CIS 610, 2009

Additional Useful References:

Geometry (General):

Ge'ome'trie 1, English edition: Geometry 1, Berger, Marcel, Universitext, Springer Verlag, 1990

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


A course in convexity, Barvinok, Alexander, AMS, (GSM Vol. 54), 2002

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:

Understanding and Using Linear Programming, Matousek, Jiri and Gartner, Bernd, Springer, (Universitext), 2007.

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):

Geometry and Topology for Mesh Generation, Edelsbrunner, Herbert, Cambdridge U. Press, 2001

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, Lie algebras, and representations, Hall, Brian, Springer (GTM No. 222)

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:

Differential Geometry. Curves, Surfaces, Manifolds, Wolfgang Kuhnel, AMS, SML, Vol. 16, 2002

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 the Mathematics of Medical Imaging, Charles L. Epstein, Prentice Hall, 2004

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

David Hilbert, Walther von Dyck,

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