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The Unapologetic Mathematician

Mathematics for the interested outsider (by John Armstrong)

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The Unapologetic Mathematician | unapologetic.wordpress.com Reviews
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Mathematics for the interested outsider (by John Armstrong)
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The Unapologetic Mathematician | unapologetic.wordpress.com Reviews

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Mathematics for the interested outsider (by John Armstrong)

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Irreducible Modules « The Unapologetic Mathematician

https://unapologetic.wordpress.com/2012/09/15/irreducible-modules

Mathematics for the interested outsider. Sorry for the delay; it’s getting crowded around here again. Anyway, an irreducible module for a Lie algebra. Is a pretty straightforward concept: it’s a module. Such that its only submodules are. As usual, Schur’s lemma. Tells us that any morphism between two irreducible modules is either. Or an isomorphism. And, as we’ve seen in other examples. Is simple then we know that. Must have its image in. But the only traceless. Matrix is the zero matrix. Setting. You ar...

2

Reducible Modules « The Unapologetic Mathematician

https://unapologetic.wordpress.com/2012/09/16/reducible-modules

Mathematics for the interested outsider. As might be surmised from irreducible modules. For a Lie algebra. Is one that contains a nontrivial proper submodule — one other than. Is a submodule we can form the quotient. This is the basic setup of a short exact sequence. The question is, does this sequence split? That is, can we write. As the direct sum of. And some other submodule isomorphic to. First of all, let’s be clear that direct sums of modules do make sense. Indeed, if. No Indeed, let. In this case,.

3

More New Modules from Old « The Unapologetic Mathematician

https://unapologetic.wordpress.com/2012/09/21/more-new-modules-from-old

Mathematics for the interested outsider. More New Modules from Old. There are a few constructions we can make, starting with the ones from last time. And applying them in certain special cases. First off, if. Modules, then I say we can put an. Module structure on the space. Of linear maps from. Indeed, we can identify. Is a basis for. Is a basis for. Then we can set up the dual basis. Form a basis for. And each one can be identified with the linear map sending. And all the other basis elements of. We con...

4

Dual Spaces « The Unapologetic Mathematician

https://unapologetic.wordpress.com/2008/05/27/dual-spaces

Mathematics for the interested outsider. Another thing vector spaces come with is duals. That is, given a vector space. We have the dual vector space. Of “linear functionals” on. 8212; linear functions from. To the base field. Again we ask how this looks in terms of bases. So let’s take a finite-dimensional vector space. And consider some linear functional. Like any linear function, we can write down matrix coefficients. Notice that since our target space (the base field. Notice that on any vector we have.

5

John Armstrong « The Unapologetic Mathematician

https://unapologetic.wordpress.com/author/drmathochist

Mathematics for the interested outsider. The Submodule of Invariants. Of a Lie algebra. There is one submodule that turns out to be rather interesting: the submodule. We call these vectors “invariants” of. As an illustration of how interesting these are, consider the modules we looked at last time. What are the invariant linear maps. We consider the action of. On a linear map. Or, in other words:. That is, a linear map. Is invariant if and only if it intertwines the actions on. September 21, 2012. In par...

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NORTH to ALASKA – DAY FOUR (8/15) | Bill Watson's Blog

https://watsonw.wordpress.com/2008/08/30/north-to-alaska-day-four-815

Bill Watson’s Blog. Blogging across the worlds of mathematics and science and travel and life. NORTH to ALASKA – DAY FOUR (8/15). August 30, 2008 in Uncategorized. Friday was a marvelous day. I left the. To meet the shuttle bus to. With the promise of lots of wild life and a great view of. If the mountain is out. It had been raining for the past four days in south central. So there were little prospects of seeing the. I took many, many photos before the clouds enveloped. I will post some of the best phot...

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Cinema | Bill Watson's Blog

https://watsonw.wordpress.com/cinema

Bill Watson’s Blog. Blogging across the worlds of mathematics and science and travel and life. I love to see movies. At various times, I have set up and run Cinema Clubs at my universities. Surely you have your own list of the best films you have seen and continue to see. Please feel free to send me your recommendations of films that I should see in the future or add to my list. THE BEST MOVIES of all TIME. In no particular order). In no particular order). Cabinet of Dr. Caligari. Treasure of Sierra Madre.

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pixeloo: Stewie Griffin Untooned

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Saturday, May 24, 2008. Gotta run this morning, but I'll post this and talk a bit more about the process later this weekend. One thing I'll say its definitely harder to get that "realistic" look with smooth skin. This seems pretty illustrated compared to Homer and Mario. Anyway, cheers, enjoy! I got a date on the Official Playstation Magazine UK magazine of Nico Bellic. It'll be on shelves June 16th, check it out if you're in the UK or somewhere that has it! May 24, 2008 at 10:18 AM. I loved this one o O.

