Joseph A. Gallian

Bio: Joseph A. Gallian is an academic researcher from University of Minnesota. The author has contributed to research in topics: Group (mathematics) & Order (group theory). The author has an hindex of 14, co-authored 67 publications receiving 3556 citations.

A Dynamic Survey of Graph Labeling

Abstract: A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

Contemporary Abstract Algebra

Abstract: Contemporary Abstract Algebra 7/e provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students.

Cross-cultural analysis of students with exceptional talent in mathematical problem solving

Abstract: A t a conference held in January 2005, Lawrence Summers, then president of Harvard University, hypothesized that a major reason for the paucity of women mathematicians among the tenured faculty of elite research universities in the USA might be sex-based differences in “intrinsic aptitude” for mathematics, especially at the very high end of the distribution [36]. This commonly held belief is largely based upon data from standardized tests such as the quantitative section of the Scholastic Aptitude Test (SAT) I. This test, designed to determine mathematical proficiency of USA eleventh and twelfth graders, identifies students who have mastered grade-level material, but does not distinguish the profoundly gifted, that is, those who are four or more standard deviations above the mean, from the merely gifted who also score in the ninety-ninth percentile on this exam. To identify students who perform above grade level, the Study of Mathematically Precocious Youth (SMPY) administered the SAT I to children younger than thirteen years of age. The SMPY defined children as highly gifted in mathematics if they scored at least 700 (on a 200 to 800 scale) on the quantitative section of this test. Using this criterion, Benbow and Stanley reported in 1980 large gender differences in “mathematical reasoning ability” [4]. They concluded that “sex differences in achievement in and attitude towards mathematics result from superior male mathematical ability . . . [it] is probably an expression of a combination of both endogenous and exogenous variables.” Since these tests lack questions that require creative thinking and insight into higher-level mathematical concepts, they do not identify children with extremely high innate ability in mathematics, that is, ones who may go on to become top research mathematicians. They cannot differentiate between profoundly and moderately gifted children, regardless of age at which the examinations are administered. Thus, the SMPY identified thousands of children who, while quite bright and ambitious, were not necessarily profoundly gifted in mathematics. The SMPY also failed to identify many children with extreme ability in mathematics who lacked one or more of the socio-economically privileged environmental factors necessary to be recognized by this mechanism. Coincidentally, the ratio of boys to girls identified in the SMPY has dramatically declined during the past quarter century from the high of 13:1 originally reported in 1983 [5] to 2.8:1 in a 2005 report [6]. The fact that 29% of Ph.D.’s awarded to USA citizens in the mathematical sciences went to women in the 2006–2007 academic year [30] supports the idea that this latter ratio is a more accurate reflection of current Titu Andreescu is professor of science/mathematics education at the University of Texas, Dallas. His email address is txa051000@utdallas.edu.

