Skip to main content

TUM Classification System - Mathematics

ALL
ARC
BAU
BER
BIO
BRA
CHE
CIT
DAT
EDU
ELT
ERG
FEI
FER
FOR
GEO
GES
HUE
IND
INF
JUR
KOM
KUN
LAN
LEB
LIN
LIT
MAS
MAT
MED
MSR
MTA
NAT
NUC
OEK
PHI
PHY
POL
PSY
REL
RPL
SOZ
SPO
TEC
UMW
VER
VET
WEH
WER
WIR
WIS
X
Back to subject overview
Register
MAT 000Belonging to the Subject; not further Classified
MAT 001Mathematics in General; Complete Overviews
MAT 030Mathematical Logic
MAT 040Set Theory
MAT 050Combinatorics; Classical Problems
MAT 060Lattice Theory
MAT 080General Algebraic Systems
MAT 100Number Theory; Elementary Number Theory
MAT 110Algebraic Theories (Textbooks Covering Several Areas from 120 - 220)
MAT 120Algebraic Number Theory; Fields; Polynomials
MAT 130Commutative Algebra
MAT 140Algebraic Geometry
MAT 150Linear Algebra; Matrix Theory
MAT 160Associative Rings and Algebras
MAT 170Nonassociative Rings and Algebras
MAT 180Category Theory
MAT 200Group Theory
MAT 220Topological Groups
MAT 260Calculus; Differentiation; Integration; Real Functions (Complete Overviews; Textbooks)
MAT 280Measure and Integration
MAT 300Functions of a Complex Variable
MAT 310Potential Theory; Harmonic Functions
MAT 320Functions of Several Complex Variables
MAT 330Special Functions
MAT 340Ordinary Differential Equations
MAT 350Partial Differential Equations
MAT 390Difference and Functional Equations; Integro Differential Equations; Algebraic Differential Equations
MAT 400Convergence; Summability; Limiting Processes
MAT 410Approximation Theory
MAT 420Harmonic Analysis; Fourier Analysis
MAT 430Abstract Harmonic Analysis
MAT 440Integral Transforms; Operational Calculus; Laplace Transform; Transforms of Special Functions
MAT 450Integral Equations
MAT 460Functional Analysis
MAT 470Operator Theory; Linear Operators
MAT 490Calculus of Variations and Optimal Control; Optimization
MAT 500Geometry in General (Textbooks Covering Several Areas from Mat 510 - 539)
MAT 540General Topology
MAT 550Algebraic Topology
MAT 570Topology of Manifolds
MAT 580Global Analysis; Analysis on Manifolds
MAT 600Probability Theory (incl. Textbooks on Probability Theory and Statistics)
MAT 620Statistics
MAT 650Numerical Analysis
MAT 900Operations Research; Management Science
MAT 910Mathematical Programming
MAT 920Game Theory
MAT 990Other Topics on Mat
  • MAT 000: Belonging to the Subject; not further Classified
  • MAT 001: Mathematics in General; Complete Overviews
    • MAT 002: Biographies, Festschrift, Commemorative Publications
    • MAT 003: Collected Works
    • MAT 006: Popular Science; Mathematics in Daily Life
    • MAT 007: Mathematical Basics; Elementary Mathematics
    • MAT 010: Philosophy of Science; Philosophy of Mathematics; Methodology and Sociology of Mathematics;
    • MAT 015: Training; Career; Professional Organisations; Academic Associations; Interest Groups
    • MAT 020: Didactics
    • MAT 021: Mathematics in Other Scholarly Disciplines (Comprehensive Literature)
      • MAT 022: Mathematics in the Natural and Life Sciences
      • MAT 023: Mathematics in Engineering Sciences and Computer Science
      • MAT 024: Mathematics in Economics and Social Sciences
      • MAT 025: Mathematics in Other Disciplines
    • MAT 029: Other
  • MAT 030: Mathematical Logic
    • MAT 032: Model Theory
    • MAT 034: Recursion Theory
    • MAT 036: Proof Theory; Constructive Mathematics
    • MAT 038: Nonstandard Models
    • MAT 039: Other
  • MAT 040: Set Theory
  • MAT 050: Combinatorics; Classical Problems
    • MAT 052: Designs and Configurations (Block Designs, Difference Sets, Matroids, Boolean Matrices, Steiner Systems, Tessellation, ...)
