Philip Melanchthon (1497–1560), humanist and colleague of Martin Luther, is best known for his educational reforms, for which he earned the title Praeceptor Germaniae (the Teacher of Germany). His most influential form of philosophical writing was the academic oration, and this volume, first published in 1999, presents a large and wide-ranging selection of his orations and textbook prefaces translated into English. They set out his views on the distinction between faith and reason, the role of philosophy in education, moral philosophy, natural philosophy, astronomy and astrology, and the importance of philosophy to a true Christian, as well as his views on Classical philosophical authorities such as Plato and Aristotle and on contemporaries such as Erasmus and Luther. Powerfully influential in their time, inspiring many Protestant students to study philosophy, mathematics and natural philosophy, they illuminate the relationship between Renaissance and Reformation thought.
It was as a political thinker that Thomas Hobbes first came to prominence, and it is as a political theorist that he is most studied today. Yet the range of his writings extends well beyond morals and politics. Hobbes had distinctive views in metaphysics and epistemology, and wrote about such subjects as history, law, and religion. He also produced full-scale treatises in physics, optics, and geometry. All of these areas are covered in this Companion, most in considerable detail. The volume also reflects the multidisciplinary nature of current Hobbes scholarship by drawing together perspectives that are now being developed in parallel by philosophers, historians of science and mathematics, intellectual historians, political scientists, and literary theorists.
The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern p
The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.
The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena. The authors consider models of different 'acoustic' media as well as equations and behaviour of finite-amplitude waves. Consideration is given to the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction upon the evolution and interaction of acoustic beams. This book will be of interest not only to specialists in acoustics, but also to a wide audience of mathematicians, physicists, and engineers working on nonlinear waves in various physical systems.
A great master of the early Renaissance, Piero della Francesca created paintings for ecclesiastics, confraternities, and illustrious nobles throughout the Italian peninsula. Since the early twentieth century, the rational space, abstract designs, lucid illumination and naturalistic details of his pictures have attracted a wide audience. Piero's treatises on mathematics and perspective also fascinate scholars in a wide range of disciplines. This 2002 Companion brings together essays that offer a synthesis and overview of Piero's life and accomplishments as a painter and theoretician. They explore a variety of themes associated with the artist's career, including the historical and religious circumstances surrounding Piero's altarpieces and frescoes; the politics underlying his portraits; the significance of clothing in his paintings; the influence of his theories on perspective and mathematics; and the artist's enduring fascination for modern painters and writers.
A great master of the early Renaissance, Piero della Francesca created paintings for ecclesiastics, confraternities, and illustrious nobles throughout the Italian peninsula. Since the early twentieth century, the rational space, abstract designs, lucid illumination and naturalistic details of his pictures have attracted a wide audience. Piero's treatises on mathematics and perspective also fascinate scholars in a wide range of disciplines. This 2002 Companion brings together essays that offer a synthesis and overview of Piero's life and accomplishments as a painter and theoretician. They explore a variety of themes associated with the artist's career, including the historical and religious circumstances surrounding Piero's altarpieces and frescoes; the politics underlying his portraits; the significance of clothing in his paintings; the influence of his theories on perspective and mathematics; and the artist's enduring fascination for modern painters and writers.
The theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.
Complex Analytic Geometry is one of the most important fields of Mathematics. It has a long history that culminated in the Cauchy integral formula in the 19th century. The theory was vastly developed
A compelling journey through history, mathematics, and philosophy, charting humanity?s struggle against randomness Our lives are played out in the arena of chance. However little we recognize it in ou
If the life of any 20th century mathematician can be said to be a history of mathematics in his time, it is that of David Hilbert. To the enchanted young mathematicians and physicists who flocked to s
Join the Cat in the Hat as he explains how to measure circles and calculate pi in this perfect choice for Pi Day celebrations and nurturing a love of math and numbers!The Cat in the Hat makes calculating pi—one of the most fascinating numbers in mathematics—as easy as pie! Using a piece of string and two sticks, the Cat first shows beginning readers how to draw a perfect circle. Then, using a can and a piece of ribbon, he shows how to measure a circle's circumference and diameter, and to use those measurements to calculate pi. Also included is information about the history of measurement and famous Pi Pioneers!Written in simple rhyme, Happy Pi Day is a natural choice for celebrating Pi Day (held annually on March 14), and for nurturing a child's interest in math. Fans of the hit PBS show The Cat in the Hat Knows a Lot About That! will be delighted at this new addition to the Learning Library series.
An insightful, revealing history of the magical mathematics that transformed our world. At a summer tea party in Cambridge, England, a guest states that tea poured into milk tastes different from mil
This book traces the history of the MIT Department of Mathematics-one of the most important mathematics departments in the world-through candid, in-depth, lively conversations with a select and diver
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of f
Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.
