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Perhaps it should not be a surprise that A Course in Cryptography, which is published by the American Mathematical Society, is a textbook that is written for a mathematically sophisticated student....

The importance of encouraging and supporting young people from underrepresented populations to study science, mathematics, technology, and engineering (STEM) is perhaps as great today as at any tim...

James Fairley McKenzie, who was a professor of applied mathematics at the University of Natal from 1981 to 1998, would have been 80 in May 2018. A Special Session was held in his honour at the Annu...

This research identifies the similarities and differences between the MathSciNet search features and functions of the American Mathematical Society (AMS) and EBSCOhost platforms. A series of iterat...

Editor’s note: We begin here an occasional feature, reviewing classic books (that are still available) rather than new ones. These books may not be widely known but, we feel, still have much to off...

‘The final abstract expression of every art is number’.– Wassily Kandinsky (1866–1944) [3, p. 73]In January 2017, Atlanta hosted the Joint Mathematics Meetings of the American Mathematical Society ...

Editor’s note: Evelyn Lamb authored a wonderful page-a-day calendar published by the American Mathematical Society that can be used in any year (it has no days of the week on it, and February 29 co...

With a book like The Math Behind the Magic: Fascinating Card and Number Tricks and How They Work by Ehrhard Behrends (published by the American Mathematical Society), the first question is not, “Is...

The ‘case’ (or, sometimes, ‘affair’) of Academician Luzin is an event that cast a long shadow over Soviet mathematics. However, the events comprising the ‘case’, which took place over several days ...

The present article addresses the subject of music in the pedagogy of mathematics from the perspective of two researchers in mathematical music theory (MMT) belonging to mathematics departments. Our first main topic is the popularization project concerning music and mathematics of the Royal Spanish Mathematical Society, and its extension to an international level is proposed. Secondly, we present some ideas and outlines for the creation of didactic material for mathematics courses within the framework of MMT.

We examine the initial layer problem and the infinite Prandtl number limit of the thermosolutal convection, which is applicable to magma chambers. We derive the effective approximating system of the Boussinesq system at large Prandtl number using two time scale approach [M. Holmes, Introduction to Perturbation Methods, Springer, New York, 1995, A. Majda, Introduction to PDEs and Waves for the Atmosphere and Ocean, Courant Lecture Notes in Mathematics, Vol. 9, New York, American Mathematical Society, Providence, RI, 2003]. We show that the effective approximating system is nothing but the infinite Prandtl number system with initial layer terms. We also show that the solutions of the Boussinesq system converge to solutions of the effective approximating system with the convergence rate of O(ϵ).

Mathematics and Music, by David Wright, American Mathematical Society, AMS Mathematical World Series, 2009, 161 pages, US $35.00 (paperback), ISBN 978-0-8218-4873-9. Genuine interdisciplinary work ...

Bard, Gregory V., Algebraic Cryptanalysis, 2009, Springer-Verlag, New York, 356 pages, $129.00, hardcover. In his 1941 address to the American Mathematical Society, A. A. Albert [2, p. 903] recogni...

When we pause to reflect on Ramanujan’s life, we see that there were certain events that seemingly were necessary in order that Ramanujan and his mathematics be brought to posterity. One of these was V. Ramaswamy Aiyer’s founding of the Indian Mathematical Society on 4 April 1907, for had he not launched the Indian Mathematical Society, then the next necessary episode, namely, Ramanujan’s meeting with Ramaswamy Aiyer at his office in Tirtukkoilur in 1910, would also have not taken place. Ramanujan had carried with him one of his notebooks, and Ramaswamy Aiyer not only recognized the creative spirit that produced its contents, but he also had the wisdom to contact others, such as R. Ramachandra Rao, in order to bring Ramanujan’s mathematics to others for appreciation and support. The large mathematical community that has thrived on Ramanujan’s discoveries for nearly a century owes a huge debt to V. Ramaswamy Aiyer. 1. THE BEGINNING. Toward the end of the first paper [57], [58 ,p . 36] that Ramanujan published in England, at the beginning of Section 13, he writes, “I shall conclude this paper by giving a few series for 1/π.” (In fact, Ramanujan concluded his paper a couple of pages later with another topic: formulas and approximations for the perimeter of an ellipse.) After sketching his ideas, which we examine in detail in Sections 3 and 9, Ramanujan records three series representations for 1/π .A s is customary, set

