When you finish Lang, you do Eisenbud - Commutative Algebra with a View Towards Algebraic Geometry. Then you are the master. I have no idea how these people wrote these books. It's so much material for one person to know well enough to write a book on! I assume to write a book, you probably know way more than what's in there.
@@pinklady7184 You learn over time as you read books or take classes. Every book will go over the notation even if it's a one-pager in the front or back.
This class was the hardest for me, since I still wasn't comfortable with abstraction. I came back to it (by self-study) after getting used to abstraction, and it was much, much easier.
Math Sorcerer does it again!!! You make learning math and the ease of learning math very, very valuable and very rewarding!!! Thank you for all the great work you've done for us!!! :) :) :) :)
This is my absolute favorite course I have taken in college! I’m currently in Abstract Algebra II and I love it as well. I do strongly recommend linear before this because I come across a lot of examples with matrices. We use the 9th edition Gallian book and I think it’s a great book. For some reason this course came very easily to me but I do have several friends who hated the course and struggled through it.
If anyone is looking for a linear path: Linear Algebra - Strang (mostly the first half) Linear Algebra - Hoffman and Kunze (slightly more than the first half) Abstract Algebra - Dummit and Foote immediately; get through Groups/Rings/Fields and the basics of Modules, with Lang as a reference when you need another perspective on something. I might consider rereading the group theory stuff again at some point further down the track. Structure Theorem for Finitely Generated Modules over a PID: online lecture notes. There are a few good ones out there. Galois Theory - Milne's notes. Stewart and Garling also work. Commutative Algebra - Atiyah/MacDonald. More Advanced Commutative Algebra - Eisenbud. Read as much as you need, when you need it. I have never sat down and read straight through even a full chapter, but I have read many individual theorems/proofs from it when needed to check things off. You may need a little more on integral closures. Many texts blackbox certain important hard IC results, and I recommend "Integral Closures of Ideals, Rings and Modules" by Swanson and Huneke if you ever run into that issue.
Not abstract algebra, but I wrote my first convincing proof today in LATEX! I went to all my friends not in the class and asked them to read it regardless of their feeling towards math.
Click on bluelighted time to view any book in particular below: (N.B. I will return with revisions. Please alert me to my errors) 0:41 "Contemporary Abstract Algebra" by Joseph A. Gallian "Abstract Algebra, a First Course" by Dan Saracino 2:56 "Modern Algebra, An Introduction" by John R. durbin. "Abstract Algebra with a Concrete Introduction" by John A. Beachy & William D. Blair. 3:41 "Group Theory" by B. Baumslag & B. Chandler. "Modern Algebra" by Frank Ayres. 4:13 "Abstract Algebra, an Introduction" by Hungerford. "Introduction to Abstract Algebra" by Ray Dubisch. "A Ccrete Approach to Abstract Algebra" by W. W. Sawyer. 5:01 "Elements of Abstract Algebra" by Allan Clark. "Algebra Structure" by Serge Lang. 6:06 "Topics in Abstract Algebra" by I. N. Herstein. 6:27 "A First Course in Abstract Algebra" by Hiram Paley & Paul Weichsel. 6:56 "A First Course in Abstract Algebra" by John B. Fraleigh. 7:58 "Concepts in Abby Charles Lanski. "Lectures in Abstract Algebra" by Jameson. 9:25 "Algebra" by Michel Artin. "Galois Theory" by Emil Artin. "Rings, Fields and Modules" by ???? "Groups" by ??? "Algebra" by Vander Waerden. 11:24 "Basic Algebra" by Anthony W. Knapp. "Algebra" by Serge Lang. 13:01 "Exercises in Classical Ring Theory" by T. Y. Lam. "Topics in Ring Theory" by Barnshay. "Ring Theory" by Burns. "The Theory of Rings" by Neal R. McCoy.
I use to feel sad because I felt cut off from the joy of learning Abstract Algebra, because I felt I was not going to understand. I was not smart as them. But what I have found is that I can actually understand this subject. I am seeing that is actually talking about very simple things. I smile all the time because I am tasting the beauty of this subject.
Well tempered klavier and professor Fraleigh both bring me back to my teens. That it reads really well is not surprising. Had the honor of meeting him at URI. We clicked.
@@TheMathSorcerer He was an articulate lecturer. And the URI professor Lojasiewicz I referred to. He carried a chalkboard eraser in one hand, but corrected his writing using the ball of his thumb. Was he any relation to Stanislaw? Always reminded me of the story of a mathematics professor at the University of Rome in the 1950's that my father described to me. An associate of Enrico Fermi himself. He said he would mid lecture scratch his right ear with his left hand. From behind his head.
I always admired a people who was so special, clever at math or physics.Someone like a scientists.I dreamed so much about my own growing. But I had to go to work and made a money for a living at very young age. I was angry but now I am so strong and happy with my grow. Always I was at math very bad because I believed other people how a common I am . I believed... It was long a way.. Now I believe in myself. Because math for me is about a path not about results. This is the reason why I have my books with math or others, I study and read it because I want.Because everything around is a math,every science, all universe. And I am so thankfull for a pages like this is. And so thankfull for person like the math sorcerer is. 🙂
Having just done Linear Algebra, I'm probably going to be doing a lot of abstract algebra over the summer because it feels like the natural next step. I'll probably be beginning with Gallian's book and, once I get through that entirely, I'll probably return here to find another book to look at.
Brilliant Video Man! I'm a Huge Fan Of C Pinter's Book On Abstract Algebra Honestly, It's just too damn good and the problems especially within the Group Theory section are Just Incredible! Also It Covers Galois Theory And Aspects Of Number Theory Which is absolutely beautiful in its own right!
I came in the comments just to see if someone had mention Pinter's book. I actually only read this one, after flipping through a couple of others mentioned here and reading a bunch of reviews online. I think it was a good choice for a first exposure to the subject
I would love to see a review of Pinter's book in this channel. I can't say how does it compare to the other beginner books, but I absolutely love how easy is it to read Pinter's. I love it!
