MATHEMATICS AND MANUFACTURING
Manufactured products account for some 60 percent of world trade
and 75 percent of U.S. trade in today's global economy.
Manufacturing is both increasingly fast-paced and internationally
competitive. New products can become obsolete within months. And,
in order to be competitive, many production processes must be
revamped every year or two. In the face of these pressures, U.S.
manufacturing needs to continually become more productive and
competitive. Such improvements will most likely result from
systematic approaches based on quantitative methods in the
mathematical and computational sciences.
The mathematical sciences have made many contributions to
manufacturing. These range from the very concrete -- materials
that go into products -- to the very abstract -- information
management. For example, statistical analysis reduces data from
manufacturing processes and systems to meaningful forms. Modeling
reduces manufacturing problems to quantitative relations and
equations suitable for attack by algorithmic methods. Mathematical
algorithms express the quantitative relations and equations in a
format suitable for computational solution.
The mathematical sciences have had a dramatic impact on materials
used in manufacturing. Mathematical models assist in the design
and processing of advanced materials, including: shape-memory
metals, high-strength ceramics, polymeric systems, and nonlinear
optical materials.
Manufacturing processes can be improved through quantitative
analysis, mathematical modeling, and computer simulation. Such
processes include: microelectronic, molding, crystal growth,
casting, joining, curing, and coating. The mathematical models for
these processes are differential, integral, and discrete equations.
Advances in mathematical control theory have led to improved
manufacturing process control. Applications are seen in chemical
process manufacturing and metal processing.
A number of areas of contemporary manufacturing are undergoing
rapid evolution. Intelligent manufacturing and solid modeling are
basic technologies that underlie other emerging manufacturing
technologies. Rapid prototyping, molecular manufacturing, and
biomanufacturing are technologies that did not exist ten years ago.
They are expected to be major factors in manufacturing ten years
from now.
The mathematical and computational sciences are also becoming more
deeply involved in developing tools for management decision making
in manufacturing. These quantitative methods supplement the
traditional humanistic approach to management decisions and
include: operations-based performance measures, computer-based
information management, flexible manufacturing systems, capital
budgeting for flexibility, and integrated manufacturing.
The rapid increase of computational capabilities and an
increasingly quantitative approach to problem solving is
transforming the manufacturing world. Expensive and time-consuming
traditional manufacturing cycles are being displaced by more
quantitative methods which increase the chances that a product will
be built right the first time it is built.

This paper, and the text on the theme poster, are drawn from the
recent report, The Mathematical and Computational Sciences in
Emerging Manufacturing Technologies and Management Practices, by
Avner Friedman, James Glimm, and John Lavery, published by the
Society for Industrial and Applied Mathematics, 1992.
For further information see also:
Advanced Materials and Processing: The Federal Program in Materials
Science and Technology. Committee on Industry and Technology;
Federal Coordinating Council for Science, Engineering, and
Technology. National Institute of Standards and Technology, 1992.
Manufacturing Systems: Foundations of World-Class Practice.
Committee on Foundations of Manufacturing, National Academy of
Engineering. National Academy Press, 1992.
Mathematical Sciences, Technology, and Economic Competitiveness,
edited by James E. Glimm. Board on Mathematical Sciences;
Commission on Physical Sciences, Mathematics, and Applications;
National Research Council. National Academy Press, 1991.
Technology Policy and Critical Technologies, by Mary Ellen Mogee.
The Manufacturing Forum, National Academy of Engineering, National
Academy of Sciences. National Academy Press, 1991.
Application of the Mathematical Sciences to Materials Science.
Board on Mathematical Sciences, National Research Council.
National Academy Press, 1991.
Engineering and the Advancement of Human Welfare, 10 Outstanding
Achievements 1964-1989. National Academy of Engineering, 1989.

