Lecture Day 1 (Outline)

* Pass out information sheet (Printout of WWW page)

    - Discuss near-term schedule; only expected missed
      lectures.

* Pass around 3x5 cards   - Name
                          - Background
                          - Contact  (email/phone)
                          - Computer Acess
                          - What hope to learn from class

* Talk about course
   - Purpose is to introduce algebraic geometry via some
     examples of applications; will teach some systems theory.
     Frank is expert in algebraic geometry, not systems theory.
   - Handouts from the drafts of the book.  Feedback is welcome,
     particularly negative comments.

* Have a round the class introductions, after the 3x5 cards.
   Take notes on them. 

* Begin Lecture
   - State-Space form of a linear system.
      proper & strictly proper linear systems
      McMillan degree
   - Controllable, observable, & minimal realizations
   - Output Feedback. 
       Response measured by autonomous system
       Dynamic output feedback
       Characteristic polynomial

   - Minimal   stability
               quick damping
               oscillation
   - Pole-Placement
      arbitrary pole-assignable

   - Summary

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Books of Frank Sottile for participants in Math 697R

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Algebraic Geometry:
  Shafarevich, Basic Algebraic Geometry.
  Atiyah & Macdonald, Introduction to Commutative Algebra.
  Fulton, Young Tableaux.
  Cox, Little, and O'Shea, Ideals, Varieties, Algorithms.
  Cox, Little, and O'Shea, Using Algebraic Geometry.
  Harris, Algebraic Geometry.
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Algebraic Geometry & Control Theory:
  Peter Falb, Methods of Algebraic Geometry in Control Theory,
              Part I: affine algebraic methods.
  Peter Falb, Methods of Algebraic Geometry in Control Theory,
              Part II: projective algebraic methods.
  S. Abhyankhar, Algebraic Geometry for Scientists and Engineers.
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Mathematical Control Theory:
  S. Barnett & R.G. Cameron, Mathematical Control Theory.
  W. Wonham, Linear Multivariate Control: Geometric methods.