Product Description
Mathematics education research in undergraduate mathematics has increased significantly in the last decade and shows no signs of abating in the near future. Thus far, this research has often been associated with innovations in curriculum such as calculus reform, statistics education, and the use of computational and graphing technology in instruction. Carefully conducted mathematics education research is something far more fundamental and widely useful than might be implied by its use by the advocates of innovation in undergraduate mathematics education. Most simply, mathematics education research is inquiry by carefully developed research methods aimed at providing evidence about the nature and relationships of many mathematics learning and teaching phenomena. It seeks to clarify the phenomena, illuminate them, explain how they are related to other phenomena, and explain how this may be related to undergraduate mathematics course organization and teaching. This book--the collaborative effort of a research mathematician, mathematics education researchers who work in a research mathematics department and a professional librarian--introduces research mathematicians to education research. The work presents a non-jargon introduction for educational research, surveys the more commonly used research methods, along with their rationales and assumptions, and provides background and careful discussions to help research mathematicians read or listen to education research more critically. This guide is of practical interest to university-based research mathematicians. It introduces the methodology of quantitative and qualitative research in education, provides critical guidelines for assessing the reliability and validity of mathematics education research, and explains how to use online database resources to locate education research. The book will also be valuable to graduate students in mathematics who are planning academic careers, and to mathematics department chairs and their deans. ... Read more

Customer Reviews (2)

Method-fetishism
This book is a manifestation of the mathematics education community's thickheaded identification with its methods rather than its results. The entire book is about delineating what constitutes "adequate research" (p. 12), "legitimate research" (p. 21), etc., and denigrating anything that does not conform to these narrow standards. This stupid method-fetishism is taken to be an end in itself. Not a single result of this so-called "research" is discussed anywhere in the book; a state of affairs that the authors apparently consider to be entirely in order.

If you go to graduate school in physics, people do not teach you five hundred "method courses." They teach you substance. And they trust that this substance is impressive enough to intrigue students into learning about the methods that produced such insights. Thus the physics community has not imposed is methodological standards upon itself in order to be able to scorn amateur work. Substantial insights about nature is the one and only goal, and methods are embraced only after they have proved their worth as a means towards this end.

Not so in mathematics education. Here "methods" are foremost, and substance nowhere to be found. In order to mask the obvious folly of this state of affairs, an ingenious trick has been devised: namely, the glorification of the vacuous word "research." "Research, research, research," is the mantra of self-justification for these anti-intellectual minions who do not have anything of substance to offer. "Research" is on the one hand assumed superior to anything that is not "research," and on the other hand it is defined as whatever it is that the math. ed. minions do. They can then bask is the glory of having defined their own superiority. If anyone should present a well-argued case for a way of approaching an issue of substance that deviates from the dogma, then one need only remind them that "yes, but that's not research," which automatically nullifies all the arguments put forth. You are doing "research" if and only if you follow the prescribed methodological dicta. Whether your "research" has anything whatever to do with substantial insights regarding education is entirely irrelevant.

Breaking the Qualitative Barrier for Research in CS
We are doing reseach in problem solving in computer science. So little is known about how the human does this that we had to start at the very beginning. We have had a hard time selling this to all the scientists and engineers because we don't have big numbers and there is a huge amount of flat misinformation out there.

This book will help you overcome these obstacles. ... Read more

Product Description
Walter Rudin's memoirs should prove to be a delightful read specifically to mathematicians, but also to historians who are interested in learning about his colorful history and ancestry. Characterized by his personal style of elegance, clarity, and brevity, Rudin presents in the first part of the book his early memories about his family history, his boyhood in Vienna throughout the 1920s and 1930s, and his experiences during World War II.Part II offers samples of his work, in which he relates where problems came from, what their solutions led to, and who else was involved. As those who are familiar with Rudin's writing will recognize, he brings to this book the same care, depth, and originality that is the hallmark of his work.Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. ... Read more

Customer Reviews (2)

Portrait of a brilliant, deeply humane man
This is an inspirational and often moving biography of one of the great mathematicians of our century. Hadamard was not only a brilliant mathematician, but a stimulating mentor, a man of wide-ranging knowledge, insatiable curiosity, humility, and most of all, great humanity. When Japaninvaded Manchuria, he proposed that the League of Nations sendpeace-keeping forces there, only to face ridicule from the French press.Hadamard, more than most of us, deeply felt the tragic wastefulness of war.He lost two beloved sons in World War I. Of his son, Etienne, he once said:"what I did in mathematics is nothing compared to what he could do ifhe were alive today." (Half of the brilliant graduates of the EcoleNormale were killed in that war). I finished this book with feelings ofgratitude and regret--gratitude to Hadamard for sharing his remarkablegifts with such generosity, and deep regret that "fate" was sogrievously unfair to him.

