Mathematicians under the Nazis

Mathematicians under the Nazis

Author: Sanford L. Segal

Publisher: Princeton University Press

Published: 2014-11-23

Total Pages: 566

ISBN-13: 0691164630

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Contrary to popular belief--and despite the expulsion, emigration, or death of many German mathematicians--substantial mathematics was produced in Germany during 1933-1945. In this landmark social history of the mathematics community in Nazi Germany, Sanford Segal examines how the Nazi years affected the personal and academic lives of those German mathematicians who continued to work in Germany. The effects of the Nazi regime on the lives of mathematicians ranged from limitations on foreign contact to power struggles that rattled entire institutions, from changed work patterns to military draft, deportation, and death. Based on extensive archival research, Mathematicians under the Nazis shows how these mathematicians, variously motivated, reacted to the period's intense political pressures. It details the consequences of their actions on their colleagues and on the practice and organs of German mathematics, including its curricula, institutions, and journals. Throughout, Segal's focus is on the biographies of individuals, including mathematicians who resisted the injection of ideology into their profession, some who worked in concentration camps, and others (such as Ludwig Bieberbach) who used the "Aryanization" of their profession to further their own agendas. Some of the figures are no longer well known; others still tower over the field. All lived lives complicated by Nazi power. Presenting a wealth of previously unavailable information, this book is a large contribution to the history of mathematics--as well as a unique view of what it was like to live and work in Nazi Germany.


An Old Heart Goes A-Journeying

An Old Heart Goes A-Journeying

Author: Hans Fallada

Publisher: Read Books Ltd

Published: 2011-03-23

Total Pages: 283

ISBN-13: 144654558X

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Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.


Proving It Her Way

Proving It Her Way

Author: David E. Rowe

Publisher:

Published: 2020

Total Pages: 259

ISBN-13: 3030628116

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The name Emmy Noether is one of the most celebrated in the history of mathematics. A brilliant algebraist and iconic figure for women in modern science, Noether exerted a strong influence on the younger mathematicians of her time and long thereafter; today, she is known worldwide as the "mother of modern algebra." Drawing on original archival material and recent research, this book follows Emmy Noethers career from her early years in Erlangen up until her tragic death in the United States. After solving a major outstanding problem in Einsteins theory of relativity, she was finally able to join the Göttingen faculty in 1919. Proving It Her Way offers a new perspective on an extraordinary career, first, by focusing on important figures in Noethers life and, second, by showing how she selflessly promoted the careers of several other talented individuals. By exploring her mathematical world, it aims to convey the personality and impact of a remarkable mathematician who literally changed the face of modern mathematics, despite the fact that, as a woman, she never held a regular professorship. Written for a general audience, this study uncovers the human dimensions of Noethers key relationships with a younger generation of mathematicians. Thematically, the authors took inspiration from their cooperation with the ensemble portraittheater Vienna in producing the play "Diving into Math with Emmy Noether." Four of the young mathematicians portrayed in Proving It Her Way - B.L. van der Waerden, Pavel Alexandrov, Helmut Hasse, and Olga Taussky - also appear in "Diving into Math.".


Finitely Presented Groups

Finitely Presented Groups

Author: Volker Diekert

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-10-07

Total Pages: 252

ISBN-13: 3111473570

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This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.


Proofs from THE BOOK

Proofs from THE BOOK

Author: Martin Aigner

Publisher: Springer

Published: 2014-08-06

Total Pages: 299

ISBN-13: 3662442051

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This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.


The Beauty of Geometry

The Beauty of Geometry

Author: H. S. M. Coxeter

Publisher: Courier Corporation

Published: 1999-01-01

Total Pages: 301

ISBN-13: 0486409198

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Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.


Logic's Lost Genius

Logic's Lost Genius

Author: Eckart Menzler-Trott

Publisher: American Mathematical Soc.

Published: 2016-05-05

Total Pages: 466

ISBN-13: 1470428121

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Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.


Chromatic Graph Theory

Chromatic Graph Theory

Author: Gary Chartrand

Publisher: CRC Press

Published: 2019-11-28

Total Pages: 459

ISBN-13: 042979827X

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With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition


Quadratic Forms and Their Applications

Quadratic Forms and Their Applications

Author: Eva Bayer-Fluckiger

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 330

ISBN-13: 0821827790

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This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.


Open and Closed Innovation

Open and Closed Innovation

Author: Philipp Herzog

Publisher: Springer Science & Business Media

Published: 2011-01-22

Total Pages: 280

ISBN-13: 3834961655

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Philipp Herzog develops a theoretical framework arguing that Open Innovation and Closed Innovation cultures need to be distinguished. The findings help firms cope with the challenges experienced in implementing the Open Innovation concept.