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Results tagged with abstract-algebra
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user 376
For questions about the study and teaching of abstract algebra, including topics such as groups, rings, fields, and vector spaces.
5
votes
Undergraduate-level abstract algebra books or courses that don't start with groups or rings
Saul Stahl's Introductory Modern Algebra: A Historical Approach, 2nd edition, starts with complex numbers and solving equations before reaching fields and then groups, following a historical route. Ga …
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5
votes
What are the differences between popular undergraduate abstract algebra books?
An alternative approach is Childs' A Concrete Introduction to Higher Algebra (3rd ed., Springer 2008). It starts with some basic number theory, followed by rings and fields. Groups don't make an appea …
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4
votes
What are the differences between popular undergraduate abstract algebra books?
An unusual choice could be Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra by Cox, Little and O'Shea. It may not necessarily be a popular …
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7
votes
3
answers
385
views
Rings in parallel with groups in abstract algebra
In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - …
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8
votes
What are the differences between popular undergraduate abstract algebra books?
Judson's Abstract Algebra: Theory and Applications is different in that it is an open source textbook that is available at no cost. I haven't used it (yet), but I think it's worth pointing out for the …
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41
votes
4
answers
5k
views
Rings before groups in abstract algebra?
The default approach to teaching abstract algebra seems to be groups first, then rings. However, occasionally a textbook pops up (e.g. Childs' A Concrete Introduction to Higher Algebra, Hodge et al's …
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2
votes
1
answer
225
views
Improving exposition of a proof about polynomials over infinite fields
This question concerns teaching a proof of the theorem that if a polynomial $f \in k[x]$ over an infinite field $k$ is the zero function (i.e. $f(a) = 0$ for all $a \in k$) then it is also the zero po …
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3
votes
Applications of abstract algebra outside of mathematics and suitable textbook
Thanks in part to Jyrki Lahtonen's remarks on coding theory and cryptography, I have an applied algebra book to suggest:
Algebra for Applications, Arkadii Slinko, 2nd ed., 2020 Springer
The preface to …
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4
votes
6
answers
669
views
Applications of abstract algebra outside of mathematics and suitable textbook
The question What are some good mathematical applications to present in an abstract algebra course? asks about mathematical applications of abstract algebra.
What are some applications of abstract alg …
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14
votes
2
answers
3k
views
Introductory real analysis before or after introductory abstract algebra?
What are the pros and cons for students of taking introductory real analysis before or after introductory abstract algebra, assuming they are going to take both?
I recognize that the overlap between …
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