Inspirational and moving
This is an inspirational and often moving biography of one of the great mathematicians of our century. Hadamard was not only a brilliant mathematician, but a stimulating mentor, a man of wide-ranging knowledge,insatiable curiosity, humility, and most of all, great humanity. When Japaninvaded Manchuria, he proposed that the League of Nations send peacekeepingforces there, only to face ridicule from the French press. Hadamard, morethan most of us, deeply felt the tragic wastefulness of war. He lost twobeloved sons in World War I. Of his son Etienne, he once said: "what Idid in mathematics is nothing compared with what he could do if he werealive today."(As the book points out, half the brilliant graduates ofthe Ecole Normale were killed in that war). I finished this book withfeelings of gratitude and regret--gratitude to Hadamard for sharing hisremarkable gifts with such generosity, and deep regret that"fate" was so grievously unfair to him. ... Read more

Product Description
This is the latest volume in the CBMS (Conference Board of the Mathematical Sciences) Issues in Mathematics Education series, which seeks to stimulate the flow of information among mathematical scientists, mathematics educators, and mathematics teachers about innovative efforts to revitalize the teaching of the mathematical sciences at all levels. The first part of this volume is devoted to detailed descriptions of a wide variety of educational projects undertaken by mathematicians. These descriptions focus for the most part on substantial enterprises with an investment of several years and systematic review and evaluation. By contrast, the second part of the book centers on ideas that could be put into action at a modest level as a springboard for longer term projects. This book is intended to stimulate and inspire mathematical scientists to pursue educational work. In addition, those who have already ventured into educational activities and may be ready for deeper involvement will also benefit from this exploration of what can be done. ... Read more

Product Description
Compiled and edited by the directors of the Mathematicians and Education Reform (MER) Network, this book contains papers by speakers and participants in MER workshops and special sessions over the last three years. Like the first volume, which also grew out of an MER workshop, this book is organized into two sections, Projects and Issues and Reactions providing a balance between descriptions of successful existing projects and more in-depth discussion of problems and issues in mathematics education reform. With contributions by some of the major leaders in this area today, this book is of interest to a broad segment of the mathematical sciences community. ... Read more

Customer Reviews (1)

Plagiarism
Consider a brief and somewhat controversial passage from Morris Kline's "Mathematical Thought from Ancient to Modern Times" (occuring on pg. 23):

"[T]he Egyptians and Babylonians were crude carpenters, whereas the Greeks were magnificent architects. One does find more favorable, even laudatory, descriptions of the Babylonian and Egyptian achievements. But these are made by specialists who become, perhaps unconsciously, overimpressed by their own field of interest."

Compare this with a passage appearing on page 149 of the new AMS publication, "History of Mathematics from a Mathematician's Vantage Point", written (according to the book's cover) by Nicolaos Artemiadis.

"[T]he Egyptians and the Babylonians were "clumsy carpenters" while the Greeks were "magnificent architects". Of course, there exist historians who gave a more favorable judgment regarding the achievements of the Babylonians and the Egyptians. But these judgments were made by specialists who were perhaps unconsciously impressed more than necessary by the object of their interest."

The title page of Artemiadis' book explains that it is an English translation of a book originally published in Greek in the year 2000. The title page neglects, however, to mention that the ostensibly original Greek text is largely a translation of an English history - Morris Kline's "Mathematical Thought from Ancient to Modern Times". Morris Kline is given no credit whatsoever in the body of Artemiadis' text (apart from being listed in the bibliography), despite the fact that he wrote much of it. Although the translation and retranslation process has altered many of Kline's individual words, even a superficial inspection reveals that sentences, paragraphs, and even whole pages of Artemiadis' writings are clearly isomorphic to passages in Kline's classic history. To put matters bluntly, "History of Mathematics from a Mathematician's Vantage Point" is a work of blatant plagiarism.

I have occasionally joked with students that "if you must cheat, at least have the good sense to cheat well." Apparently, Artemiadis never heard this advice. Rather than playing it safe and stealing from an obscure source, he chose to pilfer prose from a standard history of mathematics familiar to most mathematicians. Still worse, he made the mistake of plagiarizing the writings of a highly literate iconoclast whose ideas are easily identifiable both by their novelty and by their very phrasing.

