Mathematical Foundation of Computer Science Laboratory

/ Yasuhiko Ikebe / Professor
/ Nobuyoshi Asai / Assistant Professor

The MFSC lab operates in collaboration with Assistant Professor Y. Kikuchi from Multimedia Systems Lab. Jointly we supervised nearly 25 students, of which several were graduate students. Our educational contributions were made at a variety of fronts.

Our major research fronts may be described as follows:

1. Matrix-theoretic high-performance algorithm construction, with application to the numerical computation of critically important quantities associated with difficult special functions occurring from 3-D wave equations, such as regular Coulomb wave functions, Mathieu functions, spheroidal wave functions, Lame functions, ellipsoidal wave functions. The Bessel function of the first kind, an easier function serves as a model case, where two types of computational problems were solved in the complex domain as well as real domain: given a complex order Bessel function, compute a given number of zeros closest to the origin to a specified accuracy; and given a complex number find a specified number of orders of Bessel functions closest to the origin, to a specified accuracy. There are no comparable algorithms known elsewhere which give as accurate an error estimate as ours.

2. Virtual university content production: We have been collaborating with an foreign IT team (Center for Digital Innovation, the University of California at Los Angeles (UCLA)) to produce an interactive multimedia distance education content in linear algebra. Its first English version is available for public release at www.cdi.ucla.edu/ Linear algebra. The content is under rewrite at this writing. It has an outstanding feature in that it is organized around the ``Six Great Decompositions", so that a busy student can learn the skeleton facts of the subject matter at the earliest possible timing, in fact, right after the student learned basic matrix operations. This completely new rearrangement of the facts is a result of Ikebe's research and represents a especially welcome fact to the busy working professionals who need to learn the basics of linear algebra FAST and at an industrial-strength level. The simultaneous lectures based on this content were carried out in February, 2001 (on Feb. 7 and 28), between this university and Tsukuba Gigabit Lab (TAO).

3. Construction of hyper English word study dictionary: it is available at mnftv1.u-aizu.ac.jp/hidic/hdhome.htm. Again this represents a long-range project, aiming at compiling a database for the study of English words for Japanese students. The main feature is that the dictionary is organized to bring out the best fruits of comparative linguistics in the past century: the usefulness of Indo-European roots as presented in the wonderful book by Calvert Watkins, The American Heritage Dictionary of Indo-European Roots, Second Edition, Houghton-Mifflin, 2000. Example: The organizing principle of the dictionary will tell you that the following words are best studied as a group: riddle, garble, crime, decree, discern, secret, hypocrisy (they are all derivatives from the same Indo-European root krei-, meaning ``to sieve", indicating that a group of seemingly unrelated words come from the same notion ``to sieve"). Another example: the usage of the so-called synonyms ``anger, rage and wrath" can be clearly explained by tracing them back to their respective Indo-European root: anger to angh-, meaning painful, rage to rebh-, meaning violent, impetuous, and wrath to wreit-, meaning to turn, twist (anger is akin to angst, angina, rage is akin to rabid, rabies, and wrath is akin to wreath, writhe).

Refereed Journal Papers

1. Y. Ikebe, D.S. Cai, Y. Kikuchi, and Y. Miyazaki. A Status Report of Institution of Higher Learning in America. Information, vol. 3, pp. 89-95, 2000.

   Increasingly tighter financial conditions at all levels, coupled with the fast developing information technologies, are sending American universities into the throes of restructuring. One manifestation of this is the current proliferation of quality distance education programs, for-profit cyber universities and corporate universities that have been steadily claiming nitches that the traditional on-campus universities have been unable to fill. One notable indication from this is that the world as a whole may be heading toward a dynamic, competency-based society, where how or where one acquires desired competency is totally immaterial. In this paper we will present a factual study on the status of the American universities, based on facts and findings that we freshly gathered from our investigative travels and other sources from March 1998 to the present. The content will be intended to be useful in two ways: to give a brief up-to-date survey on their status as is remarked above, and to interpret the survey results to draw useful clues for understanding the current national government's initiative for restructuring national universities and research institutes.

2. Y. Miyazaki, Y. Kikuchi, D.S. Cai, and Y. Ikebe. Error Analysis for the Computation of Zeros of Regular Coulomb Wave Function and Its First Derivative. Math. Comp., in print.

   In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their derivatives may be reformulated as the eigenvalue problem for infinite matrices. Approximation by truncation is justified but no error estimates are given there. The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown. In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.

3. Y. Ikebe. A Skill up Method for Technical English Presentations, part 1. Journal of Human Interface, vol. 3, No. 1, pp. 27-30, 2001.

   Consider the distance learning content writing for Internet universities, now proliferating. One key issue is the content QUALITY. The distance learning materials market for Internet universities are far more competitive in quality than that for the usual textbooks for the on-campus universities.

   As a result, the conceptual design of the content, the most important upstream job, needs to be done under a far more stringent quality standard than the usual hardcopy textbooks. (This situation may be compared to the situation that the Internet stores are now finding themselves in.) The instructional design, the upstream job for the actual delivery of the content, is another important issue. This is an important old issue that has taken a new form in the context of the Internet. (A trial search made with the subject key ``instructional design" at a commercial site (amazon.com) returns over 120 items, most of which are in book form.)

   These two issues lead us to consider the re-evaluation and innovation of the so-called ``Technical Writing" paradigm. There is a rich supply of references on technical writing in book form or otherwise. But most of them were rooted in the pre-Internet days and we find their scope too narrow for us to cope with issues relating to the conceptual design or the instructional design issue of Internet universities, which represents our central concern.

