Topics in algebra
by I. N. Herstein · first published 1964
91% recommend9% neutral
Why HN recommends it
Clearly written undergraduate introduction to groups, rings and fields, praised for well-crafted progression of concepts and good problem sets; suits self-study and students moving into abstract algebra.
Summarised by Claude from recommending comments
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…Equations is nicely done and likely enough for nearly any applications might encounter. Will want some of this if do A/C circuit theory or deterministic optimal control. For basic abstract algebra Herstein, Topics in Algebra should usually be enough and is well written. With that will be well prepared for, say, algebraic coding theory which actually has some important applications. Once have a background in measure theory,…
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗…that of a set. And then you can learn about "groups", which are sets with a little more structure, if you will. And then you go on to "rings". And then "fields". For all this stuff, go get Herstein's "Topics in Algebra". It's far and away the best text. That's as far as I got. I suspect there's a ton of other fun things out there (number theory? graph and network theory?), but I don't know anything about it.
on “Learning Math” ↗…Rudin's "Principles of Mathematical Analysis" is a collection of true statements with zero motivation or exposition, and it's impossible to follow on your own. On the other end, something like Herstein's "Topics in Algebra" clearly spells out the reason for everything and is a joy to read. Most books are somewhere in between, so if a certain book isn't working for you, try something else on the same topic.
on “How to read a mathematics textbook (2016)” ↗This. For Algebra, look for Topics in Algebra by Herstein. It reads beautifully, and the problems at the end of each chapters are very good at solidifying the knowledge.
on “Ask HN: How to Study Mathematics?” ↗Herstein Topics in Algebra or Dummit and Foote.
on “Ask HN: How to self-study mathematics from the undergrad through graduate level?” ↗…returning to it (and some of its sequels) again and again. Adopting a systems thinking mindset. When analysing problems looking for the bottleneck, then figuring out how to elevate that constraint. 2. Topics in Algebra/ I. N. Herstein. During the first summer at Uni I decided to read this book cover to cover and solve every single problem in it. Which I did. Sadly, twenty years on, my algebra game is poor. But that…
on “Ask HN: Which book/essay changed your life?” ↗Great list. Another addition to the list would be 4. Topics in Algebra by I.N.Herstein. It has a slightly better (and tougher) set of problems than what you would find in the book by Artin.
on “Ask HN: Math books like SICP?” ↗'Topics In Algebra' by I.N.Herstein. Back in college years this was my first book. Despite many other books (which might look easier) I always came back here because of the care it takes to walk through well crafted progression…
on “A Brief Guide to a Few Algebraic Structures” ↗For abstract algebra, there is the polished I.\ N.\ Herstein, {\it Topics in Algebra,\/} (markup for TeX word processing). For Galois theory, took an oral exam on what was in Herstein. For linear algebra where the field is any of the rationals, reals, complex, and finite fields there…
on “Learn you Galois fields for great good (2023)” ↗…learn geometry but because of all the concerns of his kingdom he didn't have time to read the Elements. [2] "Linear Algebra done Right" by Sheldon Axler "Understanding Analysis" by Stephen Abbott "Topics in Algebra" by Herstein. this is a lovely book and beautifully written but some of the notation is a bit dated. I have two more recent algebra books but they are a bit advanced for me until I work through Herstein.…
on “Sheafification – The optimal path to mathematical mastery: The fast track (2022)” ↗> "Topics in Algebra" by Herstein. this is a lovely book and beautifully written but some of the notation is a bit dated Now you make me feel old! I had the second edition just as it came out in 1984. A long time ago but…
on “Sheafification – The optimal path to mathematical mastery: The fast track (2022)” ↗…prerequisites (more would be helpful) would be abstract algebra, linear algebra, 'analysis', measure theory, and functional analysis. For abstract algebra, there are many texts. Sufficient is I. N. Herstein, 'Topics in Algebra', Blaisdell, New York, 1964. but can consider S. Lang, etc. For linear algebra, there are many texts, but the old: Paul R. Halmos, 'Finite-Dimensional Vector Spaces, Second Edition', D. Van Nostrand…
on “Suggest good sites/books on probability” ↗…by E. Nering, some work I did in mathematical physics, the first chapters of Nickerson, Spencer, and Steenrod's Advanced Calculus, my ugrad math honors paper on group representation theory, Herstein's Topics in Algebra on abstract algebra, Halmos, FDVS, Forsythe and Molar on numerical linear algebra, applications in multivariate statistics, some work in optimization, carefully wrote out my own notes, enough for a book,…
on “The best linear algebra books” ↗…Galois theory, rings, integral domains, fields, vector spaces, even a little on quaternions. In grad school I was forced into another course in abstract algebra, this time from the book I. Herstein, Topics in Algebra. Otherwise the prof was trying to understand algebraic geometry, as in Grothendieck. After his first few lectures on group theory, after class I asked if he was going to cover group representations,…
on “Galois Groups and the Symmetries of Polynomials” ↗Was that Herstein's "Topics in Algebra" or his "Abstract Algebra"?
on “Abstract Algebra (2016) [pdf]” ↗