3

I want to enrich my intuition of the structures studied in Abstract Algebra by going through case studies of them. So, for example, I want some example to be worked through, and in process, the theory to be developed for it.

For example, something like page-298 of Gallian Helpful (section on weird-dice). Also, I liked the sections on graph theory by Kennth H Rosen in his book of discrte mathematics.

tryst with freedom
  • 11,538
  • 3
    There are many, many types of algebraic structures that have been studied. Please clarify which you have interest in, and what you mean by a "case study" (assume readers don't have access to said books). – Bill Dubuque Mar 02 '22 at 19:37
  • Hmm I have described it in the first paragraph and I gave explicit examples from standard books in the second. Is there some part particularly ambiguous? I want to study the structures which come in an abstract algebra book at an UG level. So for example Groups, Rings, Fields etc. @BillDubuque – tryst with freedom Mar 02 '22 at 19:39
  • 6
    How does a "case study" of a group, ring or field differ from the common studies already in (first) courses in algebra? It is far from clear what you seek. – Bill Dubuque Mar 02 '22 at 19:41
  • Hmm, so what I want is like, the book presents an example question, and now to solve that question, it develops the abstract algebra theory to describe various parts and hence end at solution of the problem – tryst with freedom Mar 02 '22 at 19:43
  • Usually books seperate the problems and the theory. So, the theory is developed in total generality without any reference to concrete examples and then later in chapter example is shown. I want something which takes a much less pure approach by bringing the theory out of the examples rather than examples out of the theory if it makes sense – tryst with freedom Mar 02 '22 at 19:45
  • Could you please write a fleshed out answer on the idea you are suggesting ? I think it maybe what I am looking for @Moo – tryst with freedom Mar 02 '22 at 19:50

1 Answers1

5

If I am correctly understanding your request, you are looking for ways to make abstract algebra theory computational to build intuition and experience.

There are many resources that have been created to support this using Computer Algebra Systems.

Examples include professional packages like Magma, Mathematica, Maple and open source packages like GAP, Pari/GP, FriCAS, SAGE and others.

Many books and course materials have been written to go along with these systems and to help provide a more intuitive, exploratory, and experimental approach to abstract algebra and any math area. Examples include

There are also useful resources to have handy like

You might also like to explore

Moo
  • 11,311