NEWSLETTER DEPARTMENT 01- MATHEMATICS ST JOHN'S UNIVERSITY JAMAICA. NEW YORK 11432

Vol. VI, No. 1 March, 1972 NEWSLETTER DEPARTMl:NT Of- MATHEMATICS ST JOHN'S UNIVl:RSITY JAMAICA. NEW YORK 1143:!

Editorial Board: John Tucciarone Anthony Sarno Vincent Mancuso Mary O'Shea

The NEWSLETTER is published by the Department of Mathematics for the information of staff members and students, as a vehicle for the exchange of ideas and in forma­ tion of particular interest to the department. Vol. VI, No. 1 March, 1972 ST. JOHN'S .MATHEMATICS DEPARTMENT COLLOQUIA - 1971-1972

FALL

TABLE OF CONTENTS Dr. Donald McCarthy of St. John's University A Survey of Partial Converses to Lagrange's Theorem on Finite Groups October 14

Colloquia ...... 1 Dr. Salvatore Anastasio of SUNY at New Paltz W-* Algebras: An Introduction and a Survey of Research Publications 3 Recent Results November 4

NSF Computer Capability Grant 4 Dr. Julian Gevirtz of New York University & Pace College Graduate Program . . . 5 Some Classical Topics in Convexity December 2

Undergraduate Program 7 Dr. Jerome Lurye of St. John's University The Interaction of a Viscous Wake with a Free Surface Pilot Course in Calculus 9 December 16

Pi Mu Epsilon 10 SPRING

Faculty Notes 11 Dr. Donald McCarthy of St. John's University An Introduction to Graph Theory and Applications February 3

Dr. Jonathon L. Gross of Columbia University & Princeton The Imbedding of Graphs in Surfaces February 17

Dr. Jonathon L. Gross The Imbedding of Surfaces in 3-manifolds March 2

Dr. Maurice Machover of St. John's University Partial Differential Equations Without Solutions: An Introduction and a Conjecture March 16

1 Dr. Michael I. Aissen of Rutgers University RESEARCH PUBLICATIONS A Pattern for Completion April 13

The Colloquia are generally held on Thursdays, at The following is a partial listing of the various 3 P.M. in St. John Hall at the Jamaica Campus. For publications completed or in progress during the 1971-72 academic year: information on future topics and speakers, contact Dr. Donald McCarthy, the Director of the program, at 212-969-8000. Dr. Jon Cole - A paper "A Note on a Selector Theorem in Banach Spaces," J ournaf of Optimization Theory and Applications, Vol 9, No. 3, 1972,pp.214-215.

Dr. Jerome Lurye - A final report "Wave Height and . Wave Resistance in the Presence of a Viscous Wake," to the Naval Ship Research and Development Center, in fulfillment of an $18,000. research contract with that agency.

Dr. Donald McCarthy - A paper "A Survey of Partial Converses to Lagrange's Theorem," Transactions of the N.Y . Academy of Sciences, Series II, Vol. 33, June, 1971, pp.586-594. A paper "Subgroups of the Power Semigroup of a Group," to appear in 1973 in the Journal of Combinatorial Theory, Series A.

Dr. Richard Morgan - A paper co-authored with S.N. Karp of N.Y.U., "Surface Wave Incidence on a Plane Structure Having a Multi-mode Discontinuity in Imped­ ance," to appear in the Quarterly of Applied Mathematics.

Dr. Lawrence Narici - A book "Functional Analysis and Valuation Theory," published in the Spring of 1971 by Marcel Dekker, N. Y.

., Prof. Francis Siwiec - Two papers submitted to the Rocky Mountain Journal of Mathematics: "A Survey of non-1st Countability Concepts and Examples," and "Quo­ tient Mappings with Restricted Dorr.ain and Range." A paper submitted to General Topology and its Applications: "KM-Spaces and KM-Covering Mappings."

