CIS 610, Summer 1, 2013

Some Course Notes and Slides

Notes

  • GMA, Preface and Chapter 1 (pdf)
  • GMA, Chapter 6 (pdf)
  • GMA, Chapter 11 (pdf)
  • GMA, Chapter 12 (pdf)
  • GMA, Chapter 14 (pdf)
  • GMA, Bibiography (pdf)
  • ** Notes (Dan Guralnik). Chapter 1: Duality in infinite-dimensional Vector Spaces (pdf)
  • ** Notes (Dan Guralnik). Chapter 2: Inner Product Spaces, Part a (pdf)
  • ** Notes (Dan Guralnik). Chapter 2: Inner Product Spaces, Part b (pdf)
  • ** Notes (Dan Guralnik). Chapter 3: Spectral Theory, Part a (pdf)
  • ** Notes (Dan Guralnik). Chapter 3: Spectral Theory, Part b (pdf)
  • ** Basics of Algebra, Topology, and Differential Calculus (manuscript) (html)
  • ** Fundamentals of Linear Algebra and Optimization; Some Notes (pdf)
  • ** Notes on Differential Geometry and Lie Groups   (html)
  • ** Logarithms and Square Roots of Real Matrices (Some Notes)   (pdf) (NEW!)
  • The derivation of the exponential map of matrices, by G. M. Tuynman   (pdf) (NEW!)
  • On the Early History of the Singular Value Decomposition, by G.W. Stewart   (pdf)
  • Lecture Notes on Differentiable Manifolds, Geometry of Surfaces, etc., by Nigel Hitchin   (html) (NEW!)
  • An Introduction to Riemannian Geometry, by S. Gudmundsson   (html) (NEW!)
  • ``Semi-secret'' Notes on algebraic geometry and algebra   (Algebra, html)   |  (Math 624/625, Fall 2001--Spring 2002, html)   | 
    (Math 622/623, Fall 2003--Spring 2004, html) (Algebraic geometry, html)   |  (Complex algebraic geometry, html) (NEW!)

    Slides

  • Problems, Questions and Motivations (Spring 2011)   (slides, pdf)
  • Curves. (pdf)
  • The exponential map, Lie Groups, Lie Algebras, part I   (slides, pdf)
  • Review of Multivariate Calculus. (pdf)
  • Manifolds, Lie Groups, Lie Algebras, part II   (slides, pdf)
  • Surfaces. (pdf)
  • Manifolds embedded in R^N (pdf)
  • Manifolds, Part 1 (pdf)
  • Manifolds, Part 2 (pdf)
  • Sir Walter Synnot Manifold   (jpg)
  • Group Actions, Homogeneous Spaces   (slides, pdf)
  • The Lorentz Groups   (slides, pdf)
  • Topological Groups   (slides, pdf)
  • Review of Topology   (slides, pdf)
  • Manifolds, general case   (slides, pdf)
  • More on Lie Groups, Lie algebras, and the exponential map   (slides, pdf)
  • Riemannian metrics, connections, parallel transport   (slides, pdf)
  • Geodesics, cut locus, first variation formula   (slides, pdf)

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    published by:

    Jean Gallier