    • MAT 055: Graph Theory in General
      • MAT 056: Trees
      • MAT 057: Topological Aspects of Graph Theory; Embedding; Coloring of Graphs
      • MAT 058: Digraphs; Paths
      • MAT 059: Hypergraphs, Other
  • MAT 060: Lattice Theory
    • MAT 065: Ordered Sets
    • MAT 068: Ordered Structures
  • MAT 080: General Algebraic Systems
    • MAT 085: Varieties; Free Algebras
  • MAT 100: Number Theory; Elementary Number Theory
    • MAT 102: Diophantine Equations; Diophantine Approximation
    • MAT 103: Quadratic Forms; Modular and Automorphic Functions and Forms
    • MAT 104: Geometry of Numbers
    • MAT 105: Multiplicative Number Theory
    • MAT 106: Additive Number Theory
    • MAT 107: Metric Number Theory; Probabilistic Number Theory; Analytical Number Theory
    • MAT 109: Other
  • MAT 110: Algebraic Theories (Textbooks Covering Several Areas from 120 - 220)
  • MAT 120: Algebraic Number Theory; Fields; Polynomials
    • MAT 122: Global Fields
    • MAT 123: Local and P-Adic Fields
    • MAT 124: Finite Fields
    • MAT 125: Real and Complex Fields
    • MAT 126: Field Extensions
    • MAT 127: Topological Fields; General Valuation Theory
    • MAT 129: Other
  • MAT 130: Commutative Algebra
    • MAT 135: Specifications
  • MAT 140: Algebraic Geometry
    • MAT 141: Local Theory
    • MAT 142: Cycles and Subschemes; Families; Fibrations; Maps; Correspondence
    • MAT 143: Cohomology Theory
    • MAT 144: Arithmetic Problems; Special Ground Fields
    • MAT 145: Algebraic Curves
    • MAT 146: Surfaces and Higher-Dimensional Varieties
    • MAT 147: Abelian Varieties and Schemes; Group Schemes
    • MAT 149: Other
  • MAT 150: Linear Algebra; Matrix Theory
    • MAT 151: Determinants
    • MAT 152: Eigenvalues; Eigenvectors
    • MAT 153: Reductions; Factorization
    • MAT 154: Positive Matrices
    • MAT 155: Stochastic Matrices
      For Boolean Matrices see MAT 052
    • MAT 156: Multilinear Algebra
    • MAT 157: Vector and Tensor Algebra
    • MAT 159: Other
  • MAT 160: Associative Rings and Algebras
    • MAT 162: Module Theory
    • MAT 164: Ideals
    • MAT 166: Generalizations (Semirings, Near-Rings)
    • MAT 169: Other
  • MAT 170: Nonassociative Rings and Algebras
    • MAT 173: Lie Algebras
    • MAT 176: Jordan Algebras
    • MAT 179: Other
  • MAT 180: Category Theory
    • MAT 182: Functors
    • MAT 183: Abelian Categories
    • MAT 185: Homological Algebra
    • MAT 189: Other
  • MAT 200: Group Theory
    • MAT 201: Permutation Groups
    • MAT 202: Representation Theory of Groups
    • MAT 203: Finite Groups
    • MAT 204: Linear Groups
    • MAT 205: Abelian Groups
    • MAT 206: Semigroups
    • MAT 208: Generalizations of Groups
    • MAT 209: Other
  • MAT 220: Topological Groups
    • MAT 223: Locally Compact Groups
    • MAT 225: Lie Groups
    • MAT 229: Other
  • MAT 260: Calculus; Differentiation; Integration; Real Functions (Complete Overviews; Textbooks)
    • MAT 263: Functions of Several Variables
    • MAT 266: Polynomials; Rational Functions
    • MAT 269: Other
  • MAT 280: Measure and Integration
    • MAT 285: Specifications
  • MAT 300: Functions of a Complex Variable
    • MAT 302: Series Expansions
    • MAT 303: Geometric Function Theory; Conformal Mappings
    • MAT 305: Entire and Meromorphic Functions
    • MAT 306: Riemann Surfaces
    • MAT 307: Generalized Function Theory
    • MAT 309: Other
  • MAT 310: Potential Theory; Harmonic Functions
    • MAT 315: Specifications
  • MAT 320: Functions of Several Complex Variables
    • MAT 322: Analytic Spaces
    • MAT 324: Analytic Continuation
    • MAT 325: Geometric Convexity; Deformations of Analytic Structures
    • MAT 326: Holomorphic Mappings
    • MAT 327: Holomorphic Fiber Spaces
      For Fiber Spaces in General see MAT 554
    • MAT 329: Other
  • MAT 330: Special Functions
    • MAT 331: Exponential and Trigonometric Functions
    • MAT 332: Gamma and Beta Functions
    • MAT 333: Error Functions
    • MAT 334: Elliptic Functions and Integrals
    • MAT 335: Hypergeometric Functions
    • MAT 336: Cylinder Functions; Bessel Functions
    • MAT 337: Spherical Functions; Legendre Polynomials
    • MAT 338: Orthogonal Functions
    • MAT 339: Other Specifications
  • MAT 340: Ordinary Differential Equations
