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jrhawley.ca
| | quomodocumque.wordpress.com
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| | I met Mike Freedman last week at CMSA and I learned a great metaphor about an old favorite subject of mine, random walks on groups. The Heisenberg group is the group of upper triangular matrices with 1's on the diagonal: You can take a walk on the integral or Z/pZ points of the Heisenberg group...
| | hadrienj.github.io
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| | In this post, we will see special kinds of matrix and vectors the diagonal and symmetric matrices, the unit vector and the concept of orthogonality.
| | algassert.com
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| | Craig Gidney's computer science blog
| | www.jeremykun.com
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| So far on this blog we've given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression. If the reader is comfortable with rings, then a field is extremely simple to describe: they're just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We'll give a list of all of the properties that go into this "simple" definition in a moment, but an even more simple way to describe a field is as a place where "arithmetic makes sense.