Solutions to the Exercises

Abstract

At the age of thirteen or fourteen, L.Euler used to work alone on difficult mathematical problems. Every Saturday afternoon he was admitted at the home of Johann Bernoulli, then the world-leading mathematician, to be fostered with unsolved problems and questions. Later in his life, Euler mentioned frequently1 that throughout the week he worked hard to solve as many problems as he could and to have to ask Johann Bernoulli as few questions as possible. For Euler this was the best method for making rapid progress in mathematics. Now also, 300 years later, the efforts for solving exercises without looking up a solution are of extreme importance. For those of our readers, however, who don’t have—in case of difficulties—a Johann Bernoulli at hand, we present below our solutions to the exercises. This allows the readers to compare with their own solutions and to find the one or other idea for improvements. Whenever a reader finds a shorter or more elegant solution, the authors will be glad to include it in a future edition of this book.