    • MAT 341: Initial Value Problems
    • MAT 342: Boundary Value Problems; Spectral Theory; Eigenvalue Problems
    • MAT 343: Qualitative Theory
    • MAT 344: Dynamical Systems
    • MAT 345: Stability Theory
    • MAT 346: Asymptotic Theory
    • MAT 347: Differential Equations in Abstract Spaces
    • MAT 348: Functional-Differential and Differential-Difference Equations
    • MAT 349: Other
  • MAT 350: Partial Differential Equations
    • MAT 352: Qualitative Properties of Solutions
    • MAT 353: General First-Order Equations
    • MAT 354: General Higher-Order Equations; Nonlinear Boundary Value Problems; Solitons
    • MAT 355: Elliptic Equations (Laplacian Operator, Helmholtz Equation)
    • MAT 356: Parabolic Equations (Heat Equation, Schrödinger Equation)
    • MAT 357: Hyperbolic Equations (Wave Equation, Telegraph Equation)
    • MAT 358: Spectral Theory and Eigenvalue Problems
    • MAT 359: Other
  • MAT 390: Difference and Functional Equations; Integro Differential Equations; Algebraic Differential Equations
  • MAT 400: Convergence; Summability; Limiting Processes
  • MAT 410: Approximation Theory
    • MAT 411: Interpolation
    • MAT 412: Approximation by Polynomials
    • MAT 413: Spline Approximation
    • MAT 414: Inequalities in Approximation
    • MAT 415: Approximation by Rational Functions; Pade Approximation
    • MAT 416: Approximation by Operators
    • MAT 417: Best Approximation
    • MAT 418: Series Expansions; Asymptotic Approximation; Perturbation Theory
    • MAT 419: Other
  • MAT 420: Harmonic Analysis; Fourier Analysis
    • MAT 422: Harmonic Analysis in One Variable
    • MAT 424: Fourier Transforms (with One Variable)
    • MAT 426: Harmonic Analysis in Several Variables
    • MAT 428: Nontrigonometric Harmonic Analysis; Orthogonal Functions; Wavelets
    • MAT 429: Other
  • MAT 430: Abstract Harmonic Analysis
  • MAT 440: Integral Transforms; Operational Calculus; Laplace Transform; Transforms of Special Functions
  • MAT 450: Integral Equations
    • MAT 452: Linear Integral Equations
    • MAT 454: Fredholm and Volterra Integral Equations
    • MAT 456: Nonlinear Integral Equations
    • MAT 459: Other
  • MAT 460: Functional Analysis
    • MAT 461: Topological Linear Spaces
    • MAT 462: Normed Linear Spaces and Banach Spaces
    • MAT 463: Hilbert Spaces
    • MAT 464: Function Spaces
    • MAT 465: Distributions; Generalized Functions
    • MAT 466: Topological Algebras; Normed Rings and Algebras; Banach Algebras
    • MAT 467: C*-Algebras, Von Neumann (W*-)Algebras
    • MAT 469: Other
  • MAT 470: Operator Theory; Linear Operators
    • MAT 472: Linear Operators as Elements of Algebraic Systems
    • MAT 474: Differential and Integral Operators
    • MAT 476: Nonlinear Operators
    • MAT 479: Others
  • MAT 490: Calculus of Variations and Optimal Control; Optimization
    • MAT 492: Existence Theories; Optimality Conditions
    • MAT 494: Successive Approximation Method
    • MAT 496: Optimal Control
      For Applications in Control Engineering see MSR 635
    • MAT 498: Manifolds; Variational Methods for Eigenvalues of Operators
    • MAT 499: Other
  • MAT 500: Geometry in General (Textbooks Covering Several Areas from Mat 510 - 539)
    • MAT 510: Geometry; Elementary Geometry (Planimetry, Stereometry, Trigonometry) (excl. Convex Geometry and Differential Geometry)
      • MAT 512: Axioms in Geometry; Non-Euclidean Geometries
      • MAT 513: Linear Incidence Geometry; Nonlinear Incidence Geometry
      • MAT 514: Finite Geometry
      • MAT 515: Metric Geometry; Topological Geometry
      • MAT 516: Analytic Geometry
      • MAT 517: Affine and Projective Geometry
      • MAT 518: Descriptive Geometry
      • MAT 519: Other
    • MAT 520: Convex Geometry
      • MAT 525: Specifications
    • MAT 530: Differential Geometry; Classical Differential Geometry
      • MAT 532: Curves
      • MAT 533: Surfaces
      • MAT 535: Vector and Tensor Analysis
      • MAT 536: Local Differential Geometry
      • MAT 537: Global Differential Geometry; Riemannian Manifolds
      • MAT 539: Other
  • MAT 540: General Topology
    • MAT 542: Topological Spaces and Generalizations; Convergence in General Topology
    • MAT 544: Maps
    • MAT 546: Spaces with Richer Structures (Uniform Structures, Metric Spaces ...)
