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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems.
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 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
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 crossing numbers
 extremal graph theory
 gallaisylvester problems
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976.
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.
The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publicationready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.
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File: 18319fall2005.zip
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: pset1.pdf
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: pset4.pdf
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: pset3.pdf
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: pset5.pdf
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: pset2.pdf
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: pset6.pdf
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 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
File: ackerman.pdf
This OER is part of OCW: 18.319 Geometric Combinatorics (MIT)
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 encompassing graphs
 geometric graphs
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 extremal graph theory
 gallaisylvester problems
File: pach.pdf
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This OER is part of OCW: Applied Geometric Algebra
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File: preface.pdf
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Pages: 111
This OER is part of OCW: Applied Geometric Algebra
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This OER is part of OCW: Applied Geometric Algebra
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File: chB.pdf
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File: ref.pdf
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