This course is given at Visualizing
Multidimensional Geometry and its Applications 
Prof. Alfred Inselberg (aiisreal@math.tau.ac.il) 
Office 325 Kaplun Bldg.

SYLLABUS 
· First
lecture : Introduction to Scientific, Information
and Multidimensional Visualization
 Course overview. 
· Projective
Geometry  Foundations, Duality, Homogeneous
Coordinates, Invariants  2 lectures. 
· Parallel
Coordinates in the Plane
 Dualities,
Transformations, Visual & Automatic Data Mining  1
lecture. 
· Lines
in Nspace  2 lectures 
Representations of Lines 
Distance & Proximity Properties 
Application : Collision Avoidance
Algorithms for Air Traffic Control, and others. 
· Coplanarity
 2.5 lectures 
2 Representations of Planes, Flats & Hyperplanes 
Recursive Mapping 
“Near Coplanarity”
& Applications : Data mining, Geometric Modeling
, Computer Vision, Statistics. 
· Curves  2 lectures including chapter on Envelopes . 
· Topologies
of lines & Flats. Applications : Computer Vision
& Geometric Modeling – 0.5 lecture . 
· Hypersurfaces in NSpace 
2 representations. Developable, Ruled, Quadratic & more general
surfaces. Detecting properties from their representation and approximations
of complex surfaces. Interior point Algorithms, more on Data Mining, A
Decision Support System and models of Processes (TradeOff Analysis, Sensitivities and Interelations, Impact of Constraints, a little on
Optimization) and an Automatic Rule Finder
(Classifier for Data Mining)
 1.5 lectures. 
· Time
permitting  students can choose and lecture on various topics in
Visualization, e.g. Visualizing : The Internet,
Fluid Flow, Neural Networks and others. 
The course notes (the lectures given in
class) will
be available to the students. Exercises will be assigned and graded weekly. Course
grade = .2 (exercise grades) + .8 (project grade) 