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FOR IMMEDIATE RELEASE CONTACT: Kathleen Holmay
Date Mailed: April 9, 1993
MATHEMATICS AWARENESS WEEK IS April 25 - May 1, 1993
(Washington, DC) . . . . . Mathematics & Manufacturing is the theme
for Mathematics Awareness Week, which is being observed nationwide
from April 25 - May 1, 1993. This theme recognizes the importance
of manufacturing to the nation's competitive position in the global
economy. The theme also highlights the critical involvement of the
mathematical and computational sciences in developing new
technologies and decision making tools in manufacturing.
A number of areas of contemporary manufacturing that rely on
mathematics are undergoing especially rapid evolution. These
include intelligent manufacturing and solid modeling - basic
technologies that underlie other emerging manufacturing
technologies; and, rapid prototyping, molecular manufacturing, and
biomanufacturing - technologies that did not exist ten years ago.
Branches of mathematics, known collectively as quantitative
methods, now supplement the traditional humanistic approach to
management decisions and include: operations-based performance
measures, flexible manufacturing systems, computer-based
information management, and integrated manufacturing.
1993 Mathematics Awareness Week
events mark the significant contributions mathematics is making to
American manufacturing and the critical role it plays in helping the
United States increase its manufacturing capabilities. Nationwide
celebrations of Mathematics Awareness Week feature proclamations from
many of the nation's governors, legislators, and mayors. Colleges,
universities, and research laboratories across the country hold
competitions, exhibits, demonstrations, lectures and other events
to mark the week.
On three Sundays in April the Public Broadcasting Service will
air hour-long special MATHNET programs produced by the Children's
Television Workshop. The dates and titles are:
April 11 - The Case of the Mystery Weekend
April 18 - The Case of the Smart Dummy
April 25 - The Case of the Bermuda Triangle
The applications of mathematics to manufacturing are
symbolized by the Mathematics Awareness Week poster, an
illustration of how surface molecules might be moved by a scanning
tunneling microscope probe, part of a Molecular Manufacturing
Machine being developed by the National Institute of Standards and
Technology. The poster text is drawn from the recent report, The
Mathematical and Computational Sciences in Emerging Manufacturing
Technologies and Management Practices, by Avner Friedman, James
Glimm, and John Lavery, published last year by the Society for
Industrial and Applied Mathematics. The report focuses on the
contributions that the mathematical and computational sciences
community makes to technology, management, and education for
manufacturing, and on the opportunities for
mathematical/computational research that manufacturing creates.
Mathematics Awareness Week is coordinated by the Joint Policy
Board for Mathematics which represents three national mathematics
organizations, the American Mathematical Society, the Mathematical
Association of America, and the Society for Industrial and Applied
Mathematics. Funding for the week is provided, in part, by the
U.S. Army Research Office.

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NATIONAL EVENTS TO MARK MATHEMATICS AWARENESS WEEK
April 25 - May 1, 1993
Mathematics Awareness Week will be celebrated throughout the
United States from April 25 - May 1, 1993. This year's theme is
Mathematics and Manufacturing. In addition to hundreds of
activities taking place at schools, colleges and universities, and
at research labs and within business and industry, several national
events and programs are planned.
During Mathematics Awareness Week the Manufacturing
Technologies Laboratory from the National Center for Manufacturing
Sciences will be in the Washington, D.C region. The 36-foot mobile
lab contains state of the art technology including robotics and
computer-aided design stations. The work stations are networked,
machine cells are set up, and robots are programmed. These
technologies are used for the design and production of actual
products. Dates and locations are:
Monday, April 26 - American Chemical Society
Tuesday-Wednesday, April 27-28 - Baltimore Museum of
Industry
Thursday, April 29 - U. S. Capitol, offering hands-on
demonstrations to recipients of Presidential Awards
for Excellence in Science and Mathematics Teaching
and to Members of Congress.
On Friday, April 30, University of Chicago Professor Zalman
Usiskin, Director of the University of Chicago School Mathematics
Project, will be the keynote speaker at a Washington, D.C.
reception honoring recipients of Presidential Awards for Excellence
in Science and Mathematics Teaching. His topic will be, "The
Current State of Elementary School Mathematics and Science, and
What We Can Do About It."
On Friday April 30, a framed poster will be presented to NIST
Acting Director Raymond Kammer during ceremonies at NIST on Friday,
April 30, 1993. NIST is the source for the graphic art on the
theme poster and postcards for Mathematics Awareness Week 1993.
On Thursday and Friday, April 29 and 30, the finals of the
national MATHCOUNTS competition will be held. Seventh and eighth
grade student teams and their teacher-coaches will represent their
states in Washington, D.C.
On Sunday, April 25, the Public Broadcasting Service will air
the last in a series of three hour-long special MATHNET programs
produced by the Children's Television Workshop. The broadcast
dates and program titles are:
April 11 - The Case of the Mystery Weekend
April 18 - The Case of the Smart Dummy
April 25 - The Case of the Bermuda Triangle
Regional and local celebrations of Mathematics Awareness Week
will feature proclamations from many of the nation's governors,
legislators, and mayors as well as competitions, exhibits,
demonstrations, lectures and other events. Mathematics Awareness
Week is coordinated by the Joint Policy Board for Mathematics which
represents three national mathematics organizations, the American
Mathematical Society, the Mathematical Association of America, and
the Society for Industrial and Applied Mathematics.

