MARC Record from harvard_bibliographic_metadata

LEADER: 03457nam a22004095a 4500
001 014157773-8
005 20141003190223.0
008 110826s1994 xxu| o ||0| 0|eng d
020 $a9781461226024
020 $a9781461276029 (ebk.)
020 $a9781461226024
020 $a9781461276029
024 7 $a10.1007/978-1-4612-2602-4$2doi
035 $a(Springer)9781461226024
040 $aSpringer
050 4 $aQA174-183
072 7 $aMAT002010$2bisacsh
072 7 $aPBG$2bicssc
082 04 $a512.2$223
100 1 $aDubinsky, Ed,$eauthor.
245 10 $aLearning Abstract Algebra with ISETL /$cby Ed Dubinsky, Uri Leron.
264 1 $aNew York, NY :$bSpringer New York,$c1994.
300 $aXXI, 248 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
505 0 $a1 Mathematical Constructions in ISETL -- 1.1 Using ISETL -- 1.2 Compound objects and operations on them -- 1.3 Functions in ISETL -- 2 Groups -- 2.1 Getting acquainted with groups -- 2.2 The modular groups and the symmetric groups -- 2.3 Properties of groups -- 3 Subgroups -- 3.1 Definitions and examples -- 3.2 Cyclic groups and their subgroups -- 3.3 Lagrange’s theorem -- 4 The Fundamental Homomorphism Theorem -- 4.1 Quotient groups -- 4.2 Homomorphisms -- 4.3 The homomorphism theorem -- 5 Rings -- 5.1 Rings -- 5.2 Ideals -- 5.3 Homomorphisms and isomorphisms -- 6 Factorization in Integral Domains -- 6.1 Divisibility properties of integers and polynomials -- 6.2 Euclidean domains and unique factorization -- 6.3 The ring of polynomials over a field.
520 $aMost students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need 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 astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 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. This text section is written in an informed, discusive 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 preseted in a lecture.
650 10 $aMathematics.
650 0 $aGroup theory.
650 0 $aMathematics.
650 24 $aGroup Theory and Generalizations.
700 1 $aLeron, Uri,$eauthor.
776 08 $iPrinted edition:$z9781461276029
988 $a20140910
906 $0VEN