Nice overview of some classic abstract algebra books. Of the older books, I also like Garrett Birkhoff's Algebra book. His book with Saunders MacLane is more readable, but both are somewhat dated and without the applications in physics and other fields, and most important, without the great illustrations seen in contemporary abstract algebra books. Gallian's book seems well written and well illustrated. I'd advise getting a rather current edition as there will be more illustrations and examples of practical applications.
There is a very old Schaums Outline Guide "Abstract Algebra" by Joong Fang (1963) which I absolutely hated when I was trying to teach myself Abstract Algebra, but proved to be a very concise and deep review text after I went elswwhere to learn the topic. Fang studied at Yale and Columbia universities in the early 1950s and received his doctorate from the University of Mainz in West Germany. He joined ODU's philosophy department in 1974 after teaching philosophy and math at Memphis State University. He retired in 1990. A native of North Korea who moved to the United States in 1948 and became a naturalized citizen, Fang was a multilingual Kantian scholar, who wrote more than 30 books on philosophy and mathematics and over 300 scholarly papers in his twin fields of interest. He was also the founding editor of the journal Philosophia Mathematica, and he established his own field of study, the Sociology of Mathematics.
For the graduate level, Algebra: Chapter 0 by Paolo Aluffi is sensational, covers all the important topics from the beginning to advanced through the eyes of basic category theory. A story related to this book: me and my friends wanted an original copy real bad (it's like 90$ new), so we made a request to our uni's library to get one. Since we wanted to make sure they did order it, we told a lot of people to make a request for it. They probably though it was needed for a course, and got 2 copies. No way we need 2 copies. Whoops.
Great video The Math Sorcerer! I am self-studying undergraduate abstract algebra, and personally I think Artin's book is not too hard to follow. I am using a lecture series that uses the book so that makes it easier.
I'd like to add some topics and give my outline of a good path to study algebra. First a good understanding of linear algebra is Important. Because learning linear algebra first is a great way to familiarize your self with Ideas that a common in algebra. Vectorspaces are an algebraic structure so you already encounter questions and conceps that are quit natural to ask and discover but on the other side Vectorspaces are really well behaved so answering these questions is not that hard. I don't know of a good English Book in linear algebra but the Important Topics that a good Book should Cover in my Opinion are, 1 Vector Spaces, 2 Linear Maps, 3 Determinant, 4 Eigenvalues, 5. inner product spaces and 6. the tensor products. Additionally knowing about Decomposition and normal forms of matrices and linear maps does not hurt. After that you can Pretty much start with abstract algebra. Their are already multiple Books referenced in the Video but the most important Topics, you typical learn about in a first abstract algebra course is, an introduction to Group Theory, some basic Ring Theory that gives the prerequisites, for Field Theory and finally an introduction to Galios theory. After that you are already quit advanced and you should have witnessed some powerful results, for example the structure theorem of finite abelean groups or the fundamental theorem of galios theory. But their are other really cool Topics in algebra, one of them is representation theory. Its basically about solving questions about groups with the help of linear algebra. You pretty much only need linear algebra as a prerequisite, so you can dive in that topic even earlier. Good Books on that are Representations and Characters of Groups by james and liebeck and the harder one but written by one of the best mathematician in the last century, linear representations of finite groups by serre. A other Topic in that you also can immediately dive into after Linear Algebra is group theory. Although you learn a bit group theory in a abstract algebra course or book I will reference a nice part of group theory. Its combinatorial group theory. Its basically the combination of graph and group theory. If that sounds fantastic to you (wich it is) try introduction to group theory by oleg bogopolski. Now after we have dealt with the fun part of algebra I come to the dreary part of algebra. Its commutative algebra! The study of commutative ring. Its quit technical and their is not much motivation behind the Definitions and Theorems. Its more laying the groundwork for the cool stuff than being cool. Books I Liked on the Topic, are Bosch Commutative Algebra, Introduction to Commutative Algebra by atiyah and macdonald, undergrad commutative algebra by miles reid. Books I didn't like but because the world is bad, unjust and cruel, you still have to read them(at least some parts), if you want to learn commutative algebra: Commutative Algebra by Eisenbud. Important Topics are: Modules, the different types of rings (noetherian, artenian, regular, local etc.), integral extensions, dimension theory, Valuations and Dedekind Domains, basic homological algebra(up to derived functors) After you survived commutative algebra, fun can enter you life again. And here come the two reasons you have suffered the last months. First it is algebraic number theory. Its where many Topics you have learned before now come together to help you to understand the most basic Object in Math: The whole numbers. The main object you study in algebraic number theory are numberfields, these are finite extensions of the rational numbers. It is just really fun, because it is the first time all this stuff you have learned becomes useful (In mathematics, who cares about the real world lol). A good Book on that Topic is Jürgen Neukirchs Algebraic Number Theory. Especially the first two Chapters. The first Chapter is about understanding these Numberfields, with some really nice geometric Ideas and it culminates to a really natural proof of the quadratic reciprocity law, in just 2 lines! The other Chapter is about generalizing the theory behind the reciprocity law with the help of valuations. Wich are in it self a generalization of the norm. After that comes Class Field Theory, wich is the beginning of some the most interesting math. Like Fermats last Theorem, or the Langlands Program. The other reason to study Commutative algebra is Algebraic Geometry. That is the study of Zeros of Polynomials in multiple Variables. Infamous for being really abstract and difficult. Im just at the beginning at understanding it but its one of the interesting topics i have encountered by now. Books on that Topic are Algebraic Geometry by Hartshorne. And the rising sea by vakil. I Will end my text now with 2 quotes on algebraic geometry: "I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months - when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! . . . A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance." - Alexander Grothendieck (Who revolutionized algebraic geometry.) on his approach on math. " As it turned out, the field seems to have acquired the reputation of being esoteric, exclusive and very abstract with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate...'' - David Mumford Therefore obey our new algebraic overlords!!