The main focus of this paper is local almost periodicity, to be defined below. This notion was introduced (for integer actions) by Hedlund [G.A. Hedlund. Amer. J. Math. 66 (1944), pp. 605–620] and for general group actions in the AMS Colloquium monograph of Gottschalk and Hedlund [W.H. Gottschalk, G.A. Hedlund. American Mathematical Society, Colloquium Publications, Vol. 36, Providence, RI, (1955), p. 105]. It has been studied (mainly since 1970) by, among others, Ellis, Glasner, McMahon, Paul, Veech, Wu and the authors. Over time, the results have been sharpened, and the proofs have become more succinct. The purpose of this note is to present a largely self-contained account of local almost periodicity from a modern perspective.

There has been much debate in recent years as to the amount and type of mathematical knowledge that teachers need to acquire. One set of recommendations is provided by the Mathematical Education of Teachers (MET) report, produced jointly by the American Mathematical Society and the Mathematical Association of America. This paper reports on efforts at the University of Wisconsin-Milwaukee to implement the MET report recommendations for pre-service elementary and middle grades teachers, in the contexts of teacher education programmes and the teacher licensing structure of the state of Wisconsin. Data is also presented on the results of teaching the resulting courses to in-service teachers.

By Nevanlinna's value distribution theory, we give a more precise form of the meromorphic function f provided that f m can be expressed as a summation of n + 1 (n!≤! m) functions in family The results in this article generalize some known results obtained by Green, M., 1974, On the functional equation a new Picard theorem. Transactions of the American Mathematical Society, 195, 223–230; Noda, Y., 1993, On the fuctional equation and rigidity theorems for holomorphic curves. Kodai Mathematical Journal, 16, 90–117.

A known result of Newman and Tse asserts that every uniformly discrete sequence contained in a Stolz angle is uniformly separated (see Newman, D.J., 1959, Interpolation in . Transactions of the American Mathematical Society, 92(3), 501–507; Tse, K.-F., 1971, Nontangential interpolating sequences and interpolation by normal functions. Proceedings of the American Mathematical Society, 29, 351–354). We prove that this statement no longer holds if the sequence is located in a tangential region of certain kind. It is well known that a uniformly discrete sequence need not be a Blaschke sequence. We show, however, that every uniformly discrete sequence inside a disc tangential to the unit circle must be a Blaschke sequence.

This article examines Karl Mannheim's famous characterisation of the organisers of knowledge as an 'unanchored relatively classless stratum'. It looks closely at Ficino's Florentine Academy, Cesi's Accademia dei Lincei, the authors of the Encyclopedie, William Whewell and his circle at Cambridge, G. H. Hardy and the London Mathematical Society, Sartre and French intellectuals in the 1940s and 50s, and finally Thomas Kuhn and the Society of Fellows at Harvard, to show that knowledge is relational. It describes the social characteristics of knowledge communities, the kinds of knowledge they organise, and the relations of knowledge communities to centres of power.

This article gives a simple proof of an equivalent proposition on semiconcave function (see [L.C. Evans (1998). Partial Differential Equations. American Mathematical Society; p. 130]). The proof of sufficiency of the proposition can be easily obtained. We prove its necessity by three steps: First, we prove that the equivalent proposition holds for discrete points ; Secondly, we obtain continuity of semiconcave function; Finally, by using the fact that the sequences λm k are dense in the interval (0, 1), we prove that the equivalent proposition holds for each λ ∈ (0, 1).

