Author: Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 258
Book Description
The Messenger of Mathematics
Author: Galois Theory
Author: Jean-Pierre EscofierPublisher: Springer Science & Business Media
ISBN: 1461301912
Category : Mathematics
Languages : en
Pages : 287
Book Description
This book offers the fundamentals of Galois Theory, including a set of copious, well-chosen exercises that form an important part of the presentation. The pace is gentle and incorporates interesting historical material, including aspects on the life of Galois. Computed examples, recent developments, and extensions of results into other related areas round out the presentation.
Sotheran's Price Current of Literature
Author: Henry Sotheran LtdSotheran's Price Current of Literature
Author: Publisher:
ISBN:
Category : Catalogs, Booksellers'
Languages : en
Pages : 332
Book Description
Proof and Proving in Mathematics Education
Author: Gila HannaPublisher: Springer Science & Business Media
ISBN: 9400721293
Category : Education
Languages : en
Pages : 468
Book Description
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Advances in Iterative Methods for Nonlinear Equations
Author: Sergio AmatPublisher: Springer
ISBN: 331939228X
Category : Mathematics
Languages : en
Pages : 286
Book Description
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.
Hegel and Newtonianism
Author: Michael John PetryPublisher: Springer Science & Business Media
ISBN: 9401116628
Category : Philosophy
Languages : en
Pages : 636
Book Description
It could certainly be argued that the way in which Hegel criticizes Newton in the Dissertation, the Philosophy of Nature and the lectures on the History of Philosophy, has done more than anything else to prejudice his own reputation. At first sight, what we seem to have here is little more than the contrast between the tested accomplishments of the founding father of modern science, and the random remarks of a confused and somewhat disgruntled philosopher; and if we are persuaded to concede that it may perhaps be something more than this - between the work of a clearsighted mathematician and experimentalist, and the blind assertions of some sort of Kantian logician, blundering about among the facts of the real world. By and large, it was this clear-cut simplistic view of the matter which prevailed among Hegel's contemporaries, and which persisted until fairly recently. The modification and eventual transformation of it have come about gradually, over the past twenty or twenty-five years. The first full-scale commentary on the Philosophy of Nature was published in 1970, and gave rise to the realization that to some extent at least, the Hegelian criticism was directed against Newtonianism rather than the work of Newton himself, and that it tended to draw its inspiration from developments within the natural sciences, rather than from the exigencies imposed upon Hegel's thinking by a priori categorial relationships.
Classical Mechanics
Author: Emmanuele DiBenedettoPublisher: Springer Science & Business Media
ISBN: 0817646485
Category : Mathematics
Languages : en
Pages : 364
Book Description
* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries
Galois Theory for Beginners: A Historical Perspective, Second Edition
Author: Jörg BewersdorffPublisher: American Mathematical Soc.
ISBN: 1470465000
Category : Education
Languages : en
Pages : 217
Book Description
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
Functions and Generality of Logic
Author: Hourya Benis-SinaceurPublisher: Springer
ISBN: 3319171097
Category : Philosophy
Languages : en
Pages : 145
Book Description
This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. The second chapter reflects on Frege’s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege’s program in the foundations of mathematics, and includes comparisons of Frege’s, Russell’s and Ramsey’s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter’s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem.