« ミュージカル「蜘蛛女のキス」 | Main | メーラーのおひっこし »

February 05, 2010

「群論」

「群論」というと、大学の数学の授業で出てきました。当時は抽象的でさっぱりわかりませんでした。
その原因は、
(1)いきなり数式で説明されてもイメージが湧かない
(2)何の役にたつのかわからない
ではないかと思います。

 (1)に関しては、教科書は、どうしても"数式を用いた厳格な論述"になるのでいたしかたないと思います。一方、Web上には、サルでもわかる的なイメージ優先で説明しているサイトがありますね。

 (2)に関して、工学関係に限らず、経済、社会学の本を読んでいると、逆に「数学の○○の考え方を用いて...」なんて文章を結構目にします。習った当時は存在の意味のよくわからなかった複素数が電磁気学ではあたりまえのように使われてその有用性に驚いたり、シンセの本読んでたら三角関数やフーリエ級数がでてきて「役立つじゃん♪」みたいな驚きがあったり。「群論」も、人文から哲学まで一世を風靡した構造主義的な考え方によるものなのですね(群論が先か構造主義が先かは曖昧みたいですが)。

 群、英語ではgroupで、英語の方がイメージを掴みやすいかも。

 群とは演算をもとにしたグループ分けで、演算とは加減乗除だけでなく、移動・回転・作用...など、状態を変化させるあらゆる変換方法(そのなかには"状態を変化しない=そのまま"も当然含む)。この変換が、いわゆる写像というやつになります(丸の中にXだのYだのが描かれて、矢印で隣の丸のX'やY'に対応してるっていうやつだね)。

 で、この演算によって要素はどうなるか?その関係性(構造)に着目したのが群。集合の要素は数でなくてもよいし、演算は算術演算でなくてもよい。構造が同じであれば、全く異なる集合であっても、同型だといえます。
 例えば7回演算を行うと元にもどる群と、毎週日曜は必ずカレーが食卓にならぶ鈴木さん宅は同型。なぜ日曜がカレーなのか、鈴木さんの奥さんに聞くよりも、同じ構造の群を研究したほうが早いかもしれません。
 抽象概念ゆえに、数学以外のあらゆる分野に応用可能なんですねぇ。

参考:ムルンギン族の婚姻体系への応用
http://www.math.tohoku.ac.jp/~ytakao/papers/weil.pdf
http://www.las.osakafu-u.ac.jp/~kawazoe/lecture/math-edu01-html/node4.html

|

« ミュージカル「蜘蛛女のキス」 | Main | メーラーのおひっこし »

学問・資格」カテゴリの記事

Comments

Your website is very the most informative. I liked your website a lot. Thank you.

Posted by: loans canada | July 02, 2010 03:41 PM

kittykuma.cocolog-nifty.com is great! Cash Loans Vs Payday Loans By Brian Smithgall A cash loan is just about the same thing as a payday loan or fast cash loan These types of loans are designed to be of a shortterm nature and be able to help people get from paycheck to paycheck

Posted by: toronto payday loans | July 12, 2010 05:51 AM

Your web publication is excellent. Give thanks to you so much for sharing such an abundance of important additional info. I am going to bookmark your blog website and will be without a doubt coming back. Again, I admire your work along with providing much interesting information to the people.

Posted by: pay day loans | August 25, 2010 11:07 AM

kecjazsqjgfbzlnusmybqplluvekidyxfyn

Posted by: bc loans | September 02, 2010 10:46 AM

This article gives the light in which we can observe the reality. This is very nice one and gives in-depth information. Thanks for this nice article.

Posted by: payday loans online | September 21, 2010 06:49 PM

Usually I do not write on blogs, but I would like to say that this article really convinced me to do so! Congratulations, very nice post.

Posted by: payday loans canada | September 22, 2010 06:34 AM

Finally, an issue that I'm passionate about. I have looked for information of this caliber for the last several hours. Your web-site is greatly appreciated. egtpovykhzn

Posted by: faxless payday loans | September 23, 2010 05:35 AM

Greetings everyone, This webpage is excellent and so is how the matter was expanded. I like some of the comments as well although I would prefer we all keep it on topic in order add value to the subject. It will be

Posted by: loans no fax | September 26, 2010 06:00 AM

I'm happy to have found your very good article! I agree with some of your readers and will eagerly look forward to your coming updates. Just saying thanks will not just be adequate, for the wonderful lucidity in your writing. I will instantly grab your rss feed to stay privy of any updates. Good work and much success in your business efforts.