Introduction Contrary to a widespread assumption the modern history of modal logic did not start with C. I. Lewis’ Survey of Symbolic Logic [Lewis 1918]. His eminent work was preceded by some 20 years by H. MacColl’s fifth article on ‘The Calculus of Equivalent Statements’. This article was read at the London Mathematical Society on 12 November 1896. Some months later it was published in the Society’s Proceedings [MacColl 1896-1897]. During the following years MacColl presented his logic prim...

In 1988, Warren Lee May has asked in the Proceedings of the American Mathematical Society the following: Let G be an abelian group whose p-component G p is simply presented andlet F be a field of char F = p > 0. Then whether the F-isomorphism FH ≅ FG for any group H implies that H p ≅ G p ? The first actual positive answer isgiven by us in 1997 again in these Proceedings for the particular case when length G p < Ω. Here we shall establish an elegant positive solution of the question when length G p < Ω2 but only over the field of p-elements F p , utilizing a new criterion for simply presentedness with length Ω in the terms of summable p-groups.

Young, Anne L. Mathematical Ciphers from Caesar to RSA. The American Mathematical Society, P.O. Box 845904, Boston, MA. 2006. 159 pp. $29.00. Mathematical Ciphers is designed as a text for a mathem...

Pertinent information on statisticians available from previous studies and ASA publications is here reviewed and summarized. Sources include ASA's Schools Offering Degrees in Statistics, Amstat News articles, and surveys performed by the American Mathematical Society. In addition, results of a recent salary survey on biopharmaceutical statisticians is summarized and compared with salaries of academic biostatisticians. A longitudinal review of the profession's growth in academia is summarized with respect to number of programs, faculty size, and graduation rate changes. Suggestions are made for improvements in reporting of future survey summaries on statisticians.

Jean E. Taylor is a professor of mathematics at Rutgers University, Vice-President of the American Mathematical Society, and a member of the Board of Directors of the American Association for the Advancement of Science. She finished first in her class at Mount Holyoke College. Taylor retains the questioning manner that distinguished her as a schoolgirl, as evidenced by her fondness for the bumper sticker "QUESTION AUTHORITY!" Over the past quarter century she has studied minimal surfaces, the closed surfaces enclosing the least volume or those with a given space curve as boundary that have minimal surface area. In the early days of her career as a mathematician Professor Taylor tested her theoretical models of minimal surfaces by dunking loops of wire into her kitchen sink of soapy wa? ter. Later she turned to high technology, especially computer graphics software, to model bubbles. Today, she has moved from soap bubbles to crystals, which conform to more complicated rules about minimal surfaces. Taylor's daughter calls mathematics "the family business." Two of Taylor's three collaborators on a recent research project are in the family. With her husband Frederick J. Almgren of Princeton, her stepson Robert F. Almgren of the University of Chicago, and Andrew R. Roosen of the National Institute of Standards and Technology, Taylor is trying to model the growth of snowflakes and other crystals on a computer. Her daughter Karen Almgren, a senior at Princeton High School, gave a talk at the spring 1996 meeting of the New Jersey Section of the Mathematical Association of America: "Calculating the Capillary Forces Exerted by a Drop Between Two Cylinders." It seems the family business is expanding. Taylor loves the mountains. An accomplished climber, she was invited to join the Annapurna expedition. Which of her many achievements most pleases her? "The day I climbed both Cathedral Spires and Church Tower." Taylor was interviewed in her office in the summer of 1994.

Les Lange, Fellow of the California Academy of Sciences, Special Advisor to the Director of the Moss Landing Marine Laboratories on Monterey Bay, is Emeritus Professor of Mathe? matics and Emeritus Dean of Science of San Jose State Univer? sity. He learned mathematics at Berkeley, Valparaiso, Stanford (M.S. with George Polya), and Notre Dame (Ph.D. with Wladimir Seidel). He shared an MAA Lester R. Ford Sr. Award with Don Chakerian for a geometry paper, and an MAA George Polya Award with James W. Miller for a linear algebra paper. With G. L. Alexanderson he wrote the London Mathematical Society's extensive Polya obituary.