Am an IT professional and am reading IN Herstein once again (after having first read it few years back). I did have a copy of Artin’s Algebra and I felt Artin can be a bit cryptic at times and if you have read Herstein, you can let go of Artin. I still want to know which 2 or 3 books I should read after having read Herstein because I can’t read all these books suggested here..
@@TheMathSorcerer Keep up the good work! One day I hope to be able to learn abstract algebra. Or at least get a taste of it. See what the fuss is about if you know what I mean. I have one question. What would you use abstract algebra for? Because I have heard that you use it in topology to solve questions in physics. But is that the only thing?
That's so relatable! I'm currently studying for my undergraduate admission exam. I'm gonna study computer engineering (a course that mixes computer science with some physics and engineering stuff), but I'm really into maths. And here I am, watching math divulgation videos just for fun.
@@martanetto3087 It seems interesting as to what you are going to be doing in college. Sounds fun. Good luck on your exam! I am sort of in the same situation as you are in to be fair.
it took a little warming up to, at least for me, but I am now a pretty big fan of Algebra: Chapter 0 by Aluffi. I think it is a pretty good stepping stone to "next steps," e.g. Commutative Algebra by Atiyah (which I enjoyed right away).
Algebra by Bourbaki is also classic (BUT I guess nowadays no too much beginner will learn algebra from this book). For those proficient in the Chinese language, there is a widely read and sophisticated text by Li Wen-Wei(李文威)- 代数学方法（Method in algebra）, often referred to as "LWW". In my view, LWW can be regarded as a supplementary textbook on algebra, offering concise and somewhat unconventional proofs that diverge from the usual texts. To illustrate, in demonstrating the fundamental theorem of symmetric polynomials, he employs a Young diagram, thereby rendering the proof considerably more accessible once the underlying combinatorial principles are grasped. Furthermore, the initial three chapters introduce category theory, including the concepts of Grothedieck Universe, adjoined functor, and monoidal category. As stated in the preface of LWW, the objective of the book is to establish structural coherence between concepts. It is therefore strongly recommended that those who have completed an introductory course in algebra read LWW, in order to gain an understanding of the ways in which different concepts and techniques can be structured and linked together. You could download the PDF file from Li Wen-Wei's home page, the book was based on LWW's lectures on UCAS China and could be used as introductory text for freshman according to the preface, but personally I would not suggest this as a beginning text. (Indeed I learn algebra from Lang's "Thick Dictionary").
Legend says some well-known professors found that some "obvious" proof in Lang's algebra wasn't "obvious" at all, and they even wrote articles about that. Of course by "obvious proof" I mean sometimes he just didn't finish the proof and just wrote "Obvious." as a filler. Just have no idea what's going on when he was writing 🤯 Also it's just ok to find that you can't understand Lang's "examples". First year graduate cannot to be expected to understand many of them.
Great video! although I understand that algebra is more your field, would you consider creating a geometry one as well?I would love to see your take on this,im sure it will help me as well as others here!
As usual excellent video! I do miss my favorite algebra book (not that I have read a ton) ;Algebra: Saunders MacLane, Garrett Birkhoff. I found their use of category theory verry helpful. ( I think one of them "invented" category theory)
A similar video for Discrete Maths? Also would like to know your fav books on logical puzzles, I recently got some Raymond Smullyan's titles and enjoyed solving them.
Maybe it's just me but Dummit & Foote felt like a standard undergrad level of difficulty and was easily readable when I used it in my undergrad classes while the yellow Lang book was like drinking water from the fire hose.
If you would do this type of video for Topology also, then I will make a temple, worship you 5 times per day, and teach and memorize every book that you have recommended, page by page XD.
Good video. Makes me wonder if I have been trying it wrong. For years I have struggled with Mac Lane and Saunders Algebra (an early edition -- blue cover). It seems to require more short-term working memory that I am capable of.
This is just a theory, but I feel that if you are able to make sense of algebra, analysis will be a breeze, but even if you are good at analysis, algebra will take the same amount of time to get good at. I'm still waiting for all the group theory I learnt to "click". It is super cool though :)
The problem with Introductory Abstract Algebra is students dont get enough exposure to technicalities on Set-Theoretic Reasoning. So they're more prone to having difficulty when asked to write down their own proof They might be knowledgeble, up to certain extent, about Zorn Lemma/ Axiom of Choice; but to fathom its consequences in proving methods? Hardly! It's because the big guys in Maths, considered such technicalities as overly- redundant and inhibits students to spark some delightful curiosity into the abstract algebra. Instructors are being tormented with various ways of introducing this beautiful subject and yet still be blamed. It's quite ironic if CS students know by heart Zassenhaus Lemma but have never gotten their hands on Lattices
Hey Math Sorcerer, do you think the ideal Abstract Algebra course should start with Ring theory or Group Theory? My professor taught Rings first and later I found out it's not very common. He used Introduction to Algebra by Peter J. Cameron.
@@TheMathSorcerer Yeah, but he says the rings are more intuitive because we already worked with Z, it's kind of familiar - and then you build the theory around them and later the groups are easy :). Thanks for the reply.
Most of the American Abstract Algebra texts are difficult to learn from , I am wondering if Math Sorcerer has had any experience with Indian Math Books ......A course in Abstract Algebra by Vijay K Khanna and S K Bhambri is superb ... It covers both undergraduate and graduate level Abstract Algebra , the fourth Edition had over 500 solved problems in it , something we rarely see in American Books....
I plan to self-teach myself Abstract Algebra during my Summer break using the Fraleigh book; I'm pretty excited. Does anyone here know if the paperback version of the Fraleigh book is the same as the hardcover one on Amazon? I mean in terms of the content of the book, of course. If anyone can tell me, that would be greatly appreciated. Thank you.
Nice reference of books. Have a query, how do you recommend to learn abstract algebra, If say you want to study computational group theory and implement algorithms from that?
