Author: Ernst Schroeder Publisher: LED Edizioni Universitarie ISBN: 8879165879 Category : Mathematics Languages : en Pages : 153
Book Description
TABLE OF CONTENTS: ALGEBRA, WHAT ELSE?: 1. The Birth of a Masterwork - 2. Commutativity and Left- and Right-Division - 3. Algorithms, Algorithms, Algorithms - 4. Formalism - 5. A Fateful Choice - 6. Overview - 7. A Strange Document - 8. Acknowledgements - 9. Tools - Notes — ON THE FORMAL ELEMENTS OF THE ABSOLUTE ALGEBRA: §. 1. Character des zu behandelnden Problems. Character of the Problem in Issue - §. 2. Einschränkungen der Aufgabe. Restrictions of our Scope - §. 3. Die Fundamentalgleichungen für nur zwei Zahlen. Algorithmen. The Fundamental Equations for only Two Numbers. Algorithms - §. 4. Vertauschungsprincipien. Principles of Permutation - §. 5. Die Fundamentalgleichungen für drei Zahlen. Elementarcyklen und Gruppen. The Fundamental Equations for Three Numbers. Elementary Cycles and Groups - §. 6. Consequenzen der Algorithmen C1; C2; C3 für drei Zahlen. Consequences of the Algorithms C1; C2; C3 for Three Numbers - §. 7. Consequenzen von C0. Consequences of C0 - §. 8. Combination der Ci. Combination of the Ci - §. 9. Das Formelsystem O1 der ordinäre Algebra. The Formal System O1 of the Usual Algebra - §. 10. Untergeordnete Algorithmen von O1: Weitere ermittelte Tragweitezahlen. Subordinate Algorithms of O1: Further Sizes — FIGURES - Notes — APPENDIX - Notes — ILLUSTRATIONS - Bibliography - Index of the Main Concepts - Index of the Illustrations.
Author: Jordi Cat Publisher: Springer ISBN: 3030021289 Category : Science Languages : en Pages : 706
Book Description
This highly readable book is a collection of critical papers on Otto Neurath (1882-1945). It comprehensively re-examines Neurath’s scientific, philosophical and educational contributions from a range of standpoints including historical, sociological and problem-oriented perspectives. Leading Neurath scholars disentangle and connect Neurath’s works, ideas and ideals and evaluate them both in their original socio-historical context and in contemporary philosophical debates. Readers will discover a new critical understanding. Drawing on archive materials, essays discuss not only Neurath’s better-known works from lesser-known perspectives, but also his lesser-known works from the better-known perspective of their place in his overall philosophical oeuvre. Reflecting the full range of Neurath's work, this volume has a broad appeal. Besides scholars and researchers interested in Neurath, Carnap, the Vienna Circle, work on logical empiricism and the history and philosophy of science, this book will also appeal to graduate students in philosophy, sociology, history and education. Readers will find Neurath’s thoughts described and evaluated in an accessible manner, making it a good read for those beyond the academic world such as social leaders and activists. The book includes the edited 1940-45 Neurath-Carnap correspondence and the English translation of Neurath's logic papers.
Author: Michiel Hazewinkel Publisher: Springer Science & Business Media ISBN: 9400903650 Category : Mathematics Languages : en Pages : 743
Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author: Saunders MacLane Publisher: Springer Science & Business Media ISBN: 1461248728 Category : Mathematics Languages : en Pages : 486
Book Description
This book records my efforts over the past four years to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics. My efforts have been encouraged by lec tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications. Jean Benabou has carefully read the entire manuscript and has offered incisive comments. George Glauberman, Car los Kenig, Christopher Mulvey, R. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording. Many conversations with George Mackey have given me important insights on the nature of Mathematics. I have had similar help from Alfred Aeppli, John Gray, Jay Goldman, Peter Johnstone, Bill Lawvere, and Roger Lyndon. Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg. Ideas from Tammo Tom Dieck, Albrecht Dold, Richard Lashof, and Ib Madsen have assisted in my study of geometry. Jerry Bona and B.L. Foster have helped with my examina tion of mechanics. My observations about logic have been subject to con structive scrutiny by Gert Miiller, Marian Boykan Pour-El, Ted Slaman, R. Voreadou, Volker Weispfennig, and Hugh Woodin.
Author: Lisa Muehle Publisher: iUniverse ISBN: 1583480137 Category : Mathematics Languages : en Pages : 239
Book Description
Simple Secrets and Savvy Strategies for Acing the SAT! Today's SAT is harder, longer, and more daunting than ever before, but students armed with the proven success strategies in this one-of-a-kind study program will have all the skills and confidence they need to ace it! Renowned test prep expert Lisa Muehle explains every detail of the SAT, including what to expect and how the questions will look, ways to carefully manage time, and techniques to greatly enhance performance. She shows students how to reduce stress and minimize test anxiety, boost concentration and focus, and increase speed and accuracy. This well-illustrated edition covers the Mathematics section of the SAT with chapters on essential topics such as arithmetic and basic math; algebra; coordinate geometry and graphs in a coordinate plane; plane and solid geometry; data charts; miscellaneous math topics; and classic word problems. This indispensable guide includes: A suggested study plan as test day approaches (both an eight-week and a four-week version) A detailed breakdown of the math scoring procedure for multiple-choice and grid-in response problems A straightforward explanation of the SAT guessing penalty Tools and hints for educated guessing and avoiding attractive but wrong answer choices A smart approach to grid-in problems Tips, pointers, and step-by-step key sequences for using a graphing calculator to solve advanced algebra problems Success Strategy sidebars with seasoned advice and practical equations Sample sets for practicing new and classic SAT math problems with thorough explanations of the solutions Together with its companion guide, Strategies for Success on the SAT: Critical Reading and Writing Sections this is the comprehensive program for mastering the SAT and gaining admission into the top universities.
Author: Hans-Joachim Petsche Publisher: Springer Science & Business Media ISBN: 303460405X Category : Mathematics Languages : en Pages : 572
Book Description
On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics. In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Graßmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper "On the concept and extent of pure theory of number'' by Justus Graßmann (the father).
Author: Gérard Cohen Publisher: Springer Science & Business Media ISBN: 9783540601142 Category : Algebra Languages : en Pages : 504
Book Description
This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.
Author: Leila Haaparanta Publisher: Oxford University Press ISBN: 0199722722 Category : Philosophy Languages : en Pages : 1005
Book Description
This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy.
Author: A.I. Kostrikin Publisher: Springer Science & Business Media ISBN: 366203235X Category : Mathematics Languages : en Pages : 248
Book Description
The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.
Author: Ernst Schroeder
Author: Jordi Cat
Author: Michiel Hazewinkel
Author: Saunders MacLane
Author: Lisa Muehle
Author: Hans-Joachim Petsche
Author: Gérard Cohen
Author: Leila Haaparanta
Author: Nicolas Bourbaki
Author: A.I. Kostrikin