Conflicts Between Generalization Rigor And Intuition
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Conflicts Between Generalization Rigor And Intuition
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Author : Gert Schubring
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-10
Conflicts Between Generalization Rigor And Intuition written by Gert Schubring and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-10 with Mathematics categories.
This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
Conflicts Between Generalization Rigor And Intuition
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Author : Gert Schubring
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-14
Conflicts Between Generalization Rigor And Intuition written by Gert Schubring and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-14 with Mathematics categories.
This book deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Schubring studies often overlooked texts, in particular German and French textbooks, and reveals a much richer history than previously thought while throwing new light on major figures, such as Cauchy.
A Brief History Of Numbers
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Author : Leo Corry
language : en
Publisher: OUP Oxford
Release Date : 2015-08-27
A Brief History Of Numbers written by Leo Corry and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Mathematics categories.
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.
Epsa15 Selected Papers
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Author : Michela Massimi
language : en
Publisher: Springer
Release Date : 2017-04-26
Epsa15 Selected Papers written by Michela Massimi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-26 with Science categories.
This edited collection showcases some of the best recent research in the philosophy of science. It comprises of thematically arranged papers presented at the 5th conference of the European Philosophy of Science Association (EPSA15), covering a broad variety of topics within general philosophy of science, and philosophical issues pertaining to specific sciences. The collection will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to study the latest work on the themes discussed.
The Essence Of Numbers
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Author : Frédéric Patras
language : en
Publisher: Springer Nature
Release Date : 2020-10-06
The Essence Of Numbers written by Frédéric Patras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.
This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.
Mvt A Most Valuable Theorem
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Author : Craig Smorynski
language : en
Publisher: Springer
Release Date : 2017-04-07
Mvt A Most Valuable Theorem written by Craig Smorynski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-07 with Mathematics categories.
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mathematics majors as well as graduate students. Unlike other books, the present monograph treats the mathematical and historical aspects in equal measure, providing detailed and rigorous proofs of the mathematical results and even including original source material presenting the flavour of the history.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
History Of Mathematics And Its Contexts
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Author : Andrea Verdugo Rohrer
language : en
Publisher: Springer Nature
Release Date : 2024-11-01
History Of Mathematics And Its Contexts written by Andrea Verdugo Rohrer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
This book celebrates Gert Schubring's 80th birthday and honors his impactful contributions to the field of history of mathematics and its education. Recognized with the prestigious Hans Freudenthal Award in 2019, Schubring's academic work sets the tone for this volume. The thoughtfully curated articles in this collection offer insightful studies on textbooks and biographies of key figures in mathematics and mathematics education, contextualizing their significance within the broader historical landscape, and providing the readers with a deeper understanding of the development of the history of mathematics and its education. Researchers as well as curious readers and students will find this collection to be a valuable resource in the field.
The International Commission On Mathematical Instruction 1908 2008 People Events And Challenges In Mathematics Education
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Author : Fulvia Furinghetti
language : en
Publisher: Springer Nature
Release Date : 2023-01-30
The International Commission On Mathematical Instruction 1908 2008 People Events And Challenges In Mathematics Education written by Fulvia Furinghetti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-30 with Education categories.
The book presents the history of ICMI trough a prosopographical approach. In other words, it pays a lot of attention to the actors of the International movement. The portraits of the members of the ICMI Central Committees (1908-1936) and ICMI Executive Committees (1952-2008), and other eminent figures in ICMI history, who have passed away in the first 100 years of its life, are the guiding thread of the volume. Each portrait includes: · Biographical information · An outline of the various contributions made by the individual in question to the study of problems pertaining to mathematics teaching/education · Primary bibliography · Secondary with particular attention to the publications concerning the teaching of mathematics · Images: photos, book frontispieces, relevant manuscripts The authors of the portraits (30 altogether) are researchers in the history of mathematics, mathematics, and mathematics education. The focus on the officer’s role within ICMI and on his/her contributions to mathematics education, make the portraits different from usual biographies. In particular, since most officers were active mathematicians, the portraits shed light on aspects of their lesser-known activity. Connecting chapters place the action of these figures in the historical context and in the different phases of ICMI history.
Essays On Frege S Basic Laws Of Arithmetic
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Author : Philip A. Ebert
language : en
Publisher:
Release Date : 2019
Essays On Frege S Basic Laws Of Arithmetic written by Philip A. Ebert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
This is the first collective study of a foundational text in modern philosophy and logic, Gottlob Frege's Basic Laws of Arithmetic. Twenty-two Frege scholars discuss a wide range of philosophical and logical topics arising from Basic Laws of Arithmetic, and demonstrate the technical and philosophical richness of this great work.