1. G. Bartle, A modern theory of integration, Graduate Studies in Mathematics, 32, American Mathematical Society, Providence, 2001. 2. D. Cruz-Uribe, SFO and C. J. Neugebauer, Sharp error bounds for the trapezoidal rule and Simpson's rule, J. Inequal. Pure Appl. Math. 3 (2002), Issue 4, Article 49. Available at j ipam. vu. edu. au/v3n4/index. html. 3. A. Ghizzetti and A. Ossicini, Quadrature formulae, Academic Press, New York, 1970. 4. G. Peano, Resto nelle formule di quadratura espresso con un integrale definito, Atti Accad. naz. Lincei, Rend., Cl. sci. fis. mat. nat. (5) 22-I (1913), 562-9. 5. A. Ralston, A first course in numerical analysis, McGraw-Hill, New York, 1965. 6. W. Rudin, Real and Complex Analysis, Third Ed., McGraw-Hill, New York, 1987. 7. J. Stewart, Calculus, 4th Ed., Brooks/Cole, Pacific Grove, 1999. 8. R. von Mises, Uber allgemeine quadraturformeln, J. Reine Angew. Math. 174 (1935), 56-67; reprinted in Selected Papers of Richard von Mises, Vol. 1, 559-574, American Mathematical Society, Providence, 1963.

l . Thomas Barr, Vector Calculus, Prentice-Hall, l 997. 2. Michael J. Beeson, Triangles with vertices on lattice points, Anler. Math. Monthly, 99:3 (1992), 243-252. 3. W. Scherrer, Die einlagerung eines regularen vielecks in ein gitter, Elemente derMathematik 1, (1946), 97-98. 4. I. J. Schoenberg, Regular simplices and quadratic forms, Journal of the London Mathematical Society 12, (l 937), 48-55. 5. James Stewart, Multivariable CulculuKs: Concepts and Context,s, Brooks-Cole, 1998.

Sequences (� nr� ) for 0 1) provide examples of sequences that converge deviously (which at first might seem to diverge), as well as partitionally divergent sequences (which consist of convergent subsequences). 1. INTRODUCTION. Eleven years after receiving the first Ph.D. in mathematics ever granted by a Canadian university—and 19 years before presiding over the Cana- dian Mathematical Society and 8 more before donning the robe of the Chancellor of the University of Toronto—Samuel Beatty sent a problem proposal (2) to this MONTHLY. The proposal is often cast like this: if r and s are positive irrationals satisfying 1/r + 1/s = 1, then the sequences (� nr� ) and (� ns� ) partition the posi- tive integers. This is now known as Beatty's theorem, and the sequences as Beatty sequences (although Lord Rayleigh had published the theorem in 1894). Choosing r to be the golden ratio (ϕ = (1 + √ 5)/2) gives the lower and upper Wythoff sequences, represented here as indexed in the Online Encyclopedia of Integer Sequences (4)

Wallis, Christopher Wren and others with huge scientific appetites met to “discourse and consider Philosophical Enquiries.” In mid-seventeenth century England, the spirit of inquiry pervaded the coffee houses of London, not the two backward-looking universities at Cambridge and Oxford. (Wallis, who intended to be a professor of mathematics, had to leave Cambridge because “that study had died out there.”) The common cord that joined these early scientists more than two centuries before the word “scientist” was invented was enthusiasm.

Elizabeth B. Appelbaum, a.k.a. Elizabeth Berman (bappelba@aol.com), has taught at many colleges in and near Kansas City, Missouri. She now is community liaison for mathematics, Blue Valley School District, working with gifted children. She has published Transactions ofthe American Mathematical Society (ring theory) and the Mathematics Teacher. Studying the mathematics of tumors empowered her to face her own cancer in 1996.