@@TheMathSorcerer I've just found your channel and am finding it very useful. I'm trying to build up my skillset so I can help my kids with maths as they get older. My kids love your comedy videos. 👍
Last semester I got an A in my abstract algebra class. We used a concrete introduction to higher algebra by childs. Do you think I can start reading dummit and foote?
Very informative vid! Question: what are your thoughts on Abstract Algebra or Topics in Algebra by I.N. Herstein? I started to teach myself A.A using Topics in Algebra but found very quickly the problems quite difficult.
Linear Algebra seems to be a prerequisite for a number of math courses, Number Theory, for example, but couldn't a student take Abstract Algebra while taking Linear Algebra or even Linear Algebra after taking Abstract Algebra? And do you plan to teach Linear Algebra at Udemy in the future?
Does abstract algebra come after Linear Algebra? and does Linear Algebra come after College (Intermediate) Algebra? Or does one need to take Calculus first?
In the US, linear algebra is usually an intermediate level class that’s taught after calculus. However, you can probably learn most of it if you’ve taken college algebra. Abstract algebra is considered a higher level and sometimes even graduate level class.
I started objecting Jacobsen renaming his book Basic Algebra when one of my College Algebra students came to office hours with the library's copy. "Professor Wilson, why doesn't this look like anything we're doing in class? "
I actually bought Basic Algebra once upon a time, thinking that it was an introductory book on abstract algebra. I discussed it with a friend soon afterwards and got pointed to Fraleigh instead.
What do you think of "Abstract Algebra: Theory and Applications" by Thomas W. Judson? It's open source and my university uses it for their abstract algebra courses, of which I'm taking the first next semester. Kinda wanted to get a head start on it over winter break.
2 роки тому
I started reading the Fraleigh book today and proofs for the basic stuff are written down so badly… Is this a good book for real?
A serious question: What do we get studying this much maths? Never really liked maths not specifically but the part when maths get tough. Yeah i know basic calculus and understand its importance. But what is the use of this extra maths?
Sir, I want to read EA Behrens Ring theory book so can you please tell me what prerequisites I need? And did Behrens added Non Commutative Algebra in his book?
No J. J. Rotman? He wrote great books: A First Course in Abstract Algebra, An Introduction to the Theory of Groups, Galois Theory, Advanced Modern Algebra and others. Since I'm here, what do you think about the following books? Ian Stewart - Galois Theory; Stewart and Tall - Algebraic Number Theory and Fermat's Last Theorem; DJH Garling - Galois Theory?
do you think you could review Real Analysis for Graduate Students by Bass? it's free online, and physical copies are available for pretty cheap. it covers measure theory and functional analysis i believe
Thanks for this, some really interesting books to check out. I have used Fraleigh and Gallilan and I am loving it so far. I have another recommendation for a beginner/intermediate book and thats "Abstract Algebra Manual" by Ayman Badawi. It's quite pricey for what it is (imo) but there are lots of pdfs floating online (not that I encourage this xD) but it is basically a book of common proof questions that is a useful supplement (supplement, you can't learn lots of theory from this book) to the others.
Am self taught web developer want to learn algorithms and data structure can you please tell me what math playlist to learn in your channel I will be grateful to you because I completely forget all the math and want to do carrier shift ??
When you finish Lang, you do Eisenbud - Commutative Algebra with a View Towards Algebraic Geometry. Then you are the master. I have no idea how these people wrote these books. It's so much material for one person to know well enough to write a book on! I assume to write a book, you probably know way more than what's in there.
Can I read Eisenbud - Commutative Algebra before Lang's ?
And then you read Hartshorne - Algebraic Geometry. And then your Head explodes.
Where do you learn all your mathematical symbols/ shorthands? Or what books?
@@pinklady7184 You learn over time as you read books or take classes. Every book will go over the notation even if it's a one-pager in the front or back.
InfiniteQuest86 thanks.
I'm loving all these START to FINISH videos. Keep making more of it. The books you have are like goldmine. Thanks for this
This class was the hardest for me, since I still wasn't comfortable with abstraction. I came back to it (by self-study) after getting used to abstraction, and it was much, much easier.
Any lessons you'd share on getting used to abstraction?
Math Sorcerer does it again!!! You make learning math and the ease of learning math very, very valuable and very rewarding!!! Thank you for all the great work you've done for us!!! :) :) :) :)
❤️
This is my absolute favorite course I have taken in college! I’m currently in Abstract Algebra II and I love it as well. I do strongly recommend linear before this because I come across a lot of examples with matrices. We use the 9th edition Gallian book and I think it’s a great book. For some reason this course came very easily to me but I do have several friends who hated the course and struggled through it.
Abstract algebra is theory with roids and the father of computer science
If anyone is looking for a linear path:
Linear Algebra - Strang (mostly the first half)
Linear Algebra - Hoffman and Kunze (slightly more than the first half)
Abstract Algebra - Dummit and Foote immediately; get through Groups/Rings/Fields and the basics of Modules, with Lang as a reference when you need another perspective on something. I might consider rereading the group theory stuff again at some point further down the track.
Structure Theorem for Finitely Generated Modules over a PID: online lecture notes. There are a few good ones out there.
Galois Theory - Milne's notes. Stewart and Garling also work.
Commutative Algebra - Atiyah/MacDonald.
More Advanced Commutative Algebra - Eisenbud. Read as much as you need, when you need it. I have never sat down and read straight through even a full chapter, but I have read many individual theorems/proofs from it when needed to check things off.
You may need a little more on integral closures. Many texts blackbox certain important hard IC results, and I recommend "Integral Closures of Ideals, Rings and Modules" by Swanson and Huneke if you ever run into that issue.
Not abstract algebra, but I wrote my first convincing proof today in LATEX! I went to all my friends not in the class and asked them to read it regardless of their feeling towards math.
Another FANTASTIC presentation by the Math Sorcerer ... Thank you for the considerable effort you put into these videos!
4:31 "An introduction to Abstract Algebra by Roy Da Bitch"
Ah yes, a classic.
