CIS 610, 2009

Additional Useful References:

Geometry (General):

Ge'ome'trie 2, English edition: Geometry 2, Berger, Marcel, Universitext, Springer Verlag, 1990

Metric Affine Geometry, Snapper, Ernst and Troyer Robert J., Dover, 1989, First Edition

A vector space approach to geometry, Hausner, Melvin, Dover, 1998

Geometry, Audin, Michele, Universitext, Springer, 2002

Geometry, A comprehensive course, Pedoe, Dan, Dover, 1988, First Edition

Introduction to Geometry, Coxeter, H.S.M. , Wiley, 1989, Second edition

Geometry And The Immagination, Hilbert, D. and Cohn-Vossen, S., AMS Chelsea, 1932

Methodes Modernes en Geometrie, Fresnel, Jean , Hermann, 1996

Computational Line Geometry, Pottman, H. and Wallner, J., Springer, 2001

Topological Geometry, Porteous, I.R., Cambridge University Press, 1981

Lectures on Discrete Geometry, Jiri Matousek, Springer, GTM No. 212, 2002

Convexity:

Lectures on Polytopes, Gunter Ziegler, Springer (GTM No. 152), 1997

Convex Polytopes, Branko Grunbaum, Springer (GTM No. 221), 2003, Second Edition

Combinatorial Convexity and Algebraic Geometry, Gunter Ewald, Springer (GTM No. 168), 1996

Polyhedra, Peter Cromwell, Cambridge University Press, 1999

Convex Sets, Valentine, Frederick, McGraw-Hill, 1964

Convex Analysis, Rockafellar, Tyrrell, Princeton University Press, 1970

Linear Programming and Convex Optimization:

Linear Programming, Chvatal, Vasek, W.H. Freeman, 1983.

Convex Optimization, Boyd, Stephen and Vandenberghe, Lieven, Cambridge University Press, 2004.

Combinatorial Optimization, Papadimitriou, Christos and Steigliz, Kenneth, Dover, 1998.

Computational Geometry (Voronoi diagrams, Delaunay triangulations):

Algorithmic Geometry, Boissonnat, Jean-Daniel and Yvinnec, Mariette (Bronniman, H., translator), Cambridge U. Press, 2001

Computational Geometry in C, O'Rourke, Joseph, Cambridge University Press, 1998, Second Edition

Lie Groups:

Lie Groups. An introduction through linear Linear groups, Wulf Rossmann, Oxford Science Publications, 2002

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces, Arvanitoyeogos, Andreas, AMS, SML, Vol. 22, 2003

Lectures on Lie Groups and Lie Algebras, Carter, Roger and Segal, Graeme and Macdonald, Ian, Cambridge University Press, 1995

Lie Groups, Duistermaat, J.J. and Kolk, J.A.C., Springer Verlag, Universitext, 2000

Lie Groups Beyond an Introduction, Knapp, Anthony W., Birkhauser, Progress in Mathematics, Vol. 140, Second Edition, 2002

Theory of Lie Groups I, Chevalley, Claude, Princeton University Press, first edition, Eighth printing, Princeton Mathematical Series, No. 8, 1946

Foundations of Differentiable Manifolds and Lie Groups, Warner, Frank, Springer Verlag, GTM No. 94, 1983

Introduction to Lie Groups and Lie Algebras, Sagle, Arthur A. and Walde, Ralph E., Academic Press, 1973

Representation of Compact Lie Groups, Brocker, T. and tom Dieck, T., Springer Verlag, GTM, Vol. 98, 1985

Elements of Mathematics. Lie Groups and Lie Algebras, Chapters 1--3, Bourbaki, Nicolas, Springer, 1989

Introduction a la Theorie des Groupes de Lie Classiques, Mneimne', R. and Testard, F., Hermann, 1997

Manifolds and Differential Geometry:

Riemannian Geometry, Do Carmo, Manfredo, Birkhauser, 1992.

Differential Geometry of Curves and Surfaces, Do Carmo, Manfredo P., Prentice Hall, 1976.

Riemannian Geometry. A beginner's guide, Frank Morgan, A.K. Peters, 1998, Second Edition

A Panoramic View of Riemannian Geometry, Marcel Berger, Springer, 2003, First Edition.

Geometry of Differential Forms, Shigeyuki Morita, AMS, Translations of Mathematical Monographs, Vol. 201, First, Edition.

