Mathematica 8 adds major new areas, including probability and statistics, graphs and networks, computational finance, control systems, wavelet analysis, and group theory. Each of these areas represents major progress in the ability to work at a high level of abstraction supported by in-depth algorithmic coverage and advanced automation. This should enable rapid progress in these areas, and also in the ability to combine tools from several disjoint areas as functions are designed to fit together even across different domains.

Probability & Statistics »

Probability — compute probabilities for general events

Expectation — compute expectations for general expressions

EstimatedDistribution — automatically estimate parameters in a distribution from data

Distributed()▫ Conditioned()  ▪  NExpectation  ▪  MomentConvert  ▪  ...

New Properties for Distributions »

SurvivalFunction — survival function for a distribution

Moment — general moment for a distribution

HazardFunction  ▪  LogLikelihood  ▪  Cumulant  ▪  MomentGeneratingFunction  ▪  ...

New Parametric Distributions »

StableDistribution — stable distribution

MaxStableDistribution  ▪  BinormalDistribution  ▪  ErlangDistribution  ▪  DirichletDistribution  ▪  GompertzMakehamDistribution  ▪  ...

New Nonparametric Distributions »

SmoothKernelDistribution — nonparametric kernel density estimate-based distribution

EmpiricalDistribution  ▪  HistogramDistribution  ▪  ...

New Derived Distributions »

TransformedDistribution — transformation of an existing distribution

OrderDistribution  ▪  MarginalDistribution  ▪  CopulaDistribution  ▪  ...

New Hypothesis Testing »

DistributionFitTest — test for goodness-of-fit to a distribution or data

LocationTest — test means or mean differences of one or two datasets

VarianceTest  ▪  LocationEquivalenceTest  ▪  VarianceEquivalenceTest  ▪  KolmogorovSmirnovTest  ▪  AndersonDarlingTest  ▪  MannWhitneyTest  ▪  ...

Graphs & Networks »

Graph — construct a graph from vertices and edges

GraphData, ExampleData — collection of theoretical and empirical graphs

CompleteGraph  ▪  GridGraph  ▪  CompleteKaryTree  ▪  ButterflyGraph

AdjacencyGraph  ▪  IncidenceGraph  ▪  AdjacencyMatrix  ▪  ...

UniformGraphDistribution  ▪  BarabasiAlbertGraphDistribution  ▪  ...

New in Styling and Labeling of Graphs »

HighlightGraph — highlight vertices, edges, or whole subgraphs

VertexStyle  ▪  EdgeStyle  ▪  VertexLabels  ▪  EdgeLabels  ▪  ...

New Predicates and Properties »

IsomorphicGraphQ — test whether two graphs are isomorphic

GraphQ  ▪  DirectedGraphQ  ▪  ConnectedGraphQ  ▪  EulerianGraphQ  ▪  ...

New Graph Measures and Metrics »

VertexCount  ▪  VertexDegree  ▪  VertexInDegree  ▪  GraphDistance  ▪  ...

ClosenessCentrality  ▪  BetweennessCentrality  ▪  PageRankCentrality  ▪  ...

New Graph Computations »

FindShortestPath — find the shortest path from the source to one or all vertices

FindEulerianCycle  ▪  FindHamiltonianCycle  ▪  GraphDiameter  ▪  ...

ConnectedComponents  ▪  KCoreComponents  ▪  VertexOutComponent  ▪  ...

FindClique  ▪  FindEdgeCover  ▪  BreadthFirstScan  ▪  ...

New Built-in Control Systems Functionality »

TransferFunctionModel — transfer-function model object

StateSpaceModel  ▪  ToContinuousTimeModel  ▪  ToDiscreteTimeModel  ▪  ...

SystemsModelStateFeedbackConnect  ▪  OutputResponse  ▪  ...

Classical Analysis and Design »

RootLocusPlot — plot pole locations as function of parameter

BodePlot  ▪  NyquistPlot  ▪  GainPhaseMargins  ▪  SingularValuePlot  ▪  ...

State-Space Analysis »

ControllabilityMatrix — gives the controllability matrix

ControllabilityGramian  ▪  ObservabilityMatrix  ▪  ObservabilityGramian  ▪  ...

MinimalStateSpaceModel  ▪  InternallyBalancedDecomposition  ▪  ...

State-Space Design »

KalmanEstimator — Kalman filter-based optimal observer

LQGRegulator — linear quadratic Gaussian optimal regulator

StateFeedbackGains  ▪  EstimatorGains  ▪  DiscreteLQRegulatorGains  ▪  ...

New in Computational Finance »

FinancialDerivative — financial derivative valuations

FinancialBond — financial bond valuations

TimeValue — time value of money computations

EffectiveInterest  ▪  Annuity  ▪  AnnuityDue  ▪  Cashflow  ▪  ...

New Built-in Wavelet Analysis »

ContinuousWaveletTransform — gives the continuous wavelet transform

DiscreteWaveletTransform — gives the discrete wavelet transform

DaubechiesWavelet  ▪  LiftingWaveletTransform  ▪  WaveletThreshold  ▪  ...

StationaryWaveletPacketTransform  ▪  WaveletScalogram  ▪  ...

New Permutation Functionality »

Cycles — disjoint cyclic notation for permutations

PermutationCycles  ▪  PermutationListQ  ▪  RandomPermutation  ▪  ...

PermutationSupport  ▪  PermutationMax  ▪  ...

PermutationProduct  ▪  InversePermutation  ▪  PermutationPower  ▪  PermutationOrder

Permute  ▪  FindPermutation  ▪  PermutationReplace

New Group Theory Capabilities »

PermutationGroup — representation for a permutation group

GroupOrder — number of elements in a group

GroupElements  ▪  GroupElementQ  ▪  ...

GroupGenerators  ▪  GroupMultiplicationTable  ▪  CayleyGraph

GroupOrbits  ▪  GroupStabilizer  ▪  GroupStabilizerChain  ▪  ...

SymmetricGroup  ▪  CyclicGroup  ▪  DihedralGroup  ▪  ...

MathieuGroupM24  ▪  JankoGroupJ2  ▪  RudvalisGroupRu  ▪  ...

New Equation-Solving Capabilities

Solve (modified), NSolve (modified) — solve equations and inequalities over domains

ConditionalExpression — an expression defined when a condition holds

New Numerics Capabilities

NIntegrate (modified) — integration of univariate and multivariate oscillatory functions

New in Special Functions »

MarcumQ — Marcum's Q function

OwenT  ▪  WignerD  ▪  BellY  ▪  RankedMin  ▪  RankedMax

Fast Exact Linear Algebra »

LinearSolve — fast methods for integer and rational inputs

NullSpace  ▪  MatrixRank  ▪  Inverse  ▪  LeastSquares  ▪  ...

PseudoInverse  ▪  Det  ▪  Dot  ▪  ...

New in Matrix Decompositions »

HessenbergDecomposition (modified) — Hessenberg decomposition for a matrix pair

SchurDecomposition (modified) — Schur decomposition for a matrix pair