LOL
Click on bluelighted time to view any book in particular below:
(N.B. I will return with revisions. Please alert me to my errors)
0:41 "Contemporary Abstract Algebra" by Joseph A. Gallian
"Abstract Algebra, a First Course" by Dan Saracino
2:56 "Modern Algebra, An Introduction" by John R. durbin.
"Abstract Algebra with a Concrete Introduction" by John A. Beachy & William D. Blair.
3:41 "Group Theory" by B. Baumslag & B. Chandler.
"Modern Algebra" by Frank Ayres.
4:13 "Abstract Algebra, an Introduction" by Hungerford.
"Introduction to Abstract Algebra" by Ray Dubisch.
"A Ccrete Approach to Abstract Algebra" by W. W. Sawyer.
5:01 "Elements of Abstract Algebra" by Allan Clark.
"Algebra Structure" by Serge Lang.
6:06 "Topics in Abstract Algebra" by I. N. Herstein.
6:27 "A First Course in Abstract Algebra" by Hiram Paley & Paul Weichsel.
6:56 "A First Course in Abstract Algebra" by John B. Fraleigh.
7:58 "Concepts in Abby Charles Lanski.
"Lectures in Abstract Algebra" by Jameson.
9:25 "Algebra" by Michel Artin.
"Galois Theory" by Emil Artin.
"Rings, Fields and Modules" by ????
"Groups" by ???
"Algebra" by Vander Waerden.
11:24 "Basic Algebra" by Anthony W. Knapp.
"Algebra" by Serge Lang.
13:01 "Exercises in Classical Ring Theory" by T. Y. Lam.
"Topics in Ring Theory" by Barnshay.
"Ring Theory" by Burns.
"The Theory of Rings" by Neal R. McCoy.
awesome!
It is gratifying to experience the love you have for your books.
Vous cultivez l'amour du savoir ....
pretty rare ....
❤️
Wow, I literally just bought my first abstract algebra book today!
Awesome !
@@TheMathSorcerer --as a possum with a blossom, Blanka!!! :) :) :)
@@TheMathSorcerer Excellent video.
Thank you!
I use to feel sad because I felt cut off from the joy of learning Abstract Algebra, because I felt I was not going to understand. I was not smart as them. But what I have found is that I can actually understand this subject. I am seeing that is actually talking about very simple things. I smile all the time because I am tasting the beauty of this subject.
Well tempered klavier and professor Fraleigh both bring me back to my teens. That it reads really well is not surprising. Had the honor of meeting him at URI. We clicked.
oh wow very nice!!
@@TheMathSorcerer He was an articulate lecturer. And the URI professor Lojasiewicz I referred to. He carried a chalkboard eraser in one hand, but corrected his writing using the ball of his thumb. Was he any relation to Stanislaw? Always reminded me of the story of a mathematics professor at the University of Rome in the 1950's that my father described to me. An associate of Enrico Fermi himself. He said he would mid lecture scratch his right ear with his left hand. From behind his head.
I always admired a people who was so special, clever at math or physics.Someone like a scientists.I dreamed so much about my own growing.
But I had to go to work and made a money for a living at very young age.
I was angry but now I am so strong and happy with my grow.
Always I was at math very bad because I believed other people how a common I am . I believed...
It was long a way..
Now I believe in myself.
Because math for me is about a path not about results.
This is the reason why I have my books with math or others, I study and read it because I want.Because everything around is a math,every science, all universe.
And I am so thankfull for a pages like this is.
And so thankfull for person like the math sorcerer is. 🙂
:)
Having just done Linear Algebra, I'm probably going to be doing a lot of abstract algebra over the summer because it feels like the natural next step. I'll probably be beginning with Gallian's book and, once I get through that entirely, I'll probably return here to find another book to look at.
THANK YOU!!!! I needed this video so badly 😅😅 just about to start the second part of abstract algebra and surely i have to look to some of this books.
I bough Gallian and Fraleigh's books and they're a very good combo so far! thanks for the recommendation for sure.
They are!
Brilliant Video Man! I'm a Huge Fan Of C Pinter's Book On Abstract Algebra Honestly, It's just too damn good and the problems especially within the Group Theory section are Just Incredible!
Also It Covers Galois Theory And Aspects Of Number Theory Which is absolutely beautiful in its own right!
I came in the comments just to see if someone had mention Pinter's book. I actually only read this one, after flipping through a couple of others mentioned here and reading a bunch of reviews online. I think it was a good choice for a first exposure to the subject
I would love to see a review of Pinter's book in this channel. I can't say how does it compare to the other beginner books, but I absolutely love how easy is it to read Pinter's. I love it!
Do you know where I can get the solutions for the exercises in that book?
@@mlunghisintlakuso3216 If you're willing to pay a subscription to Chegg, they have every solution to Pinter's book, even the proofs.
Nice overview of some classic abstract algebra books. Of the older books, I also like Garrett Birkhoff's Algebra book. His book with Saunders MacLane is more readable, but both are somewhat dated and without the applications in physics and other fields, and most important, without the great illustrations seen in contemporary abstract algebra books. Gallian's book seems well written and well illustrated. I'd advise getting a rather current edition as there will be more illustrations and examples of practical applications.
There is a very old Schaums Outline Guide "Abstract Algebra" by Joong Fang (1963) which I absolutely hated when I was trying to teach myself Abstract Algebra, but proved to be a very concise and deep review text after I went elswwhere to learn the topic.
Fang studied at Yale and Columbia universities in the early 1950s and received his doctorate from the University of Mainz in West Germany. He joined ODU's philosophy department in 1974 after teaching philosophy and math at Memphis State University. He retired in 1990.
A native of North Korea who moved to the United States in 1948 and became a naturalized citizen, Fang was a multilingual Kantian scholar, who wrote more than 30 books on philosophy and mathematics and over 300 scholarly papers in his twin fields of interest. He was also the founding editor of the journal Philosophia Mathematica, and he established his own field of study, the Sociology of Mathematics.
Damn no "Visual group theory", by far the best introduction to group theory.
