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A Concrete Introduction to Higher Algebra
This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.
Historical Studies in the Physical Sciences, Volume 7
The first article in this volume, by Tetu Hirosige, is a definitive study of the genesis of Einstein's theory of relativity. Other articles treat topics—theoretical, experimental, philosophical, and institutional—in the history of physics and chemistry from the researches of Laplace and Lavoisier in the eighteenth century to those of Dirac and Jordan in the twentieth century. Contents: The Ether Problem, the Mechanistic World View, and the Origins of the Theory of Relativity (Tetu Hirosige); Kinstein's Early Scientific Collaboration (Lewis Pyenson); Max Planck's Philosophy of Nature and His Elaboration of the Special Theory of Relativity (Stanley Goldberg); The Concept of Particle Creati...
Pierre Simon Laplace, 1749-1827
Often called the Newton of France, Pierre Simon Laplace has been called the greatest scientist of the late 18th and early 19th centuries. In this compact biography, Hahn illuminates the man in his historical setting. This book reflects a lifetime of thinking and research on a singularly important figure in the annals of Enlightenment science.
Mathematics And Its Teaching In The Southern Americas: With An Introduction By Ubiratan D'ambrosio
This anthology presents a comprehensive review of mathematics and its teaching in the following nations in South America, Central America, and the Caribbean: Argentina, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cuba, Guyana, Haiti, Honduras, México, Panamá, Paraguay, Perú, Puerto Rico, Trinidad and Tobago, and Venezuela. The last summary of mathematics education encompassing countries from the Southern Americas appeared in 1966. Progress in the field during five decades has remained unexamined until now.
An Axiomatic Approach to Geometry
Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several paral...
Matrices
This book provides mathematics teachers with an elementary introduction to matrix algebra and its uses in formulating and solving practical problems, solving systems of linear equations, representing combinations of affine (including linear) transformations of the plane and modelling finite state Markov chains.
Optimal State Estimation
A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: * Straightforward, bottom-up approach begins with basi...
