Many of the topics that are commonly placed in the area of recreational mathematics have occupied their niches for many years. Therefore, although the bulk of the material in this book was written almost four decades ago, it is largely still topical. The primary areas that are not are where the computer has increased our capability. At the time it was written, the four-color theorem was not yet proven and the largest known prime was but a shadow of what it is now.
Tantalizing teasers including coin and change problems, relative ages, time and distance, and 40 alphametics—innovative letter substitutions. Solutions. Here you will find 150 tantalizing brain-teasers devised by one of the great contemporary inventors of mathematical puzzles. Over 100 problems are in cleverly worded story forms; coin and change problems, relative ages, time and distance problems. Many of these solutions could come up in everyday life. There are also a number of fine "alphametics", innovative letter substitutions you will find specially attractive.
Here an example of the kind of mathematical teasers you will find in this book (#35. A matter of ifs): "If Sam had driven for twenty minutes less than the time he would have driven if he had driven twenty miles less than he did drive but at two-thirds the speed at which he drove, he would have driven ten miles less than he did.
To solve these 100 puzzles, the only things required are an unclouded mind, nerves of steel, and a grasp of such sentences as: "No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street."
Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes.
