Polynomials: a problem book by E. J. Barbeau

By E. J. Barbeau

The e-book extends the highschool curriculum and gives a backdrop for later examine in calculus, glossy algebra, numerical research, and intricate variable idea. workouts introduce many thoughts and issues within the thought of equations, similar to evolution and factorization of polynomials, resolution of equations, interpolation, approximation, and congruences. the idea isn't really handled officially, yet quite illustrated via examples. Over three hundred difficulties drawn from journals, contests, and examinations try out realizing, ingenuity, and ability. every one bankruptcy ends with a listing of tricks; there are solutions to a few of the workouts and ideas to all the difficulties. moreover, sixty nine "explorations" invite the reader to enquire study difficulties and similar themes.

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Extra resources for Polynomials: a problem book

Example text

134, n. 28). B. Misplaced marginal corrections. 26. Note 134 The text has a senseless wa'l-asya while al-asya would be perfectly in place just before. , a word from the text repeated in the margin in order to indicate the intended position of an addition-is suggested by the misplacement in the manuscript of marginal additions when the (presumed) catchword appears twice within a single passage: in two cases the addition was inserted in the wrong place (see the present example and no. 27 below), and in two others it was inserted in both places (see note 35 (partial repetition), and note 531 and line 1602 (catchword: saHa"J).

Three general remarks can be made from an over-all view of these readers' annotations. 1°. The annotations were not confined to any single part of the text; rather, they were distributed throughout, so that the whole text of our manuscript's ancestor(s) must have been examined, at one time or another, by one or several persons. r Despite the fact that this examination was done with some care, so that the text was (or ought to have been) clarified, completed or corrected in many places, a great number of significant omissions and shortcomings-not to mention some serious mistakes considered in §10-were not removed.

This is also true for other passages in which two consecutive wa-huwa's occur: see app. to lines 2650 and 3339, and also lines 2622-23; cf. note 97. II 33 The Extant Arabic Text 22. Line 3016 Instead of having the second condition of the text "wa-yakun kull wa~id minha murabbacan ", one would expect to read in line 3015 "let us search for three square numbers". This case reminds us of no. 17. II. Second Group The readers' additions listed in this group are those which were senselessly incorporated into the text; they are consequently to be found in the critical apparatus.