algebraic number fields and their extensions.
Commutative Algebra
Study of commutative rings and their ideals.
Complex Analysis
Study of functions of complex variables and their properties.
Differential Equations
Study of equations involving derivatives and their solutions.
Differential Geometry
Study of geometric structures using calculus.
Differential Topology
Study of differentiable functions on manifolds.
Functional Analysis
Study of infinite-dimensional vector spaces with topology.
General Topology
Study of topological spaces and continuous functions.
Graph Theory
Study of graphs and their properties.
Lie Algebra
Study of algebraic structures arising from continuous symmetries.
Linear Algebra
Study of vector spaces and linear mappings between them.
Logic and Set Theory
Study of mathematical reasoning and foundations.
Mathematical Biology
Mathematical modeling of biological systems.
Measure Theory
Study of measures and measurable functions.
Number Theory
Study of integers and their properties.
Optimization
Study of methods to find minimum or maximum values.
Probability Theory
Study of random phenomena and probability spaces.
Real Analysis
Study of real numbers and functions of a real variable.
Representation Theory
Study of abstract algebraic structures by representing their elements as linear transformations.
Statistics
Study of data collection, analysis, interpretation, and presentation.
Stochastic Processes
Study of random processes that evolve over time.
Vector Calculus
Study of differentiation and integration of vector fields.
Miscellaneous
Additional important mathematical topics and resources.