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Bayes Theorem and the Justice System | Stevethemathsman's Blog

https://stevethemathsman.wordpress.com/2009/11/22/bayes-theorem-and-the-justice-system

Just another WordPress.com weblog. Bayes Theorem and the Justice System. November 22, 2009. Posted by Stephen Godfrey in Probability. I have been reading a previous issue of New Scientist. And came across an article by Angela Saini. Which you can find here. On how probability is used in the court room. Also if you goto the page you can take an online test to determine if the article is relevant for you next time you get stuck on jury duty. Let us consider two events. Then the conditional probability of.

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Infinite Summer » Blog Archive » Mission Improbable

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Laquo; I Got This Fire In My Heart, Won’t Let Me Sleep, Can’t Concentrate…. Raquo; Greg Carlisle: Reading Infinite Jest Changed My Life (and Now It Will Change Yours). Yes, I know — the term “mission improbable” brings up. Your reward will be fruit punch and pie, and international fame. A consistent response to my last post was the assertion that the inclusion of a ghost in. Have produced creatures with hydrocephalus — the scientific term for “dude, check out that huge head.”. To become convinced that in...

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Instant Coffee: A Method to the Madness?

http://pulltechnologynews.blogspot.com/2009/10/method-to-madness.html

Friday, October 16, 2009. A Method to the Madness? In the interim, since we last left the story on Logicomix,. The Greek Logic graphic novel is currently riding high on success at # 1 on the NY Times bestseller list for paperback graphic novels. And has also debuted at #14 on the Indiebound Bestsellers list. The authors are also currently touring the United States (insert map of tour cities). The story of logic, math and madness is catching fever worldwide. Century mathematicians like Cantor. Brilliance ...

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NORTH to ALASKA — DAY ONE (8/12) | Bill Watson's Blog

https://watsonw.wordpress.com/2008/08/13/north-to-alaska-day-one

Bill Watson’s Blog. Blogging across the worlds of mathematics and science and travel and life. NORTH to ALASKA — DAY ONE (8/12). August 13, 2008 in Uncategorized. Bill Watson’s Math Page. John Armstrong's Math Blog. John Baez’ Weekly Report. Terence Tao’s Math Blog. Tim Gowers’ Math blog. David Stuart’s Maya Blog. Dawn on the Amazon blog. Putting Math into Comments. To enter LaTeX into your comments, insert $Latex [Your LaTeX code]$. NASA Photo of the Day. Spiral Meteor through the Heart Nebula.

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fashionablemathematician - mathematics: GRE Math Quick Review: Conversions

http://fashionablemathematicianmath.blogspot.com/2008/06/gre-math-quick-review-conversions.html

This blog has closed. Follow me to 3stylelife. Thursday, June 19, 2008. GRE Math Quick Review: Conversions. Rounding out the subseries on fractions, decimals, and percentages, this document covers how to convert between the three forms and offers advice on how to approach problems with such conversions. Exercises, solutions, and explanations at the end, as always. You can access the document below:. GRE Math Quick Review: Conversions. September 2, 2008 at 10:16 AM. September 2, 2008 at 10:18 AM. Nine Cha...

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fashionablemathematician - mathematics: August 2008

http://fashionablemathematicianmath.blogspot.com/2008_08_01_archive.html

This blog has closed. Follow me to 3stylelife. Thursday, August 7, 2008. After doing a lot of thinking and reading over vacation, I've decided to shut this blog down. By no means am I done with blogging, but this site really was my first attempt at the beast, and I need to make some fundamental changes. Thank you all for reading (and occasionally commenting). You can follow me to:. Links to this post. Subscribe to: Posts (Atom). Software problems in research #1: Excel turns genes into dates!

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fashionablemathematician - mathematics: GRE Math Quick Review Series

http://fashionablemathematicianmath.blogspot.com/2008/06/gre-math-quick-review-series.html

This blog has closed. Follow me to 3stylelife. Sunday, June 1, 2008. GRE Math Quick Review Series. This is another educational portal page which will house an ongoing series of documents. The documents here are intended for use when preparing for the mathematics section of the GRE (Graduate Record Exam), though they should also be useful for those studying for the SAT, SAT II (in math), or those simply wishing to review their mathematics. Subscribe to: Post Comments (Atom). GRE Math Quick Review: Decimals.

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The Unapologetic Mathematician

Mathematics for the interested outsider. The Submodule of Invariants. Of a Lie algebra. There is one submodule that turns out to be rather interesting: the submodule. We call these vectors “invariants” of. As an illustration of how interesting these are, consider the modules we looked at last time. What are the invariant linear maps. We consider the action of. On a linear map. Or, in other words:. That is, a linear map. Is invariant if and only if it intertwines the actions on. September 21, 2012. In par...

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