Ken Ross has made many contributions to mathematics over a long career. From 1971 to 1980 he served the American Mathematical Society (AMS) as Associate Secretary for the Western Section, and in 1983 he was elected Secretary of the Mathematical Association of America (MAA). When the responsibilities of the MAA Secretary were split in 1989, he became the MAA’s first Associate Secretary and continued to be responsible for the MAA presence in the national joint AMS-MAA meetings. He had long been involved with meetings; during his appointment at the AMS he was in charge of AMS regional meetings as well as any national meetings held in a Western city. In these assignments for the AMS and the MAA he traveled extensively to check out possible meeting sites. At the time of the meetings Ken was everywhere at once to ensure that everything was going smoothly. Of course, as MAA Secretary he was also responsible for keeping track of all the committees, preparing materials for Executive Committee and Board of Governors meetings, and generally keeping the business of the Association on track. In these various roles he showed great talent for working well with people, quietly making sure that everything got done. And, at least on the outside, he always appeared calm and in control. In 1993 Ken was elected MAA President and successfully led the MAA during a particularly challenging time due to financial problems. Following his term as President, he went on to chair the Response Group on the NCTM Standards, a potentially

Summary The coming of mathematicians to the United States fleeing the spread of Nazism presented a serious problem to the American mathematical community. The persistence of the Depression had endangered the promising growth of mathematics in the United States. Leading mathematicians were concerned about the career prospects of their students. They (and others) feared that placing large numbers of refugees would exacerbate already present nationalistic and anti-Semitic sentiments. The paper surveys a sequence of events in which the leading mathematicians reacted to the foreign-born and to the spread of Nazism, culminating in the decisions by the American Mathematical Society to found the journal Mathematical reviews and to form a War Preparedness Committee in September 1939. The most obvious consequence of the migration was an enlarged role for applied mathematics.

The paper presents a mathematical model of the problem of the politico‐economic stability of a welfare state. The variables characterizing the state of a government are identified. A sufficient criterion which ensures the damping out of the effects arising due to arbitrary perturbations in the variables, is obtained. The model assumes the prevalence of normal conditions, that is, times free from unforeseen calamities such as severe earthquake, outbreak of epidemic on a large scale, invasion by another country, acute famine, etc. † This forms part of a lecture delivered at the University of Kashmir in June 1970, and was also presented to the American Mathematical Society vide Notices AMS, June 1971. Reprinted from Mathematica, Vol. 2 (1973), published by Meerut University Mathematical Society.

Through a number of examples this paper illustrates the usefulness of dimensional analysis. A brief discussion shows how dimensional analysis can be generalized by studying the invariance of problems under Lie groups of transformations. † A part of this paper was presented at the Education Day instructional seminar of the Canadian Mathematical Society, December 12, 1980, in Vancouver, B.C., Canada [1].

Le but de cet article est de decrire le point de vue d’Henri Poincare sur l'axiome du choix, dont 1’explication par Zermelo en 1904, declencha une vive polemique. Agitant le monde mathematique de l'epoque, cette polemique avait ses racines dans la diversite des conceptions philosophiques que les mathematiciens avaient sur les mathematiques. Poincare avait une position originale; quelques lettres qu’il ecrivit a Zermelo (1906–1907), ainsi que les articles publies a la meme epoques dans la Revue de metaphysique et morale, eclairent ce point de vue. The aim of this paper is to describe the views of Henri Poincare concerning axiom of choice, of which the statement by Zermelo in 1904 launched a sharp polemic. Shaking the mathematical society of the time, this controversy had its roots into the diversity of philosophical conceptions that mathematicians held about mathematics. Poincare had a particular point of view; a few letters from him to Zermelo (1906–1907), together with papers published in Revue de metaph...

The American Mathematical Society has developed an online database, MATHFILE, containing bibliographic information on entries published in Mathematical Reviews since 1973, with the text of the reviews since 1980. MATHFILE becomes available on BRS and Dialog in 1982. Problems of computer transmission of special characters were solved by literalizing mathematical expressions into mnemonics enclosed in braces. Most can be deciphered from a conversion table in the User's Guide, but for a fully accurate mathematical form, the Mathematical Reviews in print must be consulted.

