Modern Mathematics, Updated Edition

Michael Bradley

Description

Praise for the previous edition:

“…ample information for reports.”—School Library Journal

During the first half of the 20th century, mathematics became an international discipline that led to major advances in science and technology. Modern Mathematics, Updated Edition provides an eye-opening introduction to those five historic decades by analyzing the advancement of the field through the accomplishments of 10 significant mathematicians. From David Hilbert and Emmy Noether, who introduced the infinite dimensional vector spaces and algebraic rings that bear their names, to Norbert Wiener, the founder of cybernetics, this in-depth title covers the early 20th-century advancements that expanded the field of mathematics and transformed the way that mathematicians do their work. This edition is ideal for middle and high school students seeking resources for research or general interest.

Sujets

• 20th Century
• Sciences et techniques
• Achievement
• Biography
• Mathematician
• Mathematics
• Succès (homonymie)
• Global
• Math (homonymie)

Informations

• Publié par: Infobase Publishing
• Date de parution: 01 novembre 2019
• Nombre de lectures: 0
• EAN13: 9781438182292
• Langue: English

Extrait

Modern Mathematics, Updated Edition
Copyright © 2019 by Michael J. Bradley
All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval systems, without permission in writing from the publisher. For more information, contact:
Chelsea House An imprint of Infobase 132 West 31st Street New York NY 10001
ISBN 978-1-4381-8229-2
You can find Chelsea House on the World Wide Web at http://www.infobase.com
Contents Chapters Hilbert, David Young, Grace Chisholm Sierpinski, Waclaw Noether, Emmy Ramanujan, Srinivasa Iyengar Wiener, Norbert Neumann, John von Hopper, Grace Murray Turing, Alan Mathison Erd s, Paul Support Materials Glossary Further Reading Associations Index
Preface

Mathematics is a human endeavor. Behind its numbers, equations, formulas, and theorems are the stories of the people who expanded the frontiers of humanity's mathematical knowledge. Some were child prodigies while others developed their aptitudes for mathematics later in life. They were rich and poor, male and female, well educated and self-taught. They worked as professors, clerks, farmers, engineers, astronomers, nurses, and philosophers. The diversity of their backgrounds testifies that mathematical talent is independent of nationality, ethnicity, religion, class, gender, or disability.
Pioneers in Mathematics is a five-volume set that profiles the lives of 50 individuals, each of whom played a role in the development and the advancement of mathematics. The overall profiles do not represent the 50 most notable mathematicians; rather, they are a collection of individuals whose life stories and significant contributions to mathematics will interest and inform middle school and high school students. Collectively, they represent the diverse talents of the millions of people, both anonymous and well known, who developed new techniques, discovered innovative ideas, and extended known mathematical theories while facing challenges and overcoming obstacles.
Each book in the set presents the lives and accomplishments of 10 mathematicians who lived during an historical period. The Birth of Mathematics profiles individuals from ancient Greece, India, Arabia, and medieval Italy who lived from 700 B.C.E. to 1300 C.E. The Age of Genius features mathematicians from Iran, France, England, Germany, Switzerland, and America who lived between the 14th and 18th centuries. The Foundations of Mathematics presents 19th-century mathematicians from various European countries. Modern Mathematics and Mathematics Frontiers profile a variety of international mathematicians who worked in the early 20th and the late 20th century, respectively.
The 50 chapters of Pioneers in Mathematics tell pieces of the story of humankind’s attempt to understand the world in terms of numbers, patterns, and equations. Some of the individuals profiled contributed innovative ideas that gave birth to new branches of mathematics. Others solved problems that had puzzled mathematicians for centuries. Some wrote books that influenced the teaching of mathematics for hundreds of years. Still others were among the first of their race, gender, or nationality to achieve recognition for their mathematical accomplishments. Each one was an innovator who broke new ground and enabled their successors to progress even further.
From the introduction of the base-10 number system to the development of logarithms, calculus, and computers, most significant ideas in mathematics developed gradually, with countless individuals making important contributions. Many mathematical ideas developed independently in different civilizations separated by geography and time. Within the same civilization, the name of the scholar who developed a particular innovation often became lost as his idea was incorporated into the writings of a later mathematician. For these reasons, it is not always possible to identify accurately any one individual as the first person to have discovered a particular theorem or to have introduced a certain idea. But then mathematics was not created by one person or for one person; it is a human endeavor.
Introduction

