The Room of Many Colours


Book Description

For over five decades, Ruskin ond has written charming tales that have mesmerized readers of all ages. This collection brings together his finest stories for children in one volume. Published previously as A Treasury of Stories for Children, this attractive rejacketed edition includes two new stories, 'The Big Race' and 'Remember This Day'. Filled with a rich cast of characters and superb illustrations, The Room of Many Colours: A Treasury of Stories for Children is the defnitive book for all Ruskin Bond fans and truly a collector's Item.




The Ultimate Challenge


Book Description

The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.




Complete Warm-Up for Classical Guitar


Book Description

This book contains short and concise exercises for use in a warm-up before practice or performance, and for general technical advancement. The book is divided into four sections: I Arpeggios, II Scales, III Tremolo, and IV Slurs. Each section contains a description of the exercises and general instructions on how to play them. The exercises are intended for guitarists who are looking for a simple warm-up that does not require learning many complicated etudes, exercises or routines. In this book, only one etude is used for a variety of arpeggio and tremolo patterns. The scale warm-ups are based on a two-octave, one-position scale that is shifted up and down the fretboard, and a simple one-position chromatic scale. The pull-off and hammer-on slurs are combined into one exercise to save time. This same routine, when practiced with the metronome gradually increasing the tempo, can also double for technical work. With the exception of one chromatic scale exercise, the rest are on closed strings. Besides being able to move the scale up and down the fretboard, the first finger can be barred. This will increase the left hand difficulty and improve the left hand position and strength.There is close to an hour's worth of material if all the exercises are played with all of their variations at different tempos. Not everything needs to be played everyday, so the warm-up session can be as long as desired or as short as time allows.




Mastering Tremolo


Book Description

Leonardo Garcia's Mastering Tremolo is an extensive guide for all aspiring guitarists wishing to develop solid tremolo technique. From a multitude of preliminary technical exercises and drills to develop a foundation for your tremolo and invigorate your technique, to more than a dozen active practice techniques detailed with musical examples to develop rhythmic precision, note consistency, tone, and speed, to the mental game of playing tremolo, this book will help improve your playing regardless of your level.