TUM Classification System – MAT

MAT: Mathematics

Übersicht

MAT 000: Belonging to the Subject; not further Classified

MAT 340: Ordinary Differential Equations

MAT 001: Mathematics in General; Complete Overviews

MAT 350: Partial Differential Equations

MAT 030: Mathematical Logic

MAT 390: Difference and Functional Equations; Integro Differential Equations; Algebraic Differential Equations

MAT 040: Set Theory

MAT 400: Convergence; Summability; Limiting Processes

MAT 050: Combinatorics; Classical Problems

MAT 410: Approximation Theory

MAT 060: Lattice Theory

MAT 420: Harmonic Analysis; Fourier Analysis

MAT 080: General Algebraic Systems

MAT 430: Abstract Harmonic Analysis

MAT 100: Number Theory; Elementary Number Theory

MAT 440: Integral Transforms; Operational Calculus; Laplace Transform; Transforms of Special Functions

MAT 110: Algebraic Theories (Textbooks Covering Several Areas from 120 - 220)

MAT 450: Integral Equations

MAT 120: Algebraic Number Theory; Fields; Polynomials

MAT 460: Functional Analysis

MAT 130: Commutative Algebra

MAT 470: Operator Theory; Linear Operators

MAT 140: Algebraic Geometry

MAT 490: Calculus of Variations and Optimal Control; Optimization

MAT 150: Linear Algebra; Matrix Theory

MAT 500: Geometry in General (Textbooks Covering Several Areas from Mat 510 - 539)

MAT 160: Associative Rings and Algebras

MAT 540: General Topology

MAT 170: Nonassociative Rings and Algebras

MAT 550: Algebraic Topology

MAT 180: Category Theory

MAT 570: Topology of Manifolds

MAT 200: Group Theory

MAT 580: Global Analysis; Analysis on Manifolds

MAT 220: Topological Groups

MAT 600: Probability Theory (incl. Textbooks on Probability Theory and Statistics)

MAT 260: Calculus; Differentiation; Integration; Real Functions (Complete Overviews; Textbooks)

MAT 620: Statistics

MAT 280: Measure and Integration

MAT 650: Numerical Analysis

MAT 300: Functions of a Complex Variable

MAT 900: Operations Research; Management Science

MAT 310: Potential Theory; Harmonic Functions

MAT 910: Mathematical Programming

MAT 320: Functions of Several Complex Variables

MAT 920: Game Theory

MAT 330: Special Functions

MAT 990: Other 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;
  Philosophy of Science see PHI 500
- MAT 015: Training; Career; Professional Organisations; Academic Associations; Interest Groups
- MAT 020: Didactics
  Mathematics Education see also EDU 730
- MAT 021: Mathematics in Other Scholarly Disciplines (Comprehensive Literature)
  - MAT 022: Mathematics in the Natural and Life Sciences
    
    Biomathematics
    see BIO 105
  - 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
  Vector and Tensor Analysis see MAT 535
- 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
  Lie Groups see MAT 225
- 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
- Topological Transformation Groups see MAT 578
- 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
  Differential Equations on Manifolds; Bifurcation; Chaos see MAT 587
- 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
  Analysis, Complex Analysis, Operators, Differential Equations, Conservation Laws, Oscillations and Wave see also PHY 013
- 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
  Function Spaces see MAT 464
- MAT 463: Hilbert Spaces
  Function Spaces see MAT 464
- 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)
- Algebraic Geometry see MAT 140
- 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
    
    Vector and Tensor Algebra see MAT 157
  - 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
  Holomorphic Fiber Spaces see MAT 327
- 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
- Probability Theory (incl. Textbooks on Probability Theory and Statistics) see also MAT 600
- 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
  Approximation Theory see MAT 410 ff
  - 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)
  Combinatorics; Classical Problems see also MAT 050
- 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