Central Department of Mathematics

Abstract: The study of Toeplitz operator was initiated in a paper of Otto Toeplitz in 1911. The objective of this paper is to discuss some algebraic properties of Toeplitz operators in Bergman Space. These properties include some general properties together with compactness and boundedness properties of operator have been studied.
Key words: Operator matrix, Bergman  space, Analytic. Reproducing Kernel, Berzin Transform

Adventure in Mathematical Sciences
for
Authentic Integration of Mathematics and Sciences
through
Movement for Awareness about Mathematical Sciences
in Nepal
(AiMS for AIMS thru MAMS in Nepal)

R. M. Shreshtha

Abstract:
Recent Trends in Mathematics can be realized as the result of massive efforts  of mathematical scientists towards reform, transformations and radical changes in teaching, learning and use of mathematics in a highly tradition dominated situation under the traditional and conservative philosophy of viewing

“Mathematics as static and based on some transcendental abstract entities
which are perfect, eternal, unchangeable, out of space & independent of human  knowledge,
or,
as an absolute, infallible,  certain, universal,
and
independent of humankind knowledge.”

One such trend is to undertake an
Adventure in Mathematical Sciences
for
Authentic Integration of Mathematics and Sciences
through
Movement for Awareness about Mathematical Sciences in Nepal
guided by a new humanistic philosophy that declares

“Mathematics is a fallible, corrigible and changing social-cultural-historical product based on what we can actually observe, fallible being done by fallible people,
and
quasi-empirical analogous to natural sciences.
It believes that mathematical truths may become uncertain like other sciences.”
Once we do so, there will exist no problem arising out of reluctance of accepting any drive aimed at replacing the traditional mathematics programmes which
a) simply produce a kind of mathematically educated persons who are usually conservative in outlook, timid in thinking and uncritical about life  in general,
b) promote a strong negative tendency of hiding oneself behind a set mathematical symbolism as if he or she is a neutral being studying only absolute and eternal truths,
c) create people who are responsible for manufacturing various mystifying ideas and antagonistic attitudes,
by programmes that will, at least,
a) make a certain minimal amount of mathematical know-how easily available, comfortably affordable and widely accessible for the welfare of all people irrespective of age, race, gender, colour, religion, language, ability, etc.
b) improve the quality and level of mathematics education so as to make the recipients able to face the problems and challenges of the science and technology dominated 21st century globalised world of work threatened by the lack of peace and disrespect of human-values; and, derive benefits from the opportunities generated by the new programme
c) help advocate the idea contained in the slogan:
“Mathematics in All and All in Mathematics”

One worldwide current trend is An Adventure in Mathematical Sciences for Authentic Integration of Mathematics and Sciences through Movement for Awareness about Mathematical Sciences which recognize Mathematical Sciences as an umbrella discipline that encompasses what is mathematical, semi-mathematical and traditionally non-mathematical that are being  considered extensively not only as open areas for mathematical study, research and applications but also as a potential source for the origin and development of new mathematical concepts and techniques
Inspired and encouraged by the unprecedented growth in the popularity of study, research and applications, strong advocacy in favour of Mathematical Sciences by world class Centres, Institutes and Universities, rapidly increasing job opportunities, preferential treatments of employers, national and international strategies like NSMS in Australia, AIMS in Africa, EMSMS and ESPRC survey and study reports of Europe, The Mathematical  Sciences in 2025,  NAS (US) Survey and study report and many more other reports and articles by experts in the field, NAMASTE (a team of mathematical minds of Nepal), has thought of making an Adventure in Mathematical Sciences for Authentic Integration of Mathematics and Sciences through Movement for Awareness about Mathematical Sciences in Nepal.
This lecture is aimed at describing briefly how we plan to make a humble beginning of our AiMS for AIMS through MAMS in Nepal: We have thought of

(1) Beginning our adventure with an awareness movement that will focus in presenting a very short glance of mathematics and mathematical environment of the pre-historic, ancient, classical and modern times.
(2) Making an attempt to convey how Mathematical Sciences is being described, adopted and promoted all over the world.
(3) Preparing a note about the state of Mathematical Sciences in Nepal together with an advocacy plan
(4) Suggesting the establishment  of  school, institute, or Centre of Mathematical Sciences in Nepal
(5) Presenting two very simple samples illustrating how a humble beginning of Nepal related Mathematical Sciences Activities can be started

Mathematical Sciences
A
Prerequisite
for
Nepal’s Graduation to Developing Country Status

R. M. Shreshtha

Abstract
Nepal’s Graduation to Developing Country Status depends heavily on the scientific knowledge, technological skill and innovative capability of her people. No Science, Technology and Innovation is perfect in the absence of Mathematical principles, Statistical methods and Computational skill. Bringing them together under the title

“Mathematical Sciences as an Umbrella Discipline”

has become one of the most popular and promising area of study, research and application in the 21st century.
Nepal, in order to attain GDCS, has to learn a lot from the knowledge and experience of the outside world, how to reform, transform and introduce radical changes in teaching, learning and use of Mathematics/Statistics/CST through a new programme that will, at least,
a) make a certain minimal amount of mathematical know-how easily available, comfortably affordable and widely accessible for the welfare of all people irrespective of age, race, gender, colour, religion, language, ability, etc.
b) improve the quality and level of mathematics education so as to make the recipients able to face the problems and challenges of the science and technology dominated 21st century globalised world of work threatened by the lack of peace and disrespect of human-values; and, derive benefits from the opportunities generated by the new programme
c) help advocate the idea contained in the slogan:
“Mathematics in All and All in Mathematics”

Today, on behalf of NAMASTE- NAtional MAthematical Sciences Team, would like to brief how, we have planned to launch an AiMS for AIMS through MAMS that will advocate  Mathematical Sciences as an umbrella discipline.