$k$-theory $k$-theoryandhomology;cyclichomologyandcohomology $k$-theoryandoperatoralgebras 13f3514b0516e4016t0519k5619d5522e4658b3453c2458j42 17thcentury 1917-1989 2007 510 510s514 510s515 515 516 abstractharmonicanalysis algebra algebraic algebraicgeometry algebraictopology analysis analysisonmanifolds analyticspaces applicationsofmathematics approximationsandexpansions approximationtheory arithmeticringsandotherspecialrings associativeringsandalgebras asymptoticexpansions averagingmethod(differentialequations) banachalgebras banachspaces bifurcationtheory biomathematics boundaryvalueproblems calculus calculusoftensors calculusofvariations calculusofvariationsandoptimalcontrol;optimization catastrophes(mathematics) cellaggregation chaoticbehaviorinsystems chemistry classicalandquantumgravitation commutativealgebra commutativerings computationalintelligence computationalmathematicsandnumericalanalysis computerscience computervision condensedmatterphysics congresses control cosmology criticalpointtheory cyclic diffeomorphisms differentiabledynamicalsystems differentiablemanifolds differential differentialalgebra differentialequations differentialgeometry differentialoperators diffusionprocesses dihedral distribution(probabilitytheory) dynamicalsystemsandergodictheory dynamics ecology economics engineering engineeringmathematics ergodictheory etc examinationsuniversityofcalifornia exercises feynmanintegrals fieldtheory(physics) finance fourieranalysis functionalanalysis functionsofboundedvariation functionsofcomplexvariables functionsofrealvariables gametheory general generalizedspaces geometry globalanalysis globalanalysisandanalysisonmanifolds globaldifferentialgeometry grouptheory hamiltoniansystems harmonicanalysis helmholtzequation higheralgebraic$k$-theory hilbertspace history historyofmathematicalsciences homologicalmethods hopfalgebras hopfalgebrasandtheirapplications indextheory infinite-dimensionalmanifolds integralgeometry integrals inverseproblems(differentialequations) laplacianoperator liegroups linearandmultilinearalgebras localtheory manifolds(mathematics) mathematical mathematicalanalysis mathematicalandcomputationalphysics mathematicalmethodsinphysics mathematicalmodels mathematicaloptimization mathematicalphysics mathematicalstatistics mathematics matrixtheory measureandintegration mechanics microlocalanalysis non-associativeringsandalgebras noncommutativealgebras noncommutativedifferentialgeometry noncommutativegeometry(àlaconnes) noncommutativeglobalanalysis noncommutativeresidues nonlinear nonlineartheories numbertheory numericalanalysis numericalandcomputationalphysics numericalrange numericalsolutions operatortheory ordinarydifferentialequations partial partialdifferentialequations partialdifferentialequationsonmanifolds;differentialoperators particles(nuclearphysics) pathintegrals physics population probabilitytheoryandstochasticprocesses problems prooftheory pseudodifferentialoperators qa qa1-939 qa276-280 qa315 qa370-380 qa372 qa401-425 qa927 quantitativefinance quantumfieldtheory quantumgroupsandrelatedtopics quantumtheory quasiconformalmappings realfunctions regionaleconomics relativitytheory rigidityresults scattering(physics) semigroups semisimpleliegroupsandtheirrepresentations shapes singh singularities spaceineconomics specialrelativity(physics) statisticalphysics statisticaltheoryandmethods statistics stochasticanalysis stochasticpartialdifferentialequations stochasticprocesses structuralanalysis(engineering) studyandteaching(higher) symbolicdynamics symmetrygroups systemstheory systemtheory textbooks theoretical theoryof time-seriesanalysis topologicaldynamics topologicalgroups topology uditanarayana vectorfields vibration visualization wave-motion waveequation wittvectorsandrelatedrings