A mathematical comedy of errors and its influence on the development of analysisI. The origins of potential theoryII. Variational principlesIII. Critisism and the developments in post critical yearsIV. Hilbert and the calculus of variationsV. Complex functions and potentialsVI. Functional-analytic approachVII. Modern developments

I. FundamentalsII. Electrical NetworksIII. Flows Connectivity and MatchingIV. Extremal ProblemsV. ColouringVI. Ramsey TheoryVII. Random GraphsVIII. Graphs and Groups

I. Introducing Graphs and complexityII. Spanning treesIII. Planar GraphsIV. NetworksV. MatchingsVI. Eulerian and Hamiltonian toursVII. Colouring GraphsVIII. Intractability

A development of recursive arithmetic in a logic-free equation calculus

I. Recursive ConvergenceII. Recursive and Relative ContinuityIII. Recursive and Relative DifferentiabilityIV. The Relative IntegralV. The Elementary FunctionsVI. Transfinite OrdinalsAppendix: Recursive Irrationality and Transcendence

1. Axioms for Numbers2. Sets and Numbers3. Vectors and Lines4. Inner Products5. The Complex Plane6. Vector Geometry7. Matrix Algebra

1. Triangles2. Regular Polygons3. Isometry in the Euclidean Plane4. Two-Dimensional Crystallography5. Similarity in the Euclidean Plane6. Circles and Spheres7. Isometry and Similarity in Euclidean Space8. Coordinates9. Complex Numbers10. The Five Platonic Solids11. The Golden Section and Phyllotaxis12. Ordered Geometry13. Affine Geometry14. Projective Geometry15. Absolute Geometry16. Hyperbolic Geometry17. Differential Geometry of Curves18. The Tensor Notation19. Differential Geometry of Surface...

Kombinatorische Topologie der streckencomplexe

Deel 1. Algemeene verzamelingsleerI. CardinaalgetallenII. OrdinaalgetallenIII. OrdegetallenDeel 2. Leer der puntverzamelingenIV. Algemeene beschouwingenV. Gesloten en perfecte puntverzamelingenVI. Inhoud en maat. Inwendige grensverzamelingen

Lie Algebras

I. History GeometryII. PrinciplesIII. Further Development Theory

I. De voorgeschiedenis der niet-Euclidische meetkundeII. De grondleggers der niet-Euclidische meetkundeIII. De analytische ruimteleerIV. De projectieve en de groepentheoretische richtingV. De moderne axiomaticaVI. Hyperbolische meetkundeVII. Elliptische meetkunde

I. Fundamental Elements and Axioms of IncidenceII. Orthogonal ProjectionIII. General or Conical ProjectionIV. Homogeneous Coordinates and the Straight LineV. Perspectivity and ProjectivityVI. Projective TransformationsVII. Cross-ratioVIII. The Generation of the ConicIX. The Conic: General PropertiesX. Special Forms of the Equations of the ConicXI. Quadrilaterals and QuadranglesXII. Pencils and Ranges of ConicsXIII. Projectivities on a ConicXIV. Distance and AngleXV. Metrical Theory of ConicsXVI....

The Entropy Concept in Probability TheoryOn the Fundamental Theorems of Information Theoryi. Elementary Inequalitiesii. Ergodic Sourcesiii. Channels and the sources driving themiv. Feinstein's Fundamental Lemmav. Shannon's TheoremsConclusion

Inleiding Een woord van dank Een chronologische lijst van wiskundigen Bibliografie Het woordenboek Register

Tweetalig: links in het Duits rechts in het Engels

I. General TheoryII. Distributions and Fourier TransformsIII. Banach Algebras and Spectral Theory

1. Een inleiding2. Fotonen: lichtdeeltjes3. Elektronen en hun wisselwerking4. Open einden

1. Kurven2. Regulare Flachen3. Die Geometrie der Gauss-Abbildung4. Die innere Geometrie von Flachen

Preface Prologue: The Exponential Function1. Abstract Integration2. Positive Borel Measures3. L p -Spaces4. Elementary Hilbert Space Theory5. Examples of Banach Space Techniques6. Complex Measures7. Integration on Product Spaces8. Differentiation9. Fourier Transforms10. Elementary Properties of Holomorphic Functions11. Harmonic Functions12. The Maximum Modulus Principle13. Approximation by Rational Functions14. Conformal Mapping15. Zeros of Holomorphic Functions16. Analytic Continuation17. H p -...