Abstract algebra - Dummit and tronunbucambrin.cf - Ebook download as PDF File .pdf) or read book online. Dummit and Foote - Abstract Algebra Third Edition - Ebook download as PDF File .pdf) or read book online. Abstract algebra textbook. subject of abstract algebra and no student should go through such a course without a  Dummit, D. and Foote, R. Abstract Algebra. 3rd ed.
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Dummit and Foote contains just about everything an undergraduate ought to know about abstract algebra. In addition, it is written in a more user-friendly. tronunbucambrin.cf~jcohen//Pinter%tronunbucambrin.cf . For self study of abstract algebra, I recommend Dummit & Foote. I used it as a. recommendations for undergraduate curricula in abstract algebra.1 We .. Dummit, David S. and Foote, Richard M, Abstract Algebra, 3rd edition, John Wiley &.
Koshkin on Mar 10, 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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Loved this book. Yes, Pinter's little book is very accessible. It's a wonderful little book. I was just reading it again this morning. Here's my very basic attempt to visualize some of the key structures: Is anyone aware of something similar, but much more comprehensive? Chinjut on Mar 11, One slight correction: I've almost-exclusively seen "Commutative Groups" referred to as "Abelian Groups".
Is there a reason you use "Commutative Groups"? I'll admit my algebra is quite limited and I may be missing a subtlety. There is no subtlety here. That groups which are commutative are referred to as "abelian" is purely historical. Refering to them as commutative helps understanding for people who are not fammillar with them, and helps highlight the structural simmilarity that the diagram is attempting to show.
Sadly, I find it unlikely that we will get mathamaticians to agree to stop calling them Abelian groups, so learners will have to learn that name eventually. That's why I always call it partition sort instead of quicksort. For those who prefer dead trees, the hardcover is miraculously inexpensive: Since everyone is pitching their favorite books on abstract algebra, here's mine: I'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?
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 memorize 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 understood the entire proof.
And it also turns out that if you understand a proof, or a set of them, you can produce new ones. Of course, almost everyone failed the course. One guy got an A, a couple of us got C's I was one and the rest got F's. Never been prouder of a C in my life. Smaug on Mar 10, Your analysis exams didn't require bookwork?
For someone who has done four years of maths at Cambridge, this idea is dumbfounding: Except, in my year, Category Theory, in which there was no bookwork at all.
Of course I don't hold a grudge about how much time I spent learning the proofs of the monadicity- and adjoint-functor theorems. I'd be appalled if a third of an exam was "reproduce this proof of this theorem". However, if a third of the exam is "Produce a proof of this theorem" and people don't care about whether the proof is original or reproduced, that seems fine.
Certainly, being able to proof any theorems your rely on is important. But being able to recall how any given theorem was proven in a book isn't important. Sure, but there's usually a reason a particular proof is used in lectures: Not sure what you mean by "bookwork". Is that what memorizing proofs is called in the UK? Most of the exams and homework were more typical math exercises, e.
I mean, I remember getting tested on parts of the "epsilon delta" definition of a limit in analysis, for example, but I don't recall ever being asked to regurgitate the entire thing correctly.
It's funny but I don't even associate important tools like Taylor series with "proofs", only applications. The lecturer would sometimes prove things, but we were never tested on the proof, only the ability to apply the result.
Mind you, I was physics not math so perhaps that's the difference. In fairness there is a LOT of math tools to learn, and I'm not sure there's really time to get into proving everything as an undergrad, but perhaps that's a mistake.
Wiktionary's definition of "bookwork" is accurate: Besides crypto. What applications does Abstract Algebra have in CS? Drup on Mar 10, I would tend to say: It's the basis of everything. Here are some examples that were not given in other comments: You get nice stuff if you use algebraic properties such as having your patch commutes and things like that.
To extend the "functional structures" comment, monoids are literally everywhere in software. I don't know about very specific applications, but I think the field itself and is very complimentary to CS, especially when considering finite or discrete structures.
As it's name suggests, abstract algebra abstracts "nice" properties of, e. Modern abstract algebra is deeply tied to category theory, and so now these "nice" properties get abstracted even further out to maps between objects, and as maps between categories i. As such abstract algebra is tied to functional programming on some level I know nothing about this connection though. Linear algebra is a subfield of abstract algebra, and lots of general theorems about what classes of matrices are diagonalizable, or what their eigenvalues look like, etc.
These types of results are relevant to many algorithms, e. Aside from that, I think abstract algebra is quite a beautiful field in its own right. Two books I would recommend are Artin's Abstract Algebra as an intro and Lang's Algebra more advanced, good bridge into the category theory perspective. I second the recommendation for Artin's Algebra. I'd also recommend Paolo Aluffi's Algebra: Chapter 0, which is a nice alternative to Lang and also uses category theory right from the beginning and doesn't require many prerequisites.
Monoids, groups, rings, fields, etc. In general algebraic constructions come up more often than you might think.
The idea of a homomorphism though not specific to algebra is prevalent in almost any formal domain. Compilers by and large can be considered homomorphisms that preserve certain semantic properties which if you dig deep enough can be expressed as algebraic structures: Developing an intuition for all those things is best accomplished by studying abstract algebra.
Monoids aren't just relevant to cryptography. Lists are a prime example. Thanks for the link, the whole site logicmatters. Smith is a great expositor. I had the joy of participating in a category theory reading group with him; he really knows his stuff. Let me just tell you some pros and cons about this bible of algebra. Pros: Tons of examples worked out. Every chapter has some general theory, followed by usually about a half dozen explicit examples.
It's really good to do these examples by yourself, and then read how the book does them, or read them in the book and then try modified examples for yourself and see if you can follow the same ideas.
Another useful thing to do is to try to work some examples as you read through theorems. A billion and two exercises. This is a must for algebra, for the same reason.
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Practice practice practice. The first dozen chapters are so have solutions online google 'project crazy project'.
This doesn't include the stuff on Galois theory you're potentially interested in, but it does include everything up to the stuff on modules over PID, if I remember correctly. It covers nearly everything one could possibly want to know.
Maybe you should look at a few syllabi from different universities then.
In the US it's unusual to get a master's in pure math. Basically people who try to get a PhD and fail are the ones who have master's degrees. However master's degrees in applied math are often terminal degrees. I learned abstract algebra by self study and I used Topics in Algebra by Herstein. It doesn't have very broad coverage, but the problems are excellent.
I was preparing for an honors senior level undergraduate course. After studying the book the course was way beneath my level, so next semester I took a graduate course which was also not challenging. I could just be extraordinarily gifted at algebra, but I think it was the book that did it. Right now, your question seems a little broad. However, you might want to look at this: At least, you can check the videos to see what topics are covered in class. Alfred Yerger Alfred Yerger It is nice to hear of someone else doing self study.
Dummit and Foote - Abstract Algebra Third Edition
I will definitely try to check out the other two books you suggested. I have also been suggested Lang but as you mentioned, I think at my level it is better used in parallel with a more accessible text.
Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. Announcing the arrival of Valued Associate Cesar Manara. Unicorn Meta Zoo 1: Why another podcast?It is nice to hear of someone else doing self study. Chinjut on Mar 11, One slight correction: It was tested out on myself and two other students in Beezer's class.
For example alen algebra applied to arithmetic of time intervals c relational database theory as relates to various ways to construct functions on relations. Guy Steele  sometimes mentions it. These types of results are relevant to many algorithms, e. 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.
One slight correction: I've used Gallian.
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