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ppt on recent trends on algebra

This workshop would provide a useful follow-up to the 5-day BIRS workshop Interactions Between Noncommutative Algebra and Algebraic Geometry (08w5072)'' from October 26-31, 2008; the 5-day Manchester workshop on Noncommutative algebraic geometry'', the University of Manchester, UK, from August 3-8, 2009; the RIMS workshop on Noncommutative Algebraic Geometry and Related Topics'', the University of Kyoto, Japan, from August 24-28, 2009; the Oberwolfach workshop on Interactions between Algebraic Geometry and N ....etc

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Relational Model & Algebra
Recall Our Initial Discussion
There are a variety of ways of representing data, each with trade-offs
Free text
Shapes/points in space
Objects with properties
In general, our emphasis will be on the last item
though there are spatial databases, OO databases, text databases, and the like
The Relational Data Model (1970)
Lessons from the Codd paper
Let s separate physical implementation from logical
Model the data independently from how it will be u ....etc

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In-Home Coordinate System: Currently, many household, self-automated robots (lawn mowers or vacuum cleaners) covers area with a random algorithm, often using 5 hours to do something it should be done in 2 since it goes over the same spot may times. Usually, it uses an infrared or other sensor system to detect obstacles and boundaries. However, the path of the robot could be more controlled if there was a way to set up a coordinate system for the robot to follow. This would allow the user to only clean/mow speci c areas, or in a speci ....etc

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Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstra ....etc

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