    • MAT 549: Other
  • MAT 550: Algebraic Topology
    • MAT 552: Homology and Cohomology Theories; K-Theory; Sheaves
    • MAT 553: Homotopy Theory; Homotopy Groups
    • MAT 554: Fiber Spaces and Bundles
    • MAT 555: Operations and Obstructions
    • MAT 556: Spectral Sequences
    • MAT 559: Other
  • MAT 570: Topology of Manifolds
    For Complex Manifolds see MAT 322
    • MAT 572: Low-Dimensional Topology
    • MAT 574: Topological Manifolds
    • MAT 576: Differential Topology; Foliations
      For Catastrophe Theory see MAT 584
    • MAT 578: Topological Transformation Groups
      For Topological Groups in General see MAT 220
    • MAT 579: Other
  • MAT 580: Global Analysis; Analysis on Manifolds
    • MAT 582: Differentiable Manifolds
    • MAT 583: Infinite-Dimensional Manifolds
    • MAT 584: Calculus on Manifolds; Catastrophe Theory
    • MAT 585: Spaces and Manifolds of Mappings
    • MAT 586: Variational Problems in Infinite-Dimensional Spaces
    • MAT 587: Differential Equations on Manifolds; Bifurcation; Chaos
    • MAT 589: Other
  • MAT 600: Probability Theory (incl. Textbooks on Probability Theory and Statistics)
    • MAT 601: Foundations of Probability Theory; Axioms
    • MAT 602: Elementary, Combinatorial, Geometric Probability Theory
    • MAT 603: Distribution Theory
    • MAT 604: Limit Theorems
    • MAT 605: Stochastic Processes; Martingales
    • MAT 606: Stochastic Analysis
    • MAT 607: Markov Processes
    • MAT 608: Renewal Theory; Queueing Theory; Demand Theory
    • MAT 609: Other
  • MAT 620: Statistics
    • MAT 622: Foundational Topics (Bayes, ...)
    • MAT 624: Decision Theory
    • MAT 625: Parametric Inference
    • MAT 626: Nonparametric Inference
    • MAT 627: Multivariate Analysis; Cluster Analysis
    • MAT 628: Linear Inference; Regression; Correlation; Analysis of Variance
    • MAT 629: Design of Experiments; Sampling; Monte Carlo Methods
    • MAT 632: Sequential Methods
    • MAT 634: Time Series; Inference from Stochastic Processes
    • MAT 639: Other
  • MAT 650: Numerical Analysis
    • MAT 652: Numerical Approximation
      • MAT 653: Interpolation; Extrapolation
      • MAT 654: Splines
      • MAT 655: Numerical Integration
    • MAT 657: Numerical Linear Algebra in General
      • MAT 658: Eigenvalues, Eigenvectors
      • MAT 659: Large Systems of Equations; Sparse Matrices
    • MAT 661: Error Analysis; Interval Analysis
    • MAT 663: Nonlinear Algebraic or Transcendental Equations
    • MAT 665: Numerical Analysis of Ordinary Differential Equations
      • MAT 666: Initial Value Problems
      • MAT 667: Boundary Value Problems
      • MAT 668: Eigenvalue Problems
    • MAT 671: Numerical Analysis of Partial Differential Equations
      • MAT 672: Initial Value Problems
      • MAT 673: Boundary Value Problems; Multigrid Methods
      • MAT 674: Finite Elements; Galerkin Methods; Boundary Element Methods
    • MAT 676: Difference and Functional Equations
    • MAT 677: Numerical Analysis of Integral Equations and Integral Transforms
    • MAT 679: Other
  • MAT 900: Operations Research; Management Science
    • MAT 902: Mathematics in Economics (Mathematical Models, ...)
    • MAT 904: Network Models
    • MAT 906: Queues and Service; Scheduling Theory; Manpower Planning; Location and Assignment
    • MAT 908: Traveling Salesman Problem (and Other Combinatorial Problems in Operations Research)
    • MAT 909: Other
  • MAT 910: Mathematical Programming
    • MAT 912: Linear Programming
    • MAT 913: Integer Programming; Discrete Optimization
    • MAT 914: Stochastic Programming
    • MAT 915: Quadratic and Convex Programming
    • MAT 916: Nonlinear Programming
    • MAT 917: Dynamic Programming
    • MAT 919: Other (e.g. Evolutionary Computation)
  • MAT 920: Game Theory
    • MAT 922: 2-Person Games
    • MAT 924: Games with Infinitely Many Players
    • MAT 926: Dynamic Games
    • MAT 928: Differential Games
    • MAT 929: Other
  • MAT 990: Other Topics on Mat