A Concrete Approach to Abstract Algebra |
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Page 17
... operations the child knows at this stage we may call the rational operations . A rational operation is any- thing that can be done by means of addition , subtrac- tion , multiplication , and division , each used as often as you like ...
... operations the child knows at this stage we may call the rational operations . A rational operation is any- thing that can be done by means of addition , subtrac- tion , multiplication , and division , each used as often as you like ...
Page 32
... operations that we can label + and , but yet fall short of being fields . One or more of statements ( 7 ) through ( 12 ) proves false . There are still other structures in which we do not have two operations , but only one . For example ...
... operations that we can label + and , but yet fall short of being fields . One or more of statements ( 7 ) through ( 12 ) proves false . There are still other structures in which we do not have two operations , but only one . For example ...
Page 37
... operations means that the operations are to be applied successively . Thus , if I want to apply ( D + 2 ) · ( D + 3 ) to f ( t ) , I begin by finding ( D + 3 ) f ( t ) . Let this be u ( t ) . I then apply the operation ( D + 2 ) to u ...
... operations means that the operations are to be applied successively . Thus , if I want to apply ( D + 2 ) · ( D + 3 ) to f ( t ) , I begin by finding ( D + 3 ) f ( t ) . Let this be u ( t ) . I then apply the operation ( D + 2 ) to u ...
Contents
Introduction | 1 |
The Viewpoint of Abstract Algebra | 5 |
Arithmetics and Polynomials | 26 |
Copyright | |
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Common terms and phrases
Accordingly addition algebra already answer appears apply arithmetic modulo axioms basis belongs calculating called chapter class containing coefficients complex consider construction contains corresponds course cubic defined definition dimensions displacement divided division earlier East elements elements of F equal equation example expression fact factor field F given gives Hence hold inches independent instance integers label leaves linear linearly dependent look machine means ments mixture multiplication multiply natural North numbers obtain occurs operations ordinary particular plane polynomial possible powers procedure proof properties prove quadratic question rational rational numbers real numbers remainder result root satisfy sequence solution square stand statement structure subtract Suppose symbol theorem things tion values vector space whole write zero