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Mengentheoretische Topologie
Mengentheoretische TopologieBoto von Querenburg0. Bezeichnungen und mengentheoretische Grundlagen
1. Metrische Räume
2. Topologische Räume und stetige Abbildungen
3. Erzeugung topologischer Räume
4. Zusammenhängende Räume
5. Filter und Konvergenz
6. Trennungseigenschaften
7. Normale Räume
8. Kompakte Räume
9. Satz von Stone-Weierstrass
10. Parakompakte Räume und Metrisationssätze
11. Uniforme Räume
12. Verollstädigung und Kompaktifizierung
13. Vollständige, Polnische und Bairesche R...
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Sternstunden der modernen Mathematik - Berühmte Probleme und neue Lösungen
Sternstunden der modernen Mathematik - Berühmte Probleme und neue LösungenKeith Devlin1. Primzahlen, Faktorzerlegung und Geheimcodes
2. Die Mengenlehre, das Unendliche und unentscheidbare Probleme
3. Zahlensysteme und das Klassenzahl-Problem
4. Schönheit aus dem Chaos
5. Einfache Gruppen
6. Das zehnte Hilbertsche Problem
7. Das Vierfarbenproblem
8. Die Fermatsche Vermutung
9. Schwierige Fragen im Zusammenhang mit den komplexen Zahlen
10. Knoten und andere topologische Begriffe
11. Die Leistun...
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Grosse Augenblicke aus der Geschichte der Mathematik
Grosse Augenblicke aus der Geschichte der MathematikRóbert Freud (Ed.)1. János Surányi - Schon die alten Griechen haben das gewusst
2. Róbert Freud - Sind Gleichungen lösbar?
3. Ákos Császár - Wie ist die mathematische Analysis erstanden?
4. György Bizám - "Aus dem Nichts habe ich eine neue, andere Welt erschaffen." Was ist die Bolyai-Lobatschewskische Geometrie?
5. Edit Gyarmati - Ideale Zahlen und die Fermatsche Vermutung
6. Ákos Császár - Wie sah Hilbert die Zukunft der Mathemati...
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Notes on Geometry
Notes on GeometryElmer G. ReesI. Euclidean Geometry
II. Projective Geometry
III. Hyperbolic Geometry
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Geometry - A Metric Approach with Models
Geometry - A Metric Approach with ModelsRichard S. Millman, George D. Parker1. Preliminary Notions
2. Incidence and Metric Geometry
3. Betweenness and Elementary Figures
4. Plane Separation
5. Angle Measure
6. Neutral Geometry
7. The Theory of Parallels
8. Hyperbolic Geometry
9. Euclidean Geometry
10. Area
11. The Theory of Isometries
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Projective Geometry and Modern Algebra
Projective Geometry and Modern AlgebraLars Kadison, Matthias T. KromannHistorical Foreword
1. Affine Geometry
2. Projective Planes
3. Desargues' Theorem and the Principle of Duality
4. A Brief Introduction to Groups
5. Elementary Synthetic Projective Geometry
6. The Fundamental Theorem for Projectivities on a Line
7. A Brief Introduction to Division Rings
8. Projective Planes over Division Rings
9. Introduction of Coordinates in a Projective Plane
10. Möbius Transformations and Cross Ratio
11. ...
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Linear Algebra Through Geometry
Linear Algebra Through GeometryThomas Banchoff, John Wermer1.0 Vectors in the Line
2.0 The Geometry of Vectors in the Plane
2.1 Transformations of the Plane
2.2 Linear Transformations and Matrices
2.3 Products of Linear Transformations
2.4 Inverses and Systems of Equations
2.5 Determinants
2.6 Eigenvalues
2.7 Classification of Conic Sections
2.8 Differential Systems
3.0 Vector Geometry in 3-Space
3.1 Transformations of 3-Space
3.2 Linear Transformations and Matrices
3.3 Sums and Products of Li...
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Transformation Geometry - An Introduction to Symmetry
Transformation Geometry - An Introduction to SymmetryGeorge E. Martin1. Introduction