For the graduate level, Algebra: Chapter 0 by Paolo Aluffi is sensational, covers all the important topics from the beginning to advanced through the eyes of basic category theory.
A story related to this book: me and my friends wanted an original copy real bad (it's like 90$ new), so we made a request to our uni's library to get one. Since we wanted to make sure they did order it, we told a lot of people to make a request for it. They probably though it was needed for a course, and got 2 copies. No way we need 2 copies. Whoops.
yeah chapter 0 is a very good book, I prefer it over Lang tbh
You're a life saver,I like how you present things 👌,your excitement gives me motivation
Great video The Math Sorcerer! I am self-studying undergraduate abstract algebra, and personally I think Artin's book is not too hard to follow. I am using a lecture series that uses the book so that makes it easier.
Are you following Benedict group Cuz I am too
I'd like to add some topics and give my outline of a good path to study algebra.
First a good understanding of linear algebra is Important. Because learning linear algebra first is a great way to familiarize your self with Ideas that a common in algebra. Vectorspaces are an algebraic structure so you already encounter questions and conceps that are quit natural to ask and discover but on the other side Vectorspaces are really well behaved so answering these questions is not that hard. I don't know of a good English Book in linear algebra but the Important Topics that a good Book should Cover in my Opinion are, 1 Vector Spaces, 2 Linear Maps, 3 Determinant, 4 Eigenvalues, 5. inner product spaces and 6. the tensor products. Additionally knowing about Decomposition and normal forms of matrices and linear maps does not hurt.
After that you can Pretty much start with abstract algebra. Their are already multiple Books referenced in the Video but the most important Topics, you typical learn about in a first abstract algebra course is, an introduction to Group Theory, some basic Ring Theory that gives the prerequisites, for Field Theory and finally an introduction to Galios theory. After that you are already quit advanced and you should have witnessed some powerful results, for example the structure theorem of finite abelean groups or the fundamental theorem of galios theory.
But their are other really cool Topics in algebra, one of them is representation theory. Its basically about solving questions about groups with the help of linear algebra. You pretty much only need linear algebra as a prerequisite, so you can dive in that topic even earlier. Good Books on that are Representations and Characters of Groups by james and liebeck and the harder one but written by one of the best mathematician in the last century, linear representations of finite groups by serre.
A other Topic in that you also can immediately dive into after Linear Algebra is group theory. Although you learn a bit group theory in a abstract algebra course or book I will reference a nice part of group theory. Its combinatorial group theory. Its basically the combination of graph and group theory. If that sounds fantastic to you (wich it is) try introduction to group theory by oleg bogopolski.
Now after we have dealt with the fun part of algebra I come to the dreary part of algebra. Its commutative algebra! The study of commutative ring. Its quit technical and their is not much motivation behind the Definitions and Theorems. Its more laying the groundwork for the cool stuff than being cool. Books I Liked on the Topic, are Bosch Commutative Algebra, Introduction to Commutative Algebra by atiyah and macdonald, undergrad commutative algebra by miles reid. Books I didn't like but because the world is bad, unjust and cruel, you still have to read them(at least some parts), if you want to learn commutative algebra: Commutative Algebra by Eisenbud. Important Topics are: Modules, the different types of rings (noetherian, artenian, regular, local etc.), integral extensions, dimension theory, Valuations and Dedekind Domains, basic homological algebra(up to derived functors)
After you survived commutative algebra, fun can enter you life again. And here come the two reasons you have suffered the last months. First it is algebraic number theory. Its where many Topics you have learned before now come together to help you to understand the most basic Object in Math: The whole numbers. The main object you study in algebraic number theory are numberfields, these are finite extensions of the rational numbers. It is just really fun, because it is the first time all this stuff you have learned becomes useful (In mathematics, who cares about the real world lol). A good Book on that Topic is Jürgen Neukirchs Algebraic Number Theory. Especially the first two Chapters. The first Chapter is about understanding these Numberfields, with some really nice geometric Ideas and it culminates to a really natural proof of the quadratic reciprocity law, in just 2 lines! The other Chapter is about generalizing the theory behind the reciprocity law with the help of valuations. Wich are in it self a generalization of the norm. After that comes Class Field Theory, wich is the beginning of some the most interesting math. Like Fermats last Theorem, or the Langlands Program.
The other reason to study Commutative algebra is Algebraic Geometry. That is the study of Zeros of Polynomials in multiple Variables. Infamous for being really abstract and difficult. Im just at the beginning at understanding it but its one of the interesting topics i have encountered by now. Books on that Topic are Algebraic Geometry by Hartshorne. And the rising sea by vakil. I Will end my text now with 2 quotes on algebraic geometry:
"I can illustrate the ... approach with the ... image of a nut to be opened. The first
analogy that came to my mind is of immersing the nut in some softening liquid, and why
not simply water? From time to time you rub so the liquid penetrates better, and otherwise
you let time pass. The shell becomes more flexible through weeks and months - when the
time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! . . .
A different image came to me a few weeks ago. The unknown thing to be known
appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea
advances insensibly in silence, nothing seems to happen, nothing moves, the water is so
far off you hardly hear it ... yet finally it surrounds the resistant substance."
- Alexander Grothendieck (Who revolutionized algebraic geometry.) on his approach on math.
" As it turned out, the field seems to have acquired the reputation of being esoteric, exclusive and very abstract with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate...''
- David Mumford
Therefore obey our new algebraic overlords!!
thank you!!!!!!!!!!!!
Thanks, this is really what I need, my fascination by Algebra will be finally calmed down by this list of books.
Greetings from Mexico :D
Hola❤️
Thanks so much , you are a passionate guy and you help sooo much people !
Am an IT professional and am reading IN Herstein once again (after having first read it few years back). I did have a copy of Artin’s Algebra and I felt Artin can be a bit cryptic at times and if you have read Herstein, you can let go of Artin. I still want to know which 2 or 3 books I should read after having read Herstein because I can’t read all these books suggested here..