A conference in operator theory and its applications commemorating : he 100th anniversary of the birth of the distinguished German mathematician Otto Toeplitz, organized by the University of Tel Aviv together with German Mathematical Society, took place in Tel Aviv, Israel, from May 11th to 15th, 1981. I give here a broad very subjective overview of the proceedings of the conference for the benefit of readers of TTSP; for those interested in further details, a forthcoming volume in the Birkhauser series “Operator Theory: Advances and Applications” will consist of expanded written versions of most of the talks given at the conference.

Describes the duties of managing databases for the American Mathematical Society as well as the rewards, the requirements and the outlook for data base managers. Marketing responsibilities are discussed as well as the technical aspects of this sort of position.

Dr. Gleason graduated from Yale in 1942 and then served four years . . j in the Navy. After the war he went to Harvard as a Junior Fellow in the ;;, Society of Fellows. Except for an interlude in the Navy from 1950-52, he has been at Harvard ever since. He now holds the Hofis Professorship of Mathematicks and Natural Philosophy, a chair that was endowed in 1727. Although he has no doctor's degree, he says that George Mackey was the equivalent of his dissertation supervisor. He has worked in several areas including topological groups, Banach algebras, finite geometries, and coding theory. He received the Newcomb Cleveland prize of the AAAS in 1952. He is a member of the National Academy of Sciences and is a former president of the American Mathematical Society.

Summary In 1892, Eliakim Hastings Moore accepted the task of building a mathematics department at the University of Chicago. Working in close conjuction with the other original department members, Oskar Bolza and Heinrich Maschke, Moore established a stimulating mathematical environment not only at the University of Chicago, but also in the Midwest region and in the United States in general. In 1893, he helped organize an international congress of mathematicians. He followed this in 1896 with the organization of the Midwest Section of the New York City-based American Mathematical Society. He became the first editor-in-chief of the Society's Transactions in 1899, and rose to the presidency of the Society in 1901.

As the speaker representing the Mathematical Association of America at this session I propose this morning to call your attention to one of the more important duties of a mathematician, namely, the duty of explaining as clearly as possible mathematical truths and discoveries both to his fellow mathematicians and to students of mathematics in general. The American Mathematical Society is especially devoted to the encouragement of research and the secretary of that society has called to your attention during this meeting the remarkable increase in the number of papers presented annually to the Society during the past five years. This increase has been such as to make the problem of publishing the results of mathematical research in America a very acute and difficult one. At the same time it has become more desirable than ever before that the papers published in our American journals should be as clear and as easily readible as possible. The Mathematical Association of America is especially concerned with the teaching and exposition of mathematical truth and it is pretty generally agreed that it is highly desirable that care should be taken to make this teaching and exposition to students as good as possible. I fear, however, that some of my friends who are particularly interested in research agree to this in a rather condescending manner; their tone implying that, whilst nothing should be done to discourage anyone beginning the study of mathematics, such care is not so necessary nor even so desirable when writing for fellow mathematicians. The underlying idea is that a competent mathematician usually prefers to glance at a paper, see the results arrived at, and then derive these results in his own individual manner. I believe that this opinion is not justified by the facts and in support of this belief I shall mention two instances which have recently come to my attention where mathematicians of great competence failed, through a lack of detail or of clarity in available expositions of known results, to arrive at immediate and important corollaries of these results. I shall be happy if my talk this morning tends to make the editors of our mathematical journals insist more definitely on clearness of exposition when considering papers submitted for publication. One can surmise that the writers of at least some of our papers set down their results with the referee of the paper more in mind than the prospective readers. They neglect, therefore, to state or. emphasize points which they think will be familiar to the referee. Of course this is unfortunate since there is us'ually a one-to-one

† Paper presented to the Conference of the Indian Mathematical Society (1968) and notified in the Bulletin of the Mathematical Association of India, April 1969.

(1902). Ninth Summer Meeting of the American Mathematical Society. The American Mathematical Monthly: Vol. 9, No. 8-9, pp. 185-187.