2. Properties of Transformations
3. Translations and Halfturns
4. Reflections
5. Congruence
6. The Product of Two Reflections
7. Even Isometries
8. Classification of Plane Isometries
9. Equations for Isometries
10. The Seven Frieze Groups
11. The Seventeen Wallpaper Groups
12. Tessellations
13. Similarities on the Plane
14. Classical Theorems
15. Affine Transformations
16. Transformations on Three-space
17. Spac...
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Geometries and Groups
Geometries and GroupsV.V. Nikulin, I.R. ShafarevichI. Forming geometrical intuition; statement of the main problem
II. The theory of 2-dimensional locally Euclidean geometries
III. Generalisations and applications
IV. Geometries on the torus, complex numbers and Lobachevsky geometry
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Modern Geometry-Methods and Applications - III. Introduction to Homology Theory
Modern Geometry-Methods and Applications - III. Introduction to Homology TheoryB.A. Dubrovin, A.T. Fomenko, S.P. Novikov1. Homology and Cohomology. Computational Recipes
2. Critical Points of Smooth Functions and Homology Theory
3. Cobordisms and Smooth Structure
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A Treatise on the Analytic Geometry of Three Dimensions II
A Treatise on the Analytic Geometry of Three Dimensions IIGeorge SalmonXIII. Partial Differential Equations of Families of Surfaces. General Conception of a Family of Surfaces
XIV. The Wave Surface, The Centro-Surface, Parallel, Pedal, and Inverse Surfaces
XV. Surfaces of the Third Degree
XVI. Surfaces of the Fourth Degree
XVII. General Theory of Surfaces
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A Catalog of Special Plane Curves
A Catalog of Special Plane CurvesJ. Dennis Lawrence1. Properties of Curves
2. Types of Derived Curves
3. Conics and Polynomials
4. Cubic Curves
5. Quartic Curves
6. Algebraic Curves of High Degree
7. Transcendental Curves
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Problems in Geometry
Problems in GeometryM. Berger, P. Pansu, J.P. Berry, X. Saint-Raymond1. Groups Operating on a Set: Nomenclature, Examples, Applications
2. Affine Spaces
3. Barycenters; the Universal Space
4. Projective Spaces
5. Affine-projective Relationship: Applications
6. Projective Lines, Cross-Ratios, Homographies
7. Complexifications
8. More about Euclidean Vector Spaces
9. Euclidean Affine Spaces
10. Triangles, Spheres, and Circles
11. Convex Sets
12. Polytopes; Compact Convex Sets
13. Quadratic Forms
1...
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Modern Geometry-Methods and Applications - II. The Geometry and Topology of Manifolds
Modern Geometry-Methods and Applications - II. The Geometry and Topology of ManifoldsB.A. Dubrovin, A.T. Fomenko, S.P. Novikov1. Examples of Manifolds
2. Foundational Questions. Essential Facts Concerning Functions on a Manifold. Typical Smooth Mappings
3. The Degree of a Mapping. The Intersection Index of Submanifolds. Applications
4. Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre)
5. Homotopy Groups
6. Smooth Fibre Bundles
7. Some Examples...
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A Treatise on Conic Sections
A Treatise on Conic SectionsGeorge SalmonI. The point
II. The right line
III. Examples of the right line
IV. The right line - abridged notation
V. Right lines
VI. The circle
VII. Examples on circle
VIII. Properties of two or more circles
IX. The circle - abridged notation
X. General equation of second degree
XI. Central equations
XII. The parabola
XIII. Examples on conics
XIV. Abridged notation
XV. Reciprocal polars
XVI. Harmonic and anharmonic properties
XVII. The method of projection
XVIII. In...
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Leerboek der Beschrijvende Meetkunde deel 1 - Tekst + Atlas
Leerboek der Beschrijvende Meetkunde deel 1 - Tekst + AtlasDr. Hk. de VriesMet apart deel met Platen
Deel 1: De leer der projectiemethoden
I. Centrale projectie
II. De Perspectief
III. Aanvulling van de methode der Orthogonale Parallelprojectie
IV. A. Scheeve Parallelprojectie
IV. B. Axonometrie
IV. C. Cavalière-Perspectief
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Curves and Singularities
Curves and SingularitiesJ.W. Bruce, P.J. Giblin1. Introductory example: a gravitational catastrophe machine
2. Curves, and functions on them
3. More about functions
4. Regular values and smooth manifolds
5. Envelopes
6. Unfoldings
7. Unfoldings: applications
8. Transversality
9. Generic properties of curves
10. More on unfoldings
11. Surfaces, simple singularities and catastrophes
Appendix: Null sets and Sard's theorem
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Analytische Meetkunde deel I - Het platte vlak
Analytische Meetkunde deel I - Het platte vlakDr. J.A. BarrauI. De coördinaten en hare tranformaties
II. De cirkel. Imaginaire Elementen. Involutie van den tweeden graad
III. Coördinaten in het Algemeen. Meetkundige plaatsen. Algebraïsche Krommen
IV. De Kegelsneden
V. De Kegelsneden vervolg
VI. De Kegelsnede als grondslag voor Niet-Euclidische maatbepaling
VII. De λ-matrix. Classificatie van bundels en scharen; collineaties en correlaties
VIII. De Meetkunde als Invarianten-theorie
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Analytische Meetkunde deel II - De ruimte
Analytische Meetkunde deel II - De ruimteDr. J.A. BarrauI. De coördinaten en hare tranformaties. Punt, rechte en vlak
II. De bol en de cirkel
III. Meetkundige plaatsen. Algebraïsche oppervlakken en ruimtekrommen
IV. Het oppervlak van den tweeden graad.
V. Matrices en λ-matrices
VI. Lineaire verzamelingen van quadratische oppervlakken
VII. De meetkunde op het oppervlak van den tweeden graad
VIII. De niet-Euclidische meetkunde der ruimte. De Euclidische meetkunde in R4
IX. Lineaire ruimten
X. L...
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Leerboek der Differentiaal- en Integraalrekening, en van de theorie der Differentiaalvergelijkingen I
Leerboek der Differentiaal- en Integraalrekening, en van de theorie der Differentiaalvergelijkingen IDr. Hk. de VriesI. Grondslagen der Differentiaalrekening
II. De afgeleiden der elementaire functies
III. Hoogere afgeleiden en differentialen. Impliciete functies. Partieele afgeleiden. Het invoeren van nieuwe veranderlijken
IV. Grondslagen der Integraalrekening
V. Het integreeren van rationale en irrationale breuken
VI. Bepaalde integralen, en eenvoudige meetkundige toepassingen der Differentiaa...
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