You know this channel is good when you are watching math videos where you don’t understand anything, but still watch for the fun.
hehe
@@TheMathSorcerer Keep up the good work! One day I hope to be able to learn abstract algebra. Or at least get a taste of it. See what the fuss is about if you know what I mean.
I have one question. What would you use abstract algebra for? Because I have heard that you use it in topology to solve questions in physics. But is that the only thing?
That's so relatable!
I'm currently studying for my undergraduate admission exam. I'm gonna study computer engineering (a course that mixes computer science with some physics and engineering stuff), but I'm really into maths. And here I am, watching math divulgation videos just for fun.
@@martanetto3087 It seems interesting as to what you are going to be doing in college. Sounds fun. Good luck on your exam! I am sort of in the same situation as you are in to be fair.
it took a little warming up to, at least for me, but I am now a pretty big fan of Algebra: Chapter 0 by Aluffi. I think it is a pretty good stepping stone to "next steps," e.g. Commutative Algebra by Atiyah (which I enjoyed right away).
Great video, I think I might get the course for the summer since I’m taking Group Theory with D&F as the text this fall.
Algebra by Bourbaki is also classic (BUT I guess nowadays no too much beginner will learn algebra from this book). For those proficient in the Chinese language, there is a widely read and sophisticated text by Li Wen-Wei(李文威)- 代数学方法（Method in algebra）, often referred to as "LWW". In my view, LWW can be regarded as a supplementary textbook on algebra, offering concise and somewhat unconventional proofs that diverge from the usual texts. To illustrate, in demonstrating the fundamental theorem of symmetric polynomials, he employs a Young diagram, thereby rendering the proof considerably more accessible once the underlying combinatorial principles are grasped. Furthermore, the initial three chapters introduce category theory, including the concepts of Grothedieck Universe, adjoined functor, and monoidal category. As stated in the preface of LWW, the objective of the book is to establish structural coherence between concepts. It is therefore strongly recommended that those who have completed an introductory course in algebra read LWW, in order to gain an understanding of the ways in which different concepts and techniques can be structured and linked together. You could download the PDF file from Li Wen-Wei's home page, the book was based on LWW's lectures on UCAS China and could be used as introductory text for freshman according to the preface, but personally I would not suggest this as a beginning text. (Indeed I learn algebra from Lang's "Thick Dictionary").
Thanks sir .... for me ... this is the best video on UA-cam 👌💖🎯👑
Legend says some well-known professors found that some "obvious" proof in Lang's algebra wasn't "obvious" at all, and they even wrote articles about that. Of course by "obvious proof" I mean sometimes he just didn't finish the proof and just wrote "Obvious." as a filler. Just have no idea what's going on when he was writing 🤯
Also it's just ok to find that you can't understand Lang's "examples". First year graduate cannot to be expected to understand many of them.
thank you for making all of your videos!
My pleasure!
Thank you for this video. I'm going to get all these books.
You are a real genius
You are also a good teacher
You did a great job！
Great video! although I understand that algebra is more your field, would you consider creating a geometry one as well?I would love to see your take on this,im sure it will help me as well as others here!
We use Basic Abstract Algebra by PB Bhattacharya in India.....and it is an amzing book to start with.
My favourite subject indeed , thanx boss
As usual excellent video! I do miss my favorite algebra book (not that I have read a ton) ;Algebra: Saunders MacLane, Garrett Birkhoff. I found their use of category theory verry helpful. ( I think one of them "invented" category theory)
A similar video for Discrete Maths?
Also would like to know your fav books on logical puzzles, I recently got some Raymond Smullyan's titles and enjoyed solving them.
:)
Maybe it's just me but Dummit & Foote felt like a standard undergrad level of difficulty and was easily readable when I used it in my undergrad classes while the yellow Lang book was like drinking water from the fire hose.
If you would do this type of video for Topology also, then I will make a temple, worship you 5 times per day, and teach and memorize every book that you have recommended, page by page XD.
haha
Could you make a video where you talk about every lesson on math from first grade to bachelor/master
I mean what you have to know
I love your videos 🤩💖 you rock
When will you post a video from probability theory based on measure theory to stochastic calculus?
Good video. Makes me wonder if I have been trying it wrong. For years I have struggled with Mac Lane and Saunders Algebra (an early edition -- blue cover). It seems to require more short-term working memory that I am capable of.
Algebra is just beautiful.
This is just a theory, but I feel that if you are able to make sense of algebra, analysis will be a breeze, but even if you are good at analysis, algebra will take the same amount of time to get good at. I'm still waiting for all the group theory I learnt to "click". It is super cool though :)
👍
wow i have exam tomorrow and i just searched easiest way to study abstract and finish it fast then this video popped up .
The problem with Introductory Abstract Algebra is students dont get enough exposure to technicalities on Set-Theoretic Reasoning.
So they're more prone to having difficulty when asked to write down their own proof
They might be knowledgeble, up to certain extent, about Zorn Lemma/ Axiom of Choice; but to fathom its consequences in proving methods?
Hardly!
It's because the big guys in Maths, considered such technicalities as overly- redundant and inhibits students to spark some delightful curiosity into the abstract algebra.
Instructors are being tormented with various ways of introducing this beautiful subject and yet still be blamed.
It's quite ironic if CS students know by heart Zassenhaus Lemma but have never gotten their hands on Lattices
I love I.N. Hersteins' books on abstract algebra: Abstract Algebra, Topics in Abstract Algebra.
1:17 your friend published the book!? 1:20 oooh okay a recommendation.
Abstract algebra shows that complex number are a perfect cycle
Thancs a lot sir .for this amount of information
Hey Math Sorcerer, do you think the ideal Abstract Algebra course should start with Ring theory or Group Theory? My professor taught Rings first and later I found out it's not very common. He used Introduction to Algebra by Peter J. Cameron.
usually you start with groups, that way you can define rings in terms of groups
@@TheMathSorcerer Yeah, but he says the rings are more intuitive because we already worked with Z, it's kind of familiar - and then you build the theory around them and later the groups are easy :). Thanks for the reply.
