7
votes
3answers
727 views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
2
votes
5answers
336 views

What area of Abstract Algebra do you find most interesting? [closed]

For my Abstract Algebra class, we will be doing small presentations (2 class periods) covering some topic in Abstract Algebra. Thus far, I have studied groups, rings, fields, modules, tensor ...
1
vote
3answers
209 views

Is it possible to learn abstract algebra no precalculus or calculus?

See above. I am trying to re-teach myself mathematics in a different manner than is formally taught (i.e., set theory, number theory, mathematical logic, abstract algebra, discrete math and then ...
12
votes
5answers
2k views

Why teach linear algebra before abstract algebra?

Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra? I'm asking this because personally it seems to be much easier to understand the architecture behind ...
0
votes
1answer
70 views

Interpretation of First Isomorphism Theorem

I understand that the first isomorphism theorem basically says that any homomorphism f from group G to group G' induces an isomorphism from G/Ker(f) to the f(G). What I don't quite understand is the ...
0
votes
1answer
87 views

Severe problems understanding abstract algebra [closed]

I just came out of high school and one of my courses during my first semester of a maths B.sc. is Abstract Algebra. Now all my other courses seem logical and even easy, but this course...I just don't ...
2
votes
2answers
117 views

Examples of groups in the real world

I'm looking for some examples of groups in the real world to show students in a liberal arts math course. For example the Rubik's cube. Keep in mind these students have only a college algebra ...
1
vote
3answers
241 views

Roadway and book recommendations to math study.

I had some calculus, linear algebra and complex analysis courses back in college. But it is not comprehensive. And I felt that my college math was not taught in a logical sequence (maybe because my ...
2
votes
1answer
199 views

4 big ideas in algebra that have rich connections to other fields? [closed]

In his controversial post criticizing high school algebra, Grant Wiggins issued a challenge to his readers: Can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of ...
7
votes
2answers
420 views

How to teach a High school student that complex numbers cannot be totally ordered?

I once again need your precious knowledge! I am not sure which is the best pedagogic way to teach a High school student about why complex numbers cannot be totally ordered. When I was in High school ...
6
votes
3answers
1k views

Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...
6
votes
4answers
2k views

What are the prerequisites for taking introductory abstract algebra?

I am a maths student in my second year of university. I have taken and done quite well in Calculus I, II, III as well as a linear algebra (application focused) class. I have not worked much with ...
5
votes
1answer
192 views

Fundamental theorem Galois Theory

From time to time, I try to give my non-mathematician scientist friends descriptions of important theorems that I come across. One friend, watched a video on Galois and now I'm at a loss on how to ...
39
votes
8answers
5k views

When to learn category theory?

I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts ...
4
votes
3answers
462 views

The elementary coordinate geometry of polynomials? Of rational expressions? Of radicals?

With a few colleagues, we're trying to design an (intermediate) algebra course (US terminology) where we stress the interplay between algebra and geometry. The algebraic topics we would like to cover ...