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...

Modern Geometry-Methods and Applications - I. The Geometry of Surfaces, Transformation Groups, and FieldsB.A. Dubrovin, A.T. Fomenko, S.P. Novikov1. Geometry in Regions of a Space. Basic Concepts 2. The Theory of Surfaces 3. Tensors: The Algebraic Theory 4. The Differential Calculus of Tensors 5. The Elements of the Calculus of Variations 6. The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants

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...

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

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...

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

Circles, A Mathematical ViewDan PedoeThis revised edition of a mathematical classic originally published in 1957 will bring to a new generation of students the enjoyment of investigating that simplest of mathematical figures, the circle. The author has supplemented this new edition with a special chapter designed to introduce readers to the vocabulary of circle concepts with which the readers of two generations ago were familiar. Readers of Circles need only be armed with paper, pencil, compass,...

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

Plane Algebraic CurvesEgbert Brieskorn, Horst KnörrerI. History of algebraic curves 1. Origin and generation of curves 2. Synthetic and analytic geometry 3. The development of projective geometry II. Investigation of curves by elementary algebraic methods 4. Polynomials 5. Definition and elementary properties of plane algebraic curves 6. The intersection of plane curves 7. Some simple types of curves III. Investigation of curves by resolution of singularities 8. Local investigations 9. Global...

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

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

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...

Inleiding tot de Studie der Meetkunde van het AantalDr. Hk. de VriesI. De Incidentieformules II. De Coïncidentieformules III. Meervoudige coïncidenties en de theorie van het n-de graadsoppervlak IV. Over het bepalen van aantallen door middel van ontaardingen V. De stralencomplex van den n-den graad VI. Het karakteristiekenprobleem

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...

Non-Euclidean GeometryH.S.M. CoxeterI. The Historical Development of Non-Euclidean Geometry II. Real Projective Geometry: Foundations III. Real Projective Geometry: Polarities, Conics and Quadrics IV. Homogeneous Coordinates V. Elliptic Geometry in One Dimension VI. Elliptic Geometry in Two Dimensions VII. Elliptic Geometry in Three Dimensions VIII. Descriptive Geometry IX. Euclidean and Hyperbolic Geometry X. Hyperbolic Geometry in Two Dimensions XI. Circles and Triangles XII. The Use of a Gene...

Projective GeometryH.S.M. Coxeter1. Introduction 2. Triangles and Quadrangles 3. The Principle of Duality 4. The Fundamental Theorem and Pappus's Theorem 5. One-dimensional Projectivities 6. Two-dimensional Projectivities 7. Polarities 8. The Conic 9. The Conic, Continued 10. A Finite Projective Plane 11. Parallelism 12. Coordinates

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. ...

Projective GeometryPierre Samuel1. Projective Spaces 2. One-Dimensional Projective Geometry 3. Classification of Conics and Quadrics 4. Polarity with Respect to a Quadric Appendix: (2, 2)-Correspondences

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...

Einleitung in die Theorie der binären Formen von F. Faà di Bruno / Über das Formensystem binärer FormenDr. Theodor Walter / Dr. Paul GordanTwee boeken in één band Einleitung in die Theorie der binären Formen von F. Faà di Bruno I. Symmetrische Funktionen der Wurzeln einer Gleichung II. Resultanten und Diskriminanten III. Kanonische Formen IV. Invarianten V. Kovarianten VI. Typische Darstellungen VII. Specielle Theorien "Über das Formensystem binärer Formen ist ein Buch von Paul Gorda...