Posted by: loans in canada | September 26, 2010 03:44 PM

Excellent read, I just passed this onto a colleague who was doing a little research on that. And he actually bought me lunch because I found it for him smile So let me rephrase that: Thanks for lunch!

Posted by: loan canada bad credit | September 27, 2010 04:20 AM

Thanks for good news! Your site is very useful for me. I bookmarked your site!

Posted by: bad credit loans toronto | September 27, 2010 06:43 PM

Thanks for good news! Your site is highly useful for me. I bookmarked your internet site!

Posted by: loan in canada | September 28, 2010 05:07 AM

I will post a link to this blog on my site. I'm sure my readers will find this info really very good.

Posted by: loans ontario | September 28, 2010 06:56 PM

I will submit a link to this blog on my internet site. I'm sure my readers will find this info really impressive.

Posted by: bad credit loans | September 29, 2010 05:48 AM

Very good concepts on this web page. It's rare these days to find websites with data you are seeking. I'm happy I chanced on this webpage. I will certainly bookmark it or even register for your rss feeds simply to be updated on your new posts. Keep up the nice job and I'm sure some other folks researching valued information will actually stop by and benefit from your site for resources.

Posted by: weight loss | October 02, 2010 05:47 PM

A rather nice niche blog, and a high-quality design there sparks Simplicity yet complex algorithm of the internet. Thank You.

Posted by: bad credit loans | October 03, 2010 07:03 PM

Hi buddy, especially informative publish. Please keep them coming.

Posted by: bad credit loans calgary | October 15, 2010 07:24 AM

This web site is awesome. I continually come across some thing new & different right here. Thank you for that data.

Posted by: bad credit loans | October 16, 2010 04:55 AM

Pretty good submit. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. Any way I'll be subscribing to your feed and I hope you submit again soon.

Posted by: loan money canada | October 17, 2010 06:09 AM

Thanks for beneficial news! Your web page is exceptionally useful for me. I bookmarked your site!

Posted by: loan application | October 18, 2010 11:08 AM

Terrific read, I just passed this onto a colleague who was doing a little research on that. And he actually bought me lunch because I found it for him smile So let me rephrase that: Thanks for lunch!

Posted by: bad credit loans | October 19, 2010 12:14 PM

Amazing concepts on this web page. It's rare these days to find websites with data you are seeking. I am happy I chanced on this webpage. I will certainly bookmark it or even register for your rss feeds simply to be updated on your new posts. Keep up the nice job and I'm sure some other folks researching valued information will actually stop by and benefit from your site for resources.

Posted by: laptop deals | October 20, 2010 03:54 AM

Pretty high quality submit. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. Any way I'll be subscribing to your feed and I hope you post again soon.

Posted by: loan in canada | October 20, 2010 11:54 AM

Pretty first-rate publish. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. Any way I'll be subscribing to your feed and I hope you post again soon.

Posted by: loan with bad credit history | October 21, 2010 04:50 AM

This website is the ultimate internet site.

Posted by: loan for bad credit | October 25, 2010 06:54 PM

This website is the leading web-site.

Posted by: personal loan bad credit canada | October 26, 2010 05:36 AM

This website is the most helpful web-site.

Posted by: payday lenders | October 27, 2010 09:12 AM

This website is the highest quality ?nternet site.

Posted by: loan no credit | October 28, 2010 04:39 AM

This website is the top rated internet site.

Posted by: bad credit loan personal | October 30, 2010 03:13 AM

This website is the superior online site.

Posted by: personal loans bad credit | November 01, 2010 05:25 PM

This website is the optimum online site.

Posted by: payday loans ontario | November 02, 2010 09:02 AM

This website is the most excellent web property.

Posted by: bad credit loans canada | November 03, 2010 06:06 AM

This website is the ideal net page.

Posted by: bad credit loans | November 04, 2010 09:05 AM

This website is the most excellent web blog.

Posted by: bad credit loan canada | November 05, 2010 08:22 AM

This website is the best web property.

Posted by: bad credit loans | November 06, 2010 03:51 AM

This website is the ultimate site.

Posted by: cash advance loans | November 06, 2010 11:32 AM

This website is the highest quality world wide web site.

Posted by: loans toronto bad credit | November 07, 2010 05:31 AM

This website is the ideal internet sites.

