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In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
Eigenvalue and Singular Value Methods
The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.
What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world’s population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness? In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders. These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry.
Notions fondamentales de la théorie des probabilités - Probabilité conditionnelle et espérance conditionnelle - La théorie de la décision - La gestion des stocks - Chaînes de Markov - Distribution stationnaire d'une chaîne de Markov - Processus de décision markoviens - Loi exponentielle et processus de Poisson - Processus de renouvellement - Files d'attente - Temps d'arrêt optimal sur une chaîne de Markov - La simulation.
A Comprehensive Dictionary of Latin, Greek, and Arabic Roots
Do you ever wonder about the origins of mathematical terms such as ergodic, biholomorphic, and strophoid? Here Anthony Lo Bello explains the roots of these and better-known words like asymmetric, gradient, and average. He provides Greek, Latin, and Arabic text in its original form to enhance each explanation. This sophisticated, one-of-a-kind reference for mathematicians and word lovers is based on decades of the author's painstaking research and work. Origins of Mathematical Words supplies definitions for words such as conchoids (a shell-shaped curve derived from the Greek noun for "mussel") and zenith (Arabic for "way overhead"), as well as approximation (from the Latin proximus, meaning "nearest"). These and hundreds of other terms wait to be discovered within the pages of this mathematical and etymological treasure chest.
Bien qu’un grand nombre d’habiles mathématiciens soient actifs dans le champ grandissant de la biologie mathématique, peu d’entre eux s’intéressent à la botanique. Le Professeur Jean s’est donné pour but d’inciter un plus grand nombre de mathématiciens à se tourner vers la botanique comme source intéressante de problèmes d’un domaine mûr pour le développement mathématique. Pour cela, il a écrit cette excellente introduction à la botanique mathématique.
The Meaning of Puzzles in Human Life
One of the most famous anagrams of all time was constructed in the Middle Ages. The unknown author contrived it as a Latin dialogue between Pilate and Jesus. Jesus' answer to Pilate's question "What is truth" is phrased as an ingenious anagram of the letters of that very question: Pilate: Quid est veritas? ("What is truth?") Jesus: Est virqui adest. ("It is the man before you.")
The origin of anagrams is shrouded in mystery. One
thing is clear, however -- in the ancient world, they were thought to contain hidden
messages from the gods. Legend has it that even Alexander the Great (356--323 b.c.)
believed in their prophetic power.
-- from Chapter Two
The most obvious explanation for the popularity of puzzles is that they provide a form of constructive entertainment. But in The Puzzle Instinct Marcel Danesi contends that the fascination with puzzles throughout the ages suggests something much more profound. Puzzles serve a deeply embedded need in people to make sense of things. Emerging at the same time in human history as myth, magic, and the occult arts, the puzzle instinct, he claims, led to discoveries in mathematics and science, as well as revolutions in philosophical thought.
Puzzles fill an existential void by providing "small-scale experiences of the large-scale questions that Life poses. The puzzle instinct is, arguably, as intrinsic to human nature as is humor, language, art, music, and all the other creative faculties that distinguish humanity from all other species."