Elementary Theory of Equations Classic Reprint Leonard Eugene Dickson 9781332804023 Books
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Excerpt from Elementary Theory of Equations
The longer an engineer has been separated from his alma mater, the fewer mathematical formulas he uses and the more he relies upon tables and, when the latter fail, upon graphical methods. Although graphical methods have the advantage of being ocular, they frequently suffer from the fact that only what is seen is sensed. But this defect is due to the kind of graphics used. With the aid of the scientific art of graphing pre sented in Chapter I, one may not merely make better graphs in less time but actually draw correct negative conclusions from a graph so made, and therefore sense more than one sees. For instance, one may be sure that a given cubic equation has only the one real root seen in the graph, if the bend points lie on the same side of the x-axis.
Emphasis is here placed upon Newton's method of solving numerical equations, both from the graphical and the numerical standpoint. One of several advantages (well recognized in Europe) of Newton's method over Homer's is that it applies as well to non-algebraic as to algebraic equations.
In this elementary book, the author has of course omitted the difficult Galois theory of algebraic equations (certain texts on which are very erroneous) and has merely illustrated the subject of invariants by a few examples.
It is surprising that the theorems of Descartes, Budan, and Sturm, on the real roots of an equation, are Often stated inaccurately. Nor are the texts in English on this subject more fortunate on the score of correct proofs; for these reasons, care has been taken in selecting the books to which the reader is referred in the present text.
The material is here so arranged that, before an important general theorem is stated, the reader has had concrete illustrations and often also special cases. The exercises are so placed that a reasonably elegant and brief solution may be expected, without resort to tedious multiplications and similar manual labor. Very few Of the five hundred exercises are of the same nature.
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Elementary Theory of Equations Classic Reprint Leonard Eugene Dickson 9781332804023 Books
I agree with the other reviewer concerning the content. And this is my favorite from Dickson.So I want to address the actual qualit of the reprint. This is a photocopy of the book, which is not in itself a total negative, but for the price the publishers really have to justify it.
How do they? Well the one good point is that it is enlarged, so the presentation is better than an electronic version to a certain extent.
Is it worth it to you for a printed copy which is enlarged for easier reading? I don't know, that is for you to decide.
I personally find the price a little high for an enlargement.
But this is a great text by the author. There is gold in this book for the true students of math.
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Elementary Theory of Equations Classic Reprint Leonard Eugene Dickson 9781332804023 Books Reviews
Dickson was the first truly great mathematician from the United States. A gifted number theorist, he also cared very deeply about the pedagogy of mathematics. For those of you who teach high school mathematics, and who teach the quadratic formula every semester, have you ever been asked by precocious students about the cubic formula? the quartic formula? Dickson explains them and gives very well-written exercises throughout the book. His exposition on symmetric polynomials is first-rate (and a good introduction to Galois Theory the way that Galois would have done it). By defining polynomial differentiation by the binomial theorem for (x + delta x), he allows the power of analysis to be used without any of the thorny topological considerations best left for a Real Analysis course. I crack this book open at least once a semester. Very highly recommended.
The book is a good quality photocopy of the original. Some of the terminology is dated but it’s still a very good book.
I agree with the other reviewer concerning the content. And this is my favorite from Dickson.
So I want to address the actual qualit of the reprint. This is a photocopy of the book, which is not in itself a total negative, but for the price the publishers really have to justify it.
How do they? Well the one good point is that it is enlarged, so the presentation is better than an electronic version to a certain extent.
Is it worth it to you for a printed copy which is enlarged for easier reading? I don't know, that is for you to decide.
I personally find the price a little high for an enlargement.
But this is a great text by the author. There is gold in this book for the true students of math.
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