2 3 NSF COMPUTER CAPABILITY GRANT GRADUATE PROGRAM

In 1970, Dr. Joseph Frechen was the recipient of a During 1971, the Graduate School of Arts and two-year, $44,500. NSF grant to study academic computer Sciences conferred 13 Master's Degrees in mathematics. capabilities at SJU. During 1970-71, the first year of the The June, 1971 graduates included: George Gillen, grant, Dr. Frechen was a resident with the System Richard Greene, Hilary Huang, Joseph Lang, Dennis Development Corporation in the Los Angeles area, a large Moscowitz, Vincent Russotti, and Robert Zieminski. computer software organization. He also studied computer Those receiving degrees in September, 1971 included: facilities at UCLA, USC, Cal Tech and others. During this Michael Drinka, Joseph McDermott, James Mulloy, Takvor time, Dr. Frechen observed and studied academic com­ Ozsan, Joanne Piampiano, and Patrick Socci. The figures puter activities in diverse areas, and also participated in on M.A. recipients over the last few years show: 1969 - direct computer research. 10; 1970- 10; 1971 - 13.

During 1971-72, the second year of the grant, Dr. The department has the services of 9 graduate assist­ Frechen is conducting a computer use seminar for a group ants during 1971-72, with all but 1 assisting as in-class of faculty members from several departments at SJU. instructors for the Survey of Mathematics (Math 7-8) These include: Biology, History, Library Science, Mathe­ course. This course is being taught on closed circuit matics, Modern Foreign Languages, Philosophy and Socio­ television by Dr. Jon Cole. Dr. Cole has designed a new logy. Many of the problems with which the members of format for the course, and he is supervising the graduate this seminar are concerned are non-mathematical in nature. assistants' instructional assignments. The combination has For example, some of the capabilities being studied proven most successful. The graduate assistants have also include: concordance construction, textual analysis, index­ been conducting problem sessions for the freshman and ing of journal articles, information retrieval, authorship sophomore courses, and assisting the faculty of the tests, thematic dictionaries and foreign language exercises. department. Some of the members are using mathematical techniques in their computer-oriented research, namely, biological Among the 6 new assistants are Carmela DeMarco and data analysis, sociological data analysis and voter analysis. Diana Ruscica, both undergraduates at SJU. As an under­ graduate, Carmela was enrolled in the Honors Program, the During the Spring of 1972, the seminar will be Dean's List, and was a member of Who's Who Among extended to include faculty from other departments. The Students in American Colleges and Universities. Diana, also overall goal of the program is to strengthen the academic a Dean's List and Honors Program student, was a member computer capabilities at SJU. of Pi Mu Epsilon. Wendy Barkas received her B.A. from Queens College, graduating magna cum laude. She was a member of Phi Beta Kappa and Kappa Delta Phi. Tung­ Chien Wang received his B.S. from the National Taiwan University. His home is Taipei, Republic of China. Bob Higgins turned down an NSF fellowship and a Regents

4 5 fellowship for studies in Oceanography to study mathe­ UNDERGRADUATE PROGRAM matics at SJU. A summa cum laude graduate of St. Francis College, he also worked as an actuarial assistant at Metropolitan Life Insurance Co. Jeanne Baccash received During the year 1971, SJU conferred a total of 64 her B.A. summa cum laude from University College of baccalaureate degrees to students who majored in mathe­ SJU. She was a Dean's List student and a member of the matics. Of those, 35 were from St. John's College, 14 from Honors Program. Jeanne is assisting in the mathematics University College, and 15 from the School of Education. division of Notre Dame College, the new undergraduate The figures on the number of math graduates over the last college of SJU in Staten Island. few years show: 1969- 62; 1970-63; 1971 - 64.

