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Abstract Algebra (2016) [pdf]

254 点作者 e19293001大约 8 年前

17 条评论

qntty大约 8 年前
If you want to learn abstract algebra for the first time and you&#x27;re anything like me, don&#x27;t just read a book about it. It&#x27;ll start to sound like a bunch of abstract nonsense. Eventually you&#x27;ll have the skills needed to &quot;bring it alive&quot; for yourself with a set of concrete examples that you&#x27;ll learn to refer to again and again. I would recommend starting by watching some lectures about it (you can find some here [1] under the lecture schedule).<p>[1] <a href="https:&#x2F;&#x2F;www.math.upenn.edu&#x2F;~ted&#x2F;371F14&#x2F;math371.html" rel="nofollow">https:&#x2F;&#x2F;www.math.upenn.edu&#x2F;~ted&#x2F;371F14&#x2F;math371.html</a>
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bokumo大约 8 年前
The linked PDF also has an online version which is superior in many ways because it has inline <i>executable</i> Sage examples. It can be found at: <a href="http:&#x2F;&#x2F;abstract.pugetsound.edu&#x2F;aata&#x2F;" rel="nofollow">http:&#x2F;&#x2F;abstract.pugetsound.edu&#x2F;aata&#x2F;</a><p>Also, this textbook is one of several open source textbooks developed using MathBook XML which allows authors to create multiple output formats such as PDF, HTML and ePub from one canonical source document written in XML. If you are interested in learning about MathBook XML you should check out: <a href="http:&#x2F;&#x2F;mathbook.pugetsound.edu&#x2F;" rel="nofollow">http:&#x2F;&#x2F;mathbook.pugetsound.edu&#x2F;</a>
globuous大约 8 年前
Evariste Galois always intrigued me. He died aged 20 in a duel supposably for some love story, yet he apparently had &quot;time&quot; to lay the foundations of some pretty serious math. To quote the into from the last chapter of this book which introduces Galois Theory:<p>&quot;[...] attempts to solve the general fifth-degree, or quintic, polynomial were repulsed for the next three hundred years [...] no solution like the quadratic formula was found for the general quintic [...] Finally, at the beginning of the nineteenth century, Ruffini and Abel both found quintics that could not be solved with any formula. <i></i>It was Galois, however, who provided the full explanation by showing which polynomials could and could not be solved by formulas. He discovered the connection between groups and field extensions.<i></i> Galois theory demonstrates the strong interdependence of group and field theory, and has had far-reaching implications beyond its original purpose.&quot;<p>My mom was actually reading a novel about him (a beautiful mind kinda style) last summer. I wonder how he would have turned out if he had not passed away so young.<p>Surprisingly, the only other mathematician that died really young (aka younger than jim morrison and co) is Niels Henrik Abel, also mentioned in the quote. Makes you wonder how healthy algebra is, doesn&#x27;t it ;p
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techwizrd大约 8 年前
When I took Abstract Algebra as part of my Math degree, we used Gallian, Herstein, and Judson. Gallian had a lot of examples and felt very much like the textbooks I used in high schools (colorful, lots of prose, etc.) It is incredibly easy to get into, but sometimes you&#x27;ve understood something and you don&#x27;t need 25 more examples.<p>Herstein and Judson were both a less verbose (sometimes to the point of being unhelpful), but I&#x27;d still recommend them. I think I learned a lot from being exposed to different books. I could always look at another book if one book&#x27;s explanations, examples, proofs, exercises were an issue. The Math Stackexchange was also invaluable because many of the proofs I saw there were very different from the ones I saw in class or in textbooks.
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rckrd大约 8 年前
For self study of abstract algebra, I recommend Dummit &amp; Foote. I used it as a supplement to my undergrad algebra classes and found it to be very useful. This is in contrast to some books like Artin which leave a lot to the readers, while not necessarily bad, are sometimes difficult for self-study.<p>[0] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Abstract-Algebra-3rd-David-Dummit&#x2F;dp&#x2F;0471433349&#x2F;ref=pd_sim_14_4?_encoding=UTF8&amp;pd_rd_i=0471433349&amp;pd_rd_r=00BFEVST8PPDFE5YR12G&amp;pd_rd_w=pNsRA&amp;pd_rd_wg=9P8LG&amp;psc=1&amp;refRID=00BFEVST8PPDFE5YR12G" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Abstract-Algebra-3rd-David-Dummit&#x2F;dp&#x2F;...</a>
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Koshkin大约 8 年前
I can recommend an inexpensive little book by Pinter, which is one of the most student-friendly abstract algebra books on the market.
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mavam大约 8 年前
Here&#x27;s my very basic attempt to visualize some of the key structures: <a href="https:&#x2F;&#x2F;github.com&#x2F;mavam&#x2F;abstract-algebra-cheatsheet" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;mavam&#x2F;abstract-algebra-cheatsheet</a>.<p>Is anyone aware of something similar, but much more comprehensive?
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haldean大约 8 年前
For those who prefer dead trees, the hardcover is miraculously inexpensive: <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Abstract-Algebra-Applications-Thomas-Judson&#x2F;dp&#x2F;1944325026" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Abstract-Algebra-Applications-Thomas-...</a>
egonschiele大约 8 年前
Since everyone is pitching their favorite books on abstract algebra, here&#x27;s mine: <a href="http:&#x2F;&#x2F;a.co&#x2F;fg0OUdG" rel="nofollow">http:&#x2F;&#x2F;a.co&#x2F;fg0OUdG</a>.<p>I&#x27;d love to hear what differentiates this book. Why should I read this one instead of the existing options? Is it because Sage is used?
javajosh大约 8 年前
When I was a physics major at UCI the abstract algebra course ended up being my favorite course. The prof was young, and a real hard ass. Apart from the usual, he forced us to <i>memorize</i> proofs and regurgitate them for tests, as well as come up with original proofs. That might sound draconian (it certainly did to me; none of my real analysis classes asked that of us) but it turned out to be really hard to do unless you <i>understood</i> the entire proof. And it also turns out that if you understand a proof, or a set of them, you can produce new ones.<p>Of course, almost everyone failed the course. One guy got an A, a couple of us got C&#x27;s (I was one) and the rest got F&#x27;s. Never been prouder of a C in my life.
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hackernewsacct大约 8 年前
Besides crypto. What applications does Abstract Algebra have in CS?
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anajuoh大约 8 年前
I remember when the first version of this text came out. It was tested out on myself and two other students in Beezer&#x27;s class. It&#x27;s a solid text.
dominotw大约 8 年前
I took Abstract Algebra course at a local university couple of yrs ago. I learnt how to do proofs first from Spivak&#x27;s calculus, learning to do proofs felt very similar to writing code. I really enjoyed doing Abstract Algebra proofs. Got top score in the course and promptly forgot everything about it after a couple of months. Back to the day job fixing garbage collection on poorly written java apps.
crb002大约 8 年前
The lack of transformation semigroup coverage astounds me. Most interesting endofunctions are not permutations.
adenadel大约 8 年前
This was the book we used for my abstract algebra course. Robert Beezer also has an open linear algebra textbook<p><a href="http:&#x2F;&#x2F;linear.ups.edu&#x2F;" rel="nofollow">http:&#x2F;&#x2F;linear.ups.edu&#x2F;</a>
partycoder大约 8 年前
While great, I hope there was an interactive version, like Jupyter notebooks. Jupyter can embed Sage.
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kdazzle大约 8 年前
oh no way! Whuddup loggers. I was there in 2005.