Can you do a start to finish on set theory? Mathematical logic?
Most of the American Abstract Algebra texts are difficult to learn from , I am wondering if Math Sorcerer has had any experience with Indian Math Books ......A course in Abstract Algebra by Vijay K Khanna and S K Bhambri is superb ... It covers both undergraduate and graduate level Abstract Algebra , the fourth Edition had over 500 solved problems in it , something we rarely see in American Books....
I plan to self-teach myself Abstract Algebra during my Summer break using the Fraleigh book; I'm pretty excited. Does anyone here know if the paperback version of the Fraleigh book is the same as the hardcover one on Amazon? I mean in terms of the content of the book, of course. If anyone can tell me, that would be greatly appreciated. Thank you.
Nice reference of books. Have a query, how do you recommend to learn abstract algebra, If say you want to study computational group theory and implement algorithms from that?
Do one on number theory!
Thanks, this is very helpful.
🙂
You're welcome!
@@TheMathSorcerer I've just found your channel and am finding it very useful. I'm trying to build up my skillset so I can help my kids with maths as they get older. My kids love your comedy videos.
👍
Awesome !!
Do you have a suggestion for a beginner book that has some emphasis on linear algebra?
amazing! have you done the trig from start to finish?
i have been searching but couldn't find..
not yet!
Last semester I got an A in my abstract algebra class. We used a concrete introduction to higher algebra by childs. Do you think I can start reading dummit and foote?
yes you DEFINITELY can, it's totally worth getting that book, you love it, especially after taking abstract algebra
Very informative vid! Question: what are your thoughts on Abstract Algebra or Topics in Algebra by I.N. Herstein? I started to teach myself A.A using Topics in Algebra but found very quickly the problems quite difficult.
You are awesome!
Linear Algebra seems to be a prerequisite for a number of math courses, Number Theory, for example,
but couldn't a student take Abstract Algebra while taking Linear Algebra or even Linear Algebra after taking Abstract Algebra? And do you plan to teach Linear Algebra at Udemy in the future?
You could but most people take linear first, and yes hopefully some day!
How about Algebra by McLane and B I r k h o f f ?
Good video, man
thanks man!
Do you have any tips for learning the subject?
Tip the table over, then place Pinter on it.
And if you really want to get the chicks, put Grove on top.
haha
Agreed!
It looks there's a 2008 edition as well a 1980 Saracino. Think the 1980 is better?
Does abstract algebra come after Linear Algebra? and does Linear Algebra come after College (Intermediate) Algebra? Or does one need to take Calculus first?
In the US, linear algebra is usually an intermediate level class that’s taught after calculus. However, you can probably learn most of it if you’ve taken college algebra. Abstract algebra is considered a higher level and sometimes even graduate level class.
What might be some applications of this math?
I cry because of the intro. 😭
J.j.rotman book isn't covered. He written slightly modern view.
Where do you get your used math books cheaply, may I ask? My eyes start hurting from all the pdfs by now...
I started objecting Jacobsen renaming his book Basic Algebra when one of my College Algebra students came to office hours with the library's copy. "Professor Wilson, why doesn't this look like anything we're doing in class? "
I actually bought Basic Algebra once upon a time, thinking that it was an introductory book on abstract algebra. I discussed it with a friend soon afterwards and got pointed to Fraleigh instead.
Do I need to study analysis (baby Rudin) before abstract algebra or they aren't related
they are not related enough for it to matter so much
How rigorous is your course on abstract algebra?
What do you think of "Abstract Algebra: Theory and Applications" by Thomas W. Judson? It's open source and my university uses it for their abstract algebra courses, of which I'm taking the first next semester. Kinda wanted to get a head start on it over winter break.
I started reading the Fraleigh book today and proofs for the basic stuff are written down so badly… Is this a good book for real?
A serious question:
What do we get studying this much maths? Never really liked maths not specifically but the part when maths get tough. Yeah i know basic calculus and understand its importance. But what is the use of this extra maths?
Nice👍👍
Thx👍
Sir, I want to read EA Behrens Ring theory book so can you please tell me what prerequisites I need? And did Behrens added Non Commutative Algebra in his book?
Is there a book of 'proof' problems for just practicing LOADS of writing proofs?
No J. J. Rotman? He wrote great books: A First Course in Abstract Algebra, An Introduction to the Theory of Groups, Galois Theory, Advanced Modern Algebra and others. Since I'm here, what do you think about the following books? Ian Stewart - Galois Theory; Stewart and Tall - Algebraic Number Theory and Fermat's Last Theorem; DJH Garling - Galois Theory?
I love Rotman's books!!!!!!!!!!!
I emailed once long ago for some typos in Advanced Modern Algebra, he actually responded:)
I just googled him, wow apparently he died, wow.
I should check those other books out, thank you so much:)
@@TheMathSorcerer Hope you find something you like :)
do you think you could review Real Analysis for Graduate Students by Bass? it's free online, and physical copies are available for pretty cheap. it covers measure theory and functional analysis i believe
interesting, will try to get a copy!
what about Survey ov modern Algebra by Birkoff......
lol I was so jealous after seeing the other algebra video
Shipping costs to South Africa are a pain (as well as our postal service).
Yeah that happens. I shipped a book to India a few weeks ago and it cost a lot.
Friend can you start the course of abstract algebra
Love from IRAQ
❤️
Thanks for this, some really interesting books to check out. I have used Fraleigh and Gallilan and I am loving it so far.
I have another recommendation for a beginner/intermediate book and thats "Abstract Algebra Manual" by Ayman Badawi. It's quite pricey for what it is (imo) but there are lots of pdfs floating online (not that I encourage this xD) but it is basically a book of common proof questions that is a useful supplement (supplement, you can't learn lots of theory from this book) to the others.
Nice thank you!
Am self taught web developer want to learn algorithms and data structure can you please tell me what math playlist to learn in your channel I will be grateful to you because I completely forget all the math and want to do carrier shift ??