Modern Differential Geometry of Curves and Surfaces, Gray, A., CRC Press, 1997, Second Edition

Applied Math, Numerical Linear Algebra:

Introduction to Applied Mathematics, Strang, Gilbert, Wellesley Cambridge Press, 1986, First Edition

Linear Algebra and its Applications, Strang, Gilbert, Saunders HBJ, 1988, Third Edition

Applied Numerical Linear Algebra, Demmel, James, SIAM, 1997

Numerical Linear Algebra, L. Trefethen and D. Bau, SIAM, 1997

Matrices, Theory and Applications, Denis Serre, Springer, 2002

Matrix Analysis, R. Horn and C. Johnson, Cambridge University Press, 1985

Introduction to Matrix Analysis , Richard Bellman, SIAM Classics in Applied Mathematics, 1995

Matrix Computations, G. Golub and C. Van Loan, Johns Hopkins U. Press, 1996, Third Edition

Some Historical and Leading Figures

The MacTutor History of Mathematics archive

The Mathematics Genealogy Project

Recent Papers Relevant to the Course Material

• Computational Geometry, Lecture 3 (Shang-Hua Teng) (ps)
• CS 267 Graph Partitioning (Kathy Yellick) (pdf)
• Topics in Geometric Combinatorics (Francis E Su) (pdf)
• Jonathan Shewchuk's Home page (html)
• Lecture notes on Delaunay mesh generation, by Jonathan Shewchuk (1999) (pdf)
• Theoretically garanteed Delaunay mesh generation in practice, Short Course, 13th IMR (2004),
  by Jonathan Shewchuk (pdf)
• Constrained Delaunay Triangulations ...,
  by Jonathan Shewchuk (pdf)
• Voronoi Diagrams, by Franz Aurenhammer and Rolf Klein (1996) (ps)
• Partitioning the permutahedron, by Etienne Rassart (pdf)
• Random Monotone Paths on Polyhedra, by Gunter Ziegler et al (pdf)
• Topological Issues in Hexahedral meshing, by David Eppstein (pdf)
• Visualizing the connection among convex hull, Voronoi diagram and Delaunay triangulation, by John Fisher (pdf)
• Shelling and Ranking (pdf)

Papers or Surveys Suitable for a Project

• Visibility Constraints on Features of 2D Objects
  (Basri, ..., Klivans) (pdf)
• Approximating center points with iterative Radon points (ps)
• Approximate center points with proofs (Miller, Sheehy) (pdf)
• Points surrounding the origin (Holmsen, Pach and Tverberg) (pdf)
• A Deterministic Linear Time Algorithm for Geometric Separators and its Applications (ps)
• Regression Depth and Center Points (pdf)
• Computing a centerpoint of a finite planar set of points in linear-time (pdf)
• The complexity of finding small triangulations of convex 3-polytopes, by A. Below, J. De Loera and J. Richter-Gebert (pdf)
• A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation, by Jim Ruppert (pdf)
• When and why Ruppert's algorithm works, by G. Miller, S. Pav and N. Walkington (pdf)
• How good are convex hull algorithms, by D. Avis, D. Bremner and R. Seidel (pdf)
• Convex Hull, Oracles, and Homology, by M. Joswig and G. Ziegler (pdf)
• Algorithms for center and Tverberg points (pdf)
• From Polytopes to Enumeration, by Ed Swartz (pdf)
• Combinatorics with a geometric flavor: some examples, by Gil Kalai (pdf)
• Polytopes Skeletons and Paths, by Gil Kalai (pdf)
• An Introduction to Hyperplane Arrangements, by Richard Stanley (pdf)
• Face Numbers of Polytopes and Complexes, by Louis Bellera and A. Bjorner (pdf)
• The g-Theorem, MA715 Course Notes, by Carl Lee (pdf)
• Triangulations and meshes in computational geometry, by Herbert Edelsbrunner (pdf)
• Computational Topology, by Tamal Dey, Herbert Edelsbrunner and Sumanta Guha (pdf)
• Lectures in Geometric Combinatorics, by Rekha R. Thomas (pdf)
• Triangulations of Point Sets, By J. De Loera, J. Rambau and F. Santos (pdf)
• Convexity, by Marcel Berger (a survey) (pdf)
• A Wirlwind Tour of Computational Geometry, by Graham and Yao (pdf)
• What is Geometry? by S.S. Chern (pdf)

Back to Gallier Homepage

published by:

Jean Gallier