Modern Mathematics, the fourth volume of the Pioneers in Mathematics series, profiles the lives of 10 mathematicians who excelled during the first half of the 20th century. They made important discoveries in both pure and applied mathematics, contributed to diverse branches of science, and participated in the development of computer technology. These individuals introduced new branches of mathematics and changed the way that mathematicians do their work.
An international community of scholars who shared their innovative ideas and worked together on joint research projects characterized mathematics in the 20th century. At the Second International Congress of Mathematicians in 1900, German mathematician David Hilbert drew his colleagues' attention to a list of 23 problems that set the research agenda for the early part of the century. Polish mathematician Wacław Sierpińnski helped to establish and cultivate a productive national community of mathematicians known as the Polish school. English mathematician Godfrey Hardy brought self-taught Indian number theorist Srinivasa Iyengar Ramanujan to Cambridge University to spend five years doing research together. Hungarian mathematician Paul Erdös traveled the world writing 1,500 books and papers with 500 research collaborators. American mathematician Norbert Wiener and Hungarian mathematician John von Neumann worked with numerous scientific and engineering colleagues to produce fundamental results in physics, biology, economics, and computer technology.
For many mathematicians the realities of two world wars impacted their lives and shaped their professional careers. Sierpiński was detained as a prisoner of war during both military conflicts. World War II prevented English mathematician Grace Chisholm Young from being with her husband during the last two years of his life. At the height of her career, German Jew Amalie Emmy Noether was forced to leave her country under Adolf Hitler’s Nazi regime. During World War II, English mathematician Alan Turing devised computer techniques to decipher German naval codes, while American Grace Murray Hopper developed methods to computerize the calculation of ballistics tables. Wiener created algorithms to improve the effectiveness of antiaircraft guns and von Neumann performed essential mathematical analyses for the development of atomic bombs and nuclear weapons.
The group of mathematicians profiled in this volume made influential discoveries and pioneered new branches of mathematics, science, and technology. Hilbert and Noether introduced the infinite dimensional vector spaces and algebraic rings that bear their names. Ramanujan helped lay the foundations of probabilistic number theory. Erdös contributed to the establishment of Ramsey theory and extremal theory as new branches of mathematics. Wiener was the father of cybernetics. Turing machines and von Neumann architecture laid the foundations for modern computing machines. Hopper created the first compiler program and influenced the development of the COBOL programming language for data processing.
During the first half of the 20th century, mathematics became an international discipline that led to major advances in science and technology. The 10 individuals profiled in this volume represent the thousands of scholars who made modest and momentous mathematical discoveries that contributed to this growth of knowledge. The stories of their achievements provide a glimpse into the lives and the minds of some of the pioneers who discovered mathematics.
Chapters
Hilbert, David
(b. 1862–d. 1943)
mathematician specializing in logic, algebra, analysis, geometry

David Hilbert was a central figure in mathematics in the early 20th century, conducting research in six areas of the discipline and influencing the direction of mathematical research for the entire century. His finite basis theorem changed invariant theory from a computational discipline to an algebraic one. His report on number theory set the course for the next generation of researchers in algebraic number theory. The 21 axioms of geometry that he developed introduced a new approach to a classic area of the discipline. His introduction of infinite-dimensional Hilbert spaces played an important role in analysis and mathematical physics. The Hilbert program to establish a rigorous basis for all of mathematics was central to the development of mathematical logic. The 23 Hilbert problems that he posed at an international conference in 1900 stimulated wide-ranging mathematical research throughout the course of the 20th century.
Early Years
David Hilbert was born on January 23, 1862, in Wehlau, a small town in East Prussia near the Baltic Sea. He was the first of two children of Otto Hilbert, a county judge, and Maria Therese Erdtmann, the educated daughter of a merchant. When David's father received an appointment as a city judge a few years later, the family moved to the neighboring capital city Königsberg (present-day Kaliningrad, Russia). From 1870 to 1879 Hilbert attended school at Friedrichskolleg, a private school in Königsberg, where he studied German, Greek, Latin, history, grammar, and mathematics. He excelled in mathematics, effortlessly mastering the subject and at times explaining problems to his teachers. He completed his final year of high school at Wilhelm Gymnasium and passed the Arbitur, the entrance examination for German universities.
In 1880 Hilbert entered the University of Königsberg, where he concentrated exclusively on mathematics. After spending the spring semester of 1881 at the University of Heidelberg, he returned to Königsberg to complete his studies. In 1883 he met Hermann Minkowski, an 18-year-old fellow mathe