Learning Abstract Algebra with ISETL
Springer (Publisher)
Published in January 1994
Book
Hardback
XXI, 252 pages
978-3-540-94104-0 (ISBN)
Description
This book is based on the belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities that will establish an experiential base for any future verbal explanations and to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies, as well as on the substantial experience of the authors in teaching Abstract Algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the math-like programming language ISETL; the main tool for reflection is work in teams of two to four students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. The text section is written in an informal, discursive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture.
More details
Language
German
Place of publication
Berlin
Germany
Target group
College/higher education
Illustrations
2 figs., 1 Diskette MS-DOS
Dimensions
Height: 240 mm
Weight
600 gr
ISBN-13
978-3-540-94104-0 (9783540941040)
Schweitzer Classification
Content
1: Mathematical Constructions in ISETL. 2: Groups. 3: Subgroups. 4: The Fundamental Homomorphism Theorem. 5: Rings. 6: Homomorphisms and ismorphisms. Factorization in Integral Domains.