Questions tagged [abstract-algebra]
For questions about the study and teaching of abstract algebra, including topics such as groups, rings, fields, and vector spaces.
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An algebra student wants to learn to type commutative diagrams in LaTeX
A maths student takes his first course on homological algebra, and wants to write his answer in LaTeX. What is the simplest way for him to write commutative diagrams in LaTeX?
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Learn ring theory more fun
I asked this question at 'mathoverflow'. However, the character of this question does not match mathoverflow, so I am asking this question again on this site.
Motivation:
Among abstract algebra, I am ...
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Requesting a Polynomial System of Equations
I am teaching a course in commutative algebra, and it includes a project where the students research on a particular topic, solve a small problem and present it to the class.
I usually give my ...
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Introduction of group action as morphism of groups
The usual definition of a group action is as follows.
Let $G$ be a group and $A$ be a set. An action of $G$ on $A$ is defined to be a map $\rho:G\times A\rightarrow A$ satisfying certain conditions.
I ...
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On Teaching Cyclic Groups [closed]
My professor asked me to take 20 mins on talking about Cyclic Groups and their practical applications in front of the whole class.
How should I start? Can anyone please help me.
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Third isomorphism theorem: how important is it to state the relationship between subgroups?
In texts which present the third isomorphism theorem:
$$(G/N)/(H/N) \cong G/H$$
the relationship between the entities is often seen presented in the form:
Let $H$ and $N$ be normal subgroups of a ...
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Visual aids for understanding group theory
I want ideas for pictorial representation of groups which can help one understand the different group theorems.
Here are some examples of the type of thing I am looking for. In this video by socratica ...
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Should one teach to use equality or isomorphism in particular groups?
I am wondering the following. Suppose we have some particular space $X$ and $x_1,x_2,x_3,x_4\in X$ has the law of composition that works like Klein four-group. Is it correct to say that the structure ...
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What is a good way to broach the subject of abstract algebra, to a student in Calc 1, or pre-calc?
Background
I want to introduce my students to some big names in mathematics, and one of the names I want to bring up is Richard Borcherds, known for his contributions to the fields of number theory, ...
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is it beneficial to encourage high school students to conduct their own 'research' in mathematics?
Is it good idea to encourage students to look up more about particular topics that interest them? The idea is that I don't think they will understand how to read math literature.
for example, if a ...
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Advice on teaching advanced mathematics to high school students
I am a high school student really into algebra and algebraic geometry.
I want to expose this sort of math to other high school students that have the motivation and ability.
For a long time, I had no ...
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Can you talk about (the rest of the) field axioms when the operations are not closed? [closed]
Note: Updated based on this.
In my course, my instructor posed the following exercise:
Let $S$ be the subset of $\mathbb R^n$, $S=\{(a_1,a_2,a_3...a_n) | a_2 = \pm a_1, a_3=...=a_n=0 \}$. Define ...
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Undergraduate-level abstract algebra books or courses that don't start with groups or rings
When I was an undergrad studying abstract algebra, we used the second edition of Artin and covered groups first and then rings. Fields, vector spaces, and algebras came later, I think.
I remember ...
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in what sense is the subject of finite group theory 'algebraic'?
[cross posted from mse]
the class of all finite groups is not closed under produtcs - example: the product over all finite cyclic groups - thus it is not a variety of algebras, ie, it's not ...
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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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