Among the second year graduate assistants are Bob Dr. Miranda, the Chairman of the department, has Vincent, Ed Micca and Jerry Lucchesi. Bob plans to enter stated that the mathematics department should be aware medical school upon receiving his master's degree. Ed of the changing nature of society and how these changes Micca was an undergraduate at SJU and served in the should be reflected in the curriculum. Through his Armed Forces in Germany before continuing his studies at direction, the department is intent on fulfilling this goal. SJU. Jerry was awarded an NSF fellowship during the past During 1971, the offerings in the undergraduate and summer. He will complete his master's degree in January. graduate -curriculum will be enlarged in the social science and computer areas. Among the new offerings in mathematics on the graduate level are Introduction to Combinatorics (Math Offered for the first time in the Fall, 1972, will be a 150), and Computer Analysis I & II (Math 165,166). Dr. course designed for the liberal arts student, entitled Machover, Coordinator of Advisement for the graduate Computing for the Liberal Arts (Math 15 ). The course will program, looks toward interdepartmental cooperation with not admit math majors, but will attempt to show the both the Physics and Philosophy Departments in the capabilities and limitations of computing in settings more future. Combined supervision of graduate students is one familiar to the non-math major. A new two-term course feature that is being planned. entitled Mathematical Methods for Social Sciences (Math 62-63) will also be offered in the Fall. This course will introduce the mathematical methods most frequently used in the behavioral and social sciences, such as model building, and decision theory. Current problems will be selected from the literature of the behavioral sciences.

Commencing in the Fall, 1972, the computer will become a more integral part of the course of study of each mathematics student. In addition to the regular curri­ culum, freshmen and sophomores will be exposed to programming on the elementary and advanced levels in all their courses. Moreover, a revised Computer Analysis (Math 89) course is to be offered in the Fall. It will treat

6 7 topics in data structures, linear and multi-lists, trees, PILOT COURSE IN CALCULUS traversing algorithms, sorting techniques and storage mana­ gement. A new course, entitled Computer Applications (Math 90) will also be added. It will treat random number In September, 1971, a new course was introduced for generation, simulation, heuristic programming, artificial those students who did outstanding work in University intelligence and pattern recognition. Mathematics I and II, the freshman calculus course for math majors. Normally, these students would take Univer­ At the Dean's Convocation in the Spring of 1971, the sity Mathematics III and IV during their sophomore year, following undergraduates were honored: and Advanced Calculus (Math 77-78) during their junior year. Instead, the new course was designed to reduce the ST. JOHN'S COLLEGE time factor in the completion of the total calculus sequence. Gold Key in Mathematics (senior) ...... Patricia Greve Silver Key Uunior) ...... Gordon Feathers Experience with outstanding students in the past had indicated a need for rapid advancement. The purpose of Other nominees for the Gold Key were Donna Hanlon and the new course is to enable these students to progress more Patricia Ludwig, and for the Silver Key, Alina Espada and rapidly toward other mathematics electives or lower level Elena Salgado. graduate courses. It was felt that students from this group would more likely pursue advanced study toward masters UNIVERSITY COLLEGE and doctoral degrees. Gold Key in Mathematics (senior) ...... Jeanne Baccash Silver Key Uunior) ...... Aldina Lorenzoni Prof. John Chiaramonte was selected to give the new course with the understanding that much of the semester would be devoted to independent study. While 6 hours of Other nominees for the Gold Key were Mary Calabro and regular class lectures are given by the instructor each week, Julia Murphy, and for the Silver Key, Julia Carlucci and the students are encouraged to work on their own through Lily Wong. individual conferences with the instructor, assigned pro­ jects, etc. The content of the full year course will include topics traditionally treated in intermediate calculus, linear algebra, and advanced calculus.

The department feels that a select group of math majors such as this should be developed early, so that by the junior year, these students will have a solid foundation in theory, and experience in independent study. The success of the pilot course will be measured by the quality of the work the students will do during their junior and senior years.