1. Y. Ikebe, D. Cai. Y. Miyazaki, N. Asai, Y. Kikuchi and M. Ashour-Abdalla. Interactive Multimedia Education at a Distance - Linear Algebra (IMED-LA). Proc. 2000 Int. Conf. On Information Sciety in the 21st Century (IS2000), 2000.

   The IMED-LA or Interactive Multimedia Education at a Distance - Linear Algebra is the ongoing international joint project by the collaboration of the Japan Team currently consisting of five members and the Center for Digital Innovation (CDI) of the University of California at Los Angeles (UCLA) headed by Director Maha Ashour-Abdalla. The project started in July, 1999. Its goal is the production of virtual university content in linear algebra, intended primarily for graduate students and working students who need a fast-paced study of the basic facts from linear algebra; hence the content can also effectively be used by the beginning college students under a proper guidance from the teacher. Our partially completed content is already available on the Internet at the following URL: http://www.cdi. ucla.edu/linearalgebra. This Internet course has several special features worth mentioning: in its approach to the subject matter, the topics selected, the way and style the exercises are supported and the provision of the philosophical or historical notes for encouraging the learners or opening up new horizons for them. At the same time no mathematical rigor is sacrificed and a high level of standard is maintained. It is our pleasure to state that, thanks to our collaboration, the Japan team mainly providing authoring and the UCLA team the needed IT and project management expertise, the project has been enjoying a steady progress and the both teams are gaining valuable practical experiences. At the present this project is probably only one of its kind as an international joint Virtual University Content Production Project between Japanese and US universities. In this paper we will discuss the content under construction, the needed IT support and the project management technology being employed. For the activities of the CDI/UCLA, see their home page: http://www.cdi.ucla.edu.

2. Y. Miyazaki, D. Cai, N. Asai, Y. Kikuchi and Y. Ikebe. An Interim Assessment of Interactive Multimedia Education at a Distance - Linear Algebra (IMED-LA). Proceeding of the Third International Conference on Human and Computer (HC2000), 2000.

   The Interactive Multimedia Education at a Distance-Linear Algebra project, or IMED-LA, is the product of an ongoing international collaboration between a 5-university Japan Team and the UCLA Center for Digital Innovation. This project, which began in July, 1999, has the purpose of producing linear algebra content for presentation via a virtual university. Though it is primarily intended for graduate students and working professionals who require a fast-paced presentation of the basic concepts of linear algebra, the content can also be used effectively by beginning college students. The partially completed content is available on the Internet: http://www.cdi.ucla.edu/linearalgebra. The IMED-LA course has several notable features, which will be discussed in this work, but the main purpose of this paper is to present of an assessment of the program's content at this intermediate stage of its development. We are pleased to find our collaboration, in which the Japan team's role is primarily content authoring and the UCLA team is providing the needed IT and project management expertise, is proving to be very successful. The project has been showing steady progress, and in addition both teams are gaining valuable practical experience. This project is one of only a few known joint virtual university content production projects between Japanese and US universities.

1. Y. Ikebe and D.S. Cai. Hypertext dictionary: vocabulary building through a new etymological method. University of Tsukuba Special Project Report, 2001.

   A strong English vocabulary is an essential component for the English diction - the competence in choosing right words for a simple and straight forward expression. In this project, we will approach the vocabulary building using a totally new method - the bi-directional etymological method resulting from the recent development of comparative linguistics. Our method may be thought of as subsumed under what is loosely known as the root method or etymological method. But our method goes much more beyond any known valiant of it.

2. Y. Ikebe, M. Ashour-Abdalla, Y. Miyazaki, and D. Cai. IMED-LA demonstrations. Japan Information Processing Sciety Frontier Area Joint Workshop FJK2000, 2000.

   A joint international project for the development of Internet-based distance learning program on linear algebra started in the summer of 1999, after 3 years' preparation. Such a project is the first of its kind in Japan. Its first version is scheduled to be completed in the summer of 2000. The Japanese team (4 members, the same as the authors of this article) provides unique, quality contents based on the lecture notes by the first author (Ikebe), while the U.S. team (UCLA) with proven track records in the development of Web-based learning materials provides the needed Information Technology (IT) and Project Management Technology (PMT). The outline and the status quo of this project as well as its future plan will be discussed.

3. Y. Ikebe, D. Cai, Y. Kikuchi, Y. Miyazaki and N. Asai. Mathematics Distance Education IMED-LA. The Proceedings of the 29th Numerical Analysis Symposium, 2000.

   A joint international project for the development of Internet-based distance learning program on linear algebra started in the summer of 1999, after 3 years' preparation. Such a project is the first of its kind in Japan. Its first version is scheduled to be completed in the summer of 2000. The Japanese team (4 members, the same as the authors of this article) provides unique, quality contents based on the lecture notes by the first author (Ikebe), while the U.S. team (UCLA) with proven track records in the development of Web-based learning materials provides the needed Information Technology (IT) and Project Management Technology (PMT). The outline and the status quo of this project as well as its future plan will be discussed.

4. Y. Miyazaki, N. Asai, Y. Kikuchi, D. Cai and Y. Ikebe. Computation for Double Eigenvalue of A Class of Infinite Matrix and Its Application. Proceeding of The Japan Society for Industrial and Applied Mathematics Annual Meeting, 2000.