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Background on Mathematics and Manufacturing
Mathematics & Manufacturing is the theme for Mathematics Awareness
Week, which is being observed nationwide from April 25 - May 1,
1993. This theme recognizes the importance of manufacturing to the
nation's competitive position in the global economy. The theme
also highlights the critical involvement of the mathematical and
computational sciences in developing new technologies and decision
making tools in manufacturing.
A number of areas of contemporary manufacturing that rely on
mathematics are undergoing especially rapid evolution. These
include intelligent manufacturing and solid modeling - basic
technologies that underlie other emerging manufacturing
technologies; and, rapid prototyping, molecular manufacturing, and
biomanufacturing - technologies that did not exist ten years ago.
Branches of mathematics, known collectively as quantitative
methods, now supplement the traditional humanistic approach to
management decisions and include: operations-based performance
measures, flexible manufacturing systems, computer-based
information management, and integrated manufacturing.
Mathematics Awareness Week events mark the significant
contributions mathematics is making to American manufacturing and
the critical role it plays in helping the United States increase
its manufacturing capabilities.
The applications of mathematics to manufacturing are
symbolized by the Mathematics Awareness Week poster, an
illustration of how surface molecules might be moved by a scanning
tunneling microscope probe, part of a Molecular Manufacturing
Machine being developed by the National Institute of Standards and
Technology. The poster text is drawn from the recent report, The
Mathematical and Computational Sciences in Emerging Manufacturing
Technologies and Management Practices, by Avner Friedman, James
Glimm, and John Lavery, published last year by the Society for
Industrial and Applied Mathematics. The report focuses on the
contributions that the mathematical and computational sciences
community makes to technology, management, and education for
manufacturing, and on the opportunities for
mathematical/computational research that manufacturing creates.

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EDITORIAL - Mathematics Awareness Week
Insuring Global Competitiveness through the Mathematical Sciences
Products and entire factories designed by mathematical models
and computer simulations, computers designing other computers,
intelligent machines working on assembly lines, computers
controlling production processes and plants, and robot workers. It
sounds like science fiction, but it's happening today. A new
industrial revolution is sweeping the globe. This revolution is an
entirely new approach to manufacturing.
Previously, an inventor designed a widget and engineers
designed machines and factories. A few widgets were produced.
Then the engineers went back to the drawing board to redesign the
machines and factories and kept trying until they got a good
widget. This process is called the "build-test-fix" cycle, and
it's as obsolete as the covered wagon and going the way of the
dinosaurs.
In today's highly competitive and rapidly changing global
economy, the build-test-fix cycle is too time-consuming and
expensive. Mathematical models and computer simulations are being
used to design products such as automobile, aircraft, and TV parts,
to design the machines and factories that produce them, and to
optimize the production processes to produce the highest quality
products at the lowest cost.
A mathematical model is a way of representing the relationship
between two or more variables in a quantitative fashion, as an
equation or system of equations. For example, "distance = rate x
time" is a simple mathematical model used by everyone who has had
algebra. The design of products and manufacturing processes may
require mathematical models consisting of hundreds or thousands of
variables. Until computers developed the capability of solving
such a large system of equations, the build-test-fix cycle based on
experience and intuition was the only method available to optimize
the design-production process, and it could take months or years of
testing.
What are the implications of this new industrial revolution
for the consumer/taxpayer/wage earner? First, it can mean better
products at lower prices. Second, it can mean that the U.S. will
improve its competitive position in a rapidly changing global
economy. Third, it means that an increasing number of jobs in the
future are likely to require knowing a lot more about mathematics
and computers.
As we focus on jobs and productivity, we are also celebrating
Mathematics Awareness Week from April 25 through May 1. This
year's theme, "Mathematics and Manufacturing," highlights the
contributions mathematics is making in both research and industry.
Mathematics Awareness Week serves as an annual reminder that new
mathematical ideas and methods are constantly being developed and
applied to find the solutions to real-world problems that help our
nation compete more effectively in a global marketplace.

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