Posted by: payday cash advance canada | November 09, 2010 07:18 PM

This website is the very best online site.

Posted by: personal loans with bad credit canada | November 10, 2010 08:48 AM

This website is the most popular internet sites.

Posted by: canada cash advance | November 10, 2010 06:25 PM

This website is the ideal web-site.

Posted by: get loan with bad credit | November 11, 2010 09:05 AM

This website is the most useful net page.

Posted by: apply for loans canada | November 11, 2010 07:16 PM

This website is the finest blog site.

Posted by: cash advance online | November 12, 2010 06:36 AM

This website is the most beneficial site.

Posted by: cash advances payday loans | November 13, 2010 04:48 AM

This website is the right internet site.

Posted by: get a loan with bad credit | November 13, 2010 02:18 PM

This website is the leading site.

Posted by: national cash advance | November 14, 2010 06:14 AM

This website is the finest blog site.

Posted by: bad credit loans | November 15, 2010 05:32 AM

This website is the ideal world-wide-web site.

Posted by: personal loans canada | November 15, 2010 03:45 PM

This website is the finest web site.

Posted by: payday loans in canada | November 17, 2010 09:24 AM

This website is the most popular world-wide-web site.

Posted by: payday loans canada | November 18, 2010 05:25 AM

This website is the ultimate web property.

Posted by: personal loans bad credit | November 19, 2010 10:31 AM

This website is the perfect world-wide-web page.

Posted by: loan bad credit canada | November 20, 2010 05:31 AM

This website is the top rated blog site.

Posted by: diet for quick weight loss | November 25, 2010 05:31 PM

This website is the leading ?nternet site.

Posted by: diet for quick weight loss | November 29, 2010 04:26 PM

This website is the top internet site.

Posted by: bad credit loans | November 30, 2010 12:29 PM

This website is the top web property.

Posted by: organic mattress | December 07, 2010 06:29 PM

This website is the most reliable blog site. dkmdqpup

Posted by: online payday loans | December 18, 2010 12:18 PM

This website is the perfect web-site. nycshdyp

Posted by: college scholarships | December 19, 2010 07:21 AM

This website is the preferred internet sites. qxxjkpja

Posted by: sample resume | December 22, 2010 05:22 PM

I am looking for college football online hd. How can I find it?

Posted by: football online | December 24, 2010 05:17 PM

Thanks for the info about ????: ????????????

Posted by: calendar template | January 08, 2011 05:45 AM

Your post about ????: ???????????? rocks!

Posted by: payday loan online | January 09, 2011 08:36 AM

Amazing post about ????: ????????????!

Posted by: digital photo frame | January 09, 2011 04:32 PM

Unfogettable post about ????: ????????????!

Posted by: fitness gym | January 10, 2011 03:34 AM

Unbelievable post about ????: ????????????!

Posted by: green home | January 10, 2011 10:16 AM

Very very nice post about ????: ????????????!

Posted by: hair removal | January 10, 2011 05:23 PM

I appreciate all your hard work and your post about ????: ????????????!

Posted by: home made pizza | January 11, 2011 03:30 AM

Excellent read about ????: ????????????!

Posted by: school grants | January 12, 2011 05:20 PM

Awesome blogpost with reference to ????: ????????????!

Posted by: payday loan advance | January 13, 2011 04:35 PM

Hey would you mind sharing which blog platform you're using? I'm going to start my own blog in the neear future but I'm having a tough time deciding between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your design seems different then most blogs and I'm looking for something completely unique. P.S Apologies for getting off-topic buut I had to ask!

Posted by: http://www.thebestcarpetcleaningmachines.com/ | November 23, 2013 11:27 PM

ugg 偽物 中古品店、アンティーク ショップが見つかりますおよびファッション店をすべて症候性道路。スタイル財布のになってしまうイベントを保つことを選んだ考え方。すべきないされる、違い割合で.今まで ! アグ 激安

Posted by: ugg 偽物 | November 24, 2013 04:23 PM

Normally I don't learn post on blogs, but I would like to say that this write-up very pressured me to take a look at and do so! Your writing style has been surprised me. Thanks, very nice post.

Posted by: http://www.weddingwire.com | November 19, 2014 08:23 AM

The comments to this entry are closed.

TrackBack


Listed below are links to weblogs that reference 「群論」:

« ミュージカル「蜘蛛女のキス」 | Main | メーラーのおひっこし »