Morris Kline, incidentally, is not the only victim, though he is the most conspicuous. If nothing else, many readers will recognize the chronological table which appears in the back of "History of Mathematics from a Mathematician's Vantage Point" as a slightly abbreviated version of the table appearing in Carl Boyer's, "A History of Mathematics".

This is an appalling book - the sort of thing one hears about, but rarely actually holds in one's hands (in an AMS publication no less! How did this get by the editors?) The idea that this inept thievery is supposed to represent the "mathematician's viewpoint" only adds insult to injury.

... Read more

Product Description
Supersymmetry has been studied by theoretical physicists since the early 1970s. Nowadays, because of its novelty and significance--in both mathematics and physics--the issues it raises attract the interest of mathematicians.

Written by the well-known mathematician, V. S. Varadarajan, this book presents a cogent and self-contained exposition of the foundations of supersymmetry for the mathematically-minded reader. It begins with a brief introduction to the physical foundations of the theory, in particular, to the classification of relativistic particles and their wave equations, such as those of Dirac and Weyl. It then continues with the development of the theory of supermanifolds, stressing the analogy with the Grothendieck theory of schemes. Here, Varadarajan develops all the super linear algebra needed for the book and establishes the basic theorems: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature is the in-depth treatment of the theory of spinors in all dimensions and signatures, which is the basis of all supergeometry developments in both physics and mathematics, especially in quantum field theory and supergravity.

The material is suitable for graduate students and mathematicians interested in the mathematical theory of supersymmetry. The book is recommended for independent study.

Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University. ... Read more

Product Description
This volume represents selected proceedings of the Fourth International Congress of Chinese Mathematicians, held in Hangzhou, China. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Approximately fifteen hundred mathematicians participated in the Congress.Included in this volume are the complete Morningside Lectures, the complete plenary lectures, and selected invited lectures.Titles in this series are co-published with International Press, Cambridge, MA. ... Read more

Product Description
This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set theory courses and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle ($\diamond$), and the use of elementary submodels. Great care has been taken to motivate the concepts and theorems presented.The book is written as a dialogue with the reader. The presentation is interspersed with numerous exercises. The authors wish to entice readers into active participation in discovering the mathematics presented, making the book particularly suitable for self-study. Each topic is presented rigorously and in considerable detail. Carefully planned exercises lead the reader to active mastery of the techniques presented. Suggestions for further reading are given. Volume II can be read independently of Volume I. ... Read more

Product Description
This digital document is an article from American Scholar, published by Phi Beta Kappa Society on March 22, 1998. The length of the article is 5741 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

From the supplier: Changes in mathematicians' attitudes between 1957 and 1997 are described. The past emphasis on "pure" mathematics in graduate school, the historical records of mathematicians' interest in applications for their ideas, the influence of significant texts, and a brief history of space exploration by satellites are recounted. Many current fields depend on applying sophisticated mathematics.

Citation Details
Title: Mathematics forty years after Sputnik.
Author: Solomon W. Golomb
Publication: American Scholar (Refereed)
Date: March 22, 1998
Publisher: Phi Beta Kappa Society
Volume: v67Issue: n2Page: p89(11)

Distributed by Thomson Gale ... Read more

Product Description
This digital document is an article from American Scholar, published by Phi Beta Kappa Society on September 22, 2004. The length of the article is 1540 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Numerologies.
Author: Vijay Seshadri
Publication: American Scholar (Refereed)
Date: September 22, 2004
Publisher: Phi Beta Kappa Society
Volume: 73Issue: 4Page: 93(4)

Distributed by Thomson Gale ... Read more

Customer Reviews (1)

The Author's Perspective
This book tells of my personal, 28 year journey in Corporate America from Los Angeles to Atlanta to Chicago and back to Atlanta. In each professional position, I was the first African American hired, and I experienced the type of racism and sexism during the 60's, 70's, and 80's that,unfortunately, many women and minorities still experience today.

My bookdeals with the situations in which a single woman finds herself, thechanges that a married woman must deal with, and the challenges of theworking and traveling mother.

I am extremely proud of this, my firstbook, because it won for me the Georgia Author of the Year in the area ofNonfiction. My publisher was so pleased that I was asked to write a sequeldetailing how I overcame the racism and sexism. That sequel was BeyondLimitations, and it is based on self-esteem, success, and sustenance.

Ihave discovered that women and minorities easily identify with theexperiences I discuss, but white males have said that the book has helpedthem to understand what women and minorities have to contend with. If thebook makes them better managers and coworkers, I am grateful. ... Read more