No mathematician can be a complete mathematician unless he is also something of a poet K WeierstrassIn this lively and stimulating account, noted mathematician and educator W W Sawyer Professor Emeritus, University of Toronto defines mathematics as the classification and study of all possible patterns It is a broad definition, but one that seems appropriate to the great scope and depth of the topic Indeed, mathematics seems to have few boundaries, either in applications to practical matters or in its mind stretching excursions into realms of pure abstraction.Gearing his approach to the layman whose grasp of things mathematical may be a bit precarious, Professor Sawyer offers a lucid, accessible introduction to the mathematician s cast of mind Five well written preliminary chapters explore the beauty, power and mysticism of mathematics the role of math as an adjunct in utilitarian matters and the concepts of pattern, generalization and unification as both tools and goals of mathematical thought.After developing this conceptual groundwork, the author goes on to treat of advanced topics non Euclidean geometry, matrices, projective geometry, determinants, transformations and group theory The emphasis here is not on mathematics with great practical utility, but on those branches which are exciting in themselves mathematics which offers the strange, the novel, the apparently impossible for example, an arithmetic in which no number is larger than four.Mathematicians will appreciate the author s grasp of a wide range of important mathematical topics, and his ability to illuminate the complex issues involved laymen, especially those with a minimal math background, will appreciate the accessibility of much of the book, which affords not only a portrait of mathematics as a matchless tool for probing the nature of the universe, but a revealing glimpse of that mysterious entity called the mathematical mind Professor Sawyer has further enhanced this new Dover edition with updated material on group theory, appearing here in English for the first time....
|Title||:||Prelude to Mathematics (Dover Books on Mathematics)|
|Number of Pages||:||185 Pages|
|File Size||:||776 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
Prelude to Mathematics (Dover Books on Mathematics) Reviews
the material in it was over my head, but I had forgotten about it. What a treasure!! MATHEMATICIAN'S DELIGHT is more famous, I believe, but this book is filled with wisdom. Sawyer introduces finite geometries and group theory in simple prose. He figures out where Hall and Knight came up with the ideas for some of their exercises in their (famous) HIGHER ALGEBRA text. He introduces the hypergeometric function as a generalization of power series expressions of functions (something I feel I should certainly have heard of before reading about it here.) I can't imagine anyone with an interest in mathematics not finding something in this book to make him or her say "Hmmm..." or even make him or her pick up a pen and do some figuring.
Well, this really is a terrific book. Lots of simple ideas very well explained. He spells out the notion of pattern quite well, and what it means in terms of mathematics. It seems many modern authors just state that math is about patterns and leave it at that. He seems to get to the point on many subjects that a reader has in the back of his mind as he reads about the material.
Wow, Wow, Wow.