8 9 Pl MU EPSILON FACULTY NOTES

The SJU Chapter of Pi Mu Epsilon inducted 14 new Dr. Theresa Barz - was recently re-elected as Secretary members into the national mathematics fraternity at a of the SJU Chapter of the AAUP. She is the Secretary of special meeting in May, 1971. Fallowing a presentation on the Greater Metropolitan New York Math Fair for 1972. Vector Analysis by Dr. Miranda, the induction ceremonies Dr. Barz is preparing notes for a Geometry text. proceeded. The new members include: Jack Barocas, Joanne Canco, Marianne DeRosa, Alina Espada, Vivian Dr. Willie Callahan - delivered a paper on Vibrations Fede, Frances LaMalfa, Barbara Marga, Eloise Merlino, before the 7th International Congress on Acoustics in Susan Murphy, Diane O'Neil, Evelyn Preiss, Linda Stavola, Budapest, Hungary, during July, 1971. He delivered a Rochelle Verola, Linda Wolfe. paper in the same field at the AMS meeting in Las Vegas, Nevada, in January, 1972. The officers for 1971-72 are Gordon Feathers, Presi­ dent, and Elena Salgado, Secretary. In keeping with its Dr. Michael Capobianco - resigned his chairmanship of aims of promoting excellence in mathematics, the SJU the Mathematics Department to accept the position of Chapter of Pi Mu Epsilon plans a series of meetings Director of the Natural Sciences Division of the new throughout the year, with invited speakers from among the undergraduate unit of SJU, Notre Dame College, in Staten faculty and student body. Dr. Tucciarone spoke on the Island. summation of divergent series at the December meeting, and meetings are scheduled for February, March and April. Dr. Walter Cassidy - was honored by members of the Mathematics Department at a special dinner in June, 1971. Further information concerning future meetings may Dr. Cassidy retired from service at SJU after a long and be had by contacting Gordon Feathers, c/o Mathematics distinguished tenure as Professor of Mathematics. Department at SJU. Prof. John Chiaramonte - is serving as a member of the Greater Metropolitan New York Math Fair Committee.

Dr. Leon Gerber - joined the teaching staff at the Jamaica Campus when SJU terminated the University College at the Brooklyn Center. Dr. Gerber taught at the Brooklyn Center for 6 years. He is currently teaching analysis and computer programming.

Dr. Anne Hughes - received her doctoral degree from Yeshiva University in January, 1972. Her research was in the field of functions of several complex variables, and her dissertation, written under A. Koranyi, was titled "Bound­ ary Limits of HP -Classes of Holomorphic Functions in Tube Domains."

10 11 Dr. Rora Iacobacci - transferred to the Jamaica Dr. Edward Miranda - was elected by members of the Campus from the Brooklyn Center of SJU, where she had Mathematics Department to serve as Chairman for the taught for 7 years. Dr. Iacobacci acted as a departmental unexpired term (1971-72) of Dr. Capobianco's office. Dr. representative at the Brooklyn Center, where she counsel­ Miranda recently conducted 2 seminars for the Physics ed undergraduate math majors. She is currently teaching Department at SJU on the Mathematics of Space. courses in analysis. Prof. Anthony Sarno - was elected President of the Dr. Jerome Lurye - served as a finalist judge in the Faculty Association at SJU for 1971-72. He and the 1971 Nassau-Suffolk Math Fair. In September, 1971, Dr. Association, together with representatives of the AAUP, Lurye presented a talk on the results of his research to the will represent the entire faculty in collective bargaining Flow-Studies Panel of the Society of Naval Architects and negotiations with SJU. Prof. Sarno was re-elected to the Marine Engineers. He is acting as Sponsor of the newly­ University Personnel Committee for 1971-72. He con­ formed Math Club at SJU. tinues to serve as Coordinator of Undergraduate Advise­ ment for the Mathematics Department. Dr. Maurice Machover - has prepared five short articles for inclusion in the 1972 edition of Encyclopedia Americana on Lattice Theory, Evolutes, Ellipsoids, Epicy­ cloids and Length. He attended the AMS summer meeting at Penn State University. Dr. Machover delivered a seminar address at Notre Dame University titled "On Equations Without : Solution and Garabedian's Conjecture."

Dr. Vincent Mancuso - presented a talk at the AMS meeting in Las Vegas, Nevada, in January, 1972, entitled "Inverse Images and 1st Countability."

Dr. Donald McCarthy - was a Visiting Research Member at the Advanced Science Seminar on Combinatori­ al Mathematics held at Bowdoin College during · the summer of 1971. He also participated in the International Conference on Combinatorial Group Theory held in November, 1971, at York University, Toronto, Canada. Dr. McCarthy addressed the seminar in Group Theory at N.Y.U. in January, 1972, on "Automorphism Groups of Finite Graphs." He also served as a judge for the Greater Metropolitan New York Math Fair.

12 13 " ST . JOHN'S UNIVERSITY DEPARTMENT OF MATHEMATICS JAMAICA. NEW YORK 11432