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Two Approaches to Introducing Abstract Algebra toUndergraduate Students

Hye Sook ParkDept. of Math. Education, Seowon University, Chongju, Chungbuk 361-742, Korea

hyespark@seowon.ac.kr

Suh-Ryung KimDept. of Math. Education, Seoul National University, Seoul 151-742, Korea

srkim@snu.ac.kr

Wan Soon KimDept. of Math., Hoseo University, Asan, Chungnam 336-795, Korea

kimws@office.hoseo.ac.kr

There can be two different approaches to introducing Abstract Algebra to undergraduatestudents: One is to introduce group concept prior to ring concept, and the other is to dothe other way around. Although the former is almost conventional, it is worth while totake the latter into consideration in the viewpoint that students are already familiar to ringsof integers and polynomials. In this paper, we investigated 16 most commonly usedAbstract Algebra undergraduate textbooks and found that 5 of them introduce ring theoryprior to group theory while the rest do the other way around. In addition, we interviewedseveral undergraduate students who already have taken an Abstract Algebra course to lookinto which approach they prefer. Then we compare pros and cons of two approaches onthe basis of the results of the interview and the historico-genetic principle of teaching andlearning in Abstract Algebra and suggest that it certainly be one of alternatives tointroduce ring theory before group theory in its standpoint.