A Dynamic Survey of Graph Labeling

Abstract: A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

The World Is Flat: A Brief History of the Twenty-First Century

Abstract: The World is Flat: A Brief History of the Twenty-First Century Thomas L. Friedman Farrar, Straus and Giroux, 2005 Thomas Friedman is a widely-acclaimed journalist, foreign affairs columnist for the New York Times, and author of four best-selling books that include From Beirut to Jerusalem (1989). His eminence as a journalist is clearly demonstrated in the way he prepared for The World is Flat. He traveled throughout the world, interviewing in depth the political and business leaders who have the most direct, hands-on knowledge of the truly incredible developments occurring in the business structures and technology of globalization. Only a journalist who moves freely at the highest levels could interview the likes of Sir John Rose, the chief executive of Rolls-Royce; Nobuyuki Idei, the chairman of Sony; Richard Koo, the chief economist for the Nomura Research Institute; Bill Gates of Microsoft; Wee Theng Tan, the president of Intel China; David Baltimore, president of Caltech; Howard Schultz, founder and chairman of Starbucks; Nandan Nilekani, CEO of Infosys in Bangalore - and many others, each of whom gave him the inside story of how, specifically, the barriers of time and space separating economies, workforces, sources of capital, and technical abilities are crumbling. The result of this unfolding story, already far along but with much farther to go, according to Friedman, is that "the world is flat." With some notable exceptions in sub-Saharan Africa and the Islamic swathe, everything is connected with everything else on a horizontal basis, with distance and erstwhile time-lags no longer mattering. Friedman describes in detail the galloping globalization that has unfolded in even so limited a time as the past five years. Under the impetus of a worldwide network of interconnectivity, the world economy is much-changed from what it was at the turn of the century a mere half-decade ago. Friedman quotes the CEO of India's Infosys: "What happened over the last [few] years is that there was a massive investment in technology, especially in the bubble era, when hundreds of millions of dollars were invested in putting broadband connectivity around the world, undersea cables," while (Friedman paraphrases him) "computers became cheaper and dispersed all over the world, and there was an explosion of software - e-mail, search engines like Google, and proprietary software that can chop up any piece of work and send one part to Boston, one part to Bangalore, and one part to Beijing...." Microprocessors today have 410 million transistors compared to the 2800 they had in 1971. And now, "wireless is what will allow you to take everything that has been digitized, made virtual and personal, and do it from anywhere." The effect on productivity is revolutionary: "It now takes Boeing eleven days to build a 737, down from twenty-eight days just a few years ago. Boeing will build the next generation of planes in three days, because all the parts are computer-designed for assembly." The most strikingly informative aspect of this book, however, is not about technology. Most especially, Friedman explores the rapidly evolving global business systems, each constantly regenerating itself to keep ahead of the others. These are systems that span the continents seeking the lowest-cost providers of everything from expert scientific and engineering work to the lowliest grunt work. Friedman points out that India produces 70,000 accounting graduates each year - and that they are willing to start at $100 a month. It is no wonder that Boeing employs 800 Russian scientists and engineers for passenger-plane design when "a U.S. aeronautical engineer costs $120 per design hour, a Russian costs about one-third of that." Friedman describes a call center in India where outbound callers sell "everything from credit cards to phone minutes," while operators taking inbound calls do "everything from tracing lost luggage for U.S. and European airline passengers to solving computer problems for confused American consumers. …

Women in Academic Science: A Changing Landscape

Abstract: Summary Much has been written in the past two decades about women in academic science careers, but this literature is contradictory. Many analyses have revealed a level playing field, with men and women faring equally, whereas other analyses have suggested numerous areas in which the playing field is not level. The only widely-agreed-upon conclusion is that women are underrepresented in college majors, graduate school programs, and the professoriate in those fields that are the most mathematically intensive, such as geoscience, engineering, economics, mathematics/ computer science, and the physical sciences. In other scientific fields (psychology, life science, social science), women are found in much higher percentages. In this monograph, we undertake extensive life-course analyses comparing the trajectories of women and men in math-intensive fields with those of their counterparts in non-math-intensive fields in which women are close to parity with or even exceed the number of men. We begin by examining early-childhood differences in spatial processing and follow this through quantitative performance in middle childhood and adolescence, including high school coursework. We then focus on the transition of the sexes from high school to college major, then to graduate school, and, finally, to careers in academic science. The results of our myriad analyses reveal that early sex differences in spatial and mathematical reasoning need not stem from biological bases, that the gap between average female and male math ability is narrowing (suggesting strong environmental influences), and that sex differences in math ability at the right tail show variation over time and across nationalities, ethnicities, and other factors, indicating that the ratio of males to females at the right tail can and does change. We find that gender differences in attitudes toward and expectations about math careers and ability (controlling for actual ability) are evident by kindergarten and increase thereafter, leading to lower female propensities to major in math-intensive subjects in college but higher female propensities to major in non-math-intensive sciences, with overall science, technology, engineering, and mathematics (STEM) majors at 50% female for more than a decade. Post-college, although men with majors in math-intensive subjects have historically chosen and completed PhDs in these fields more often than women, the gap has recently narrowed by two thirds; among non-math-intensive STEM majors, women are more likely than men to go into health and other people-related occupations instead of pursuing PhDs. Importantly, of those who obtain doctorates in math-intensive fields, men and women entering the professoriate have equivalent access to tenure-track academic jobs in science, and they persist and are remunerated at comparable rates—with some caveats that we discuss. The transition from graduate programs to assistant professorships shows more pipeline leakage in the fields in which women are already very prevalent (psychology, life science, social science) than in the math-intensive fields in which they are underrepresented but in which the number of females holding assistant professorships is at least commensurate with (if not greater than) that of males. That is, invitations to interview for tenure-track positions in math-intensive fields—as well as actual employment offers—reveal that female PhD applicants fare at least as well as their male counterparts in math-intensive fields.