We know that Mathematics plays a very important role in the Modern World. We are living in a scientific era of rapid development. Things that were new or unheard of a few years ago seen commonplace today. Some of the new technical advancements may have little effect upon our personal life, but others may play a most important part in our existence. The recent developments in computers greatly affected technological advancements. Modern technology has become highly dependent on information technology, information technology refers to the use of computers and software to convert, store, protect, process, transmit, and retrieve information.
Computational theory, algorithm analysis, formal methods and data representation are just some computing techniques that require the use of mathematics. Computational theory and algorithm analysis deals with whether and how efficiently a computer is able to solve problems. Formal methods are mathematically based techniques for the specification, development and verification of software and hardware systems. Data representation refers to how computers exchange and process information using the ones and zeros of binary, rather than the more inconvenient ten-digit decimal system.
Binary basically means composed of two parts. The binary number system was started by Gottfried Leibniz back in 1666. It makes information processing simpler. For a processing system to work there must be at least two symbols therefore binary is the smallest numeral system that is usable. A CPU can only recognize two states, on or off, but from this on-off state, everything works (Mathmaze, 2006). Thanks to mathematics, complicated computations related to engineering, robotics, aviation and the like are now possible with great speed.
Schools even recognize the importance of mathematics, as a matter of fact, the prestigious Institute for Mathematics and Applications (IMA) at the University of Minnesota has devoted a whole academic year to applications of algebraic geometry. The background for this initiative is that effective use of algebraic geometry is now found in applications such as optimization, control problems, bioinformatics, data communication, and computational geometry (NTNU, 2004). Even in the prediction of weather, mathematics plays a vital role:
The National Meteorological Center, provides on an operational-round-the-clock basis, guidance material to all the national forecast services, as well as to foreign services, under the auspices of the United Nations. The guidance material consists of large scale wind and weather patterns over the entire northern hemisphere. The basis for this is the approximate numerical solution on large electronic computers of hydrodynamic and thermodynamic partial differential equations constituting a mathematical model for the behavior of the atmosphere (National Academic Press, 1968).
One of the most astounding developments of the century is also made possible due to mathematics. Robotics makes use of the coordinate system for an accurate computation of arm position. Robotics problems can be solved by defining several coordinate systems. One coordinate system assigned to the robot’s base, another coordinate system called to its hand and another to the piece that the robot must grasp. Often, the position and orientation of the piece relative to the robot’s base is known but the important thing is its position relative to the hand so that the hand can be moved correctly to pick up the piece.
This can be computed if the position and orientation of the hand relative to the base is known. Orientation as well as position is important if the hand is to be properly oriented to grasp the piece (Hiob, 1998). Not only is the application of mathematics limited to the use of the Cartesian Coordinate System in robotics but as the robotics industry grows, more complicated mathematics are being applied, some of these include: algebraic differential topology, dynamical systems theory, optimization algorithms, combinatorics, differential algebraic inequalities and statistical learning theory (National Science Foundation, 2000).
The impact of mathematics is not limited to technology, advancements in astronomy are also mainly because of mathematics. When it was discovered that the universe obeys relatively simple mathematical laws, the application of mathematics to natural phenomena followed. From the Greek’s use of the stars in computing the days of sowing and harvesting to Newton’s computation of the earth’s path around the sun, astronomy has evolved with the help of mathematics. Today, trajectory of comets and other newly discovered heavenly bodies are accurately plotted through mathematics.
Universities also offer mathematically-based courses in astronomy using algebra and geometry to better understand the stars. A branch of astronomy dependent on mathematics is Theoretical astronomy. Theoretical astronomers use a wide variety of tools which include analytical models and computational numerical simulations. Numerical models can reveal the existence of phenomena and effects that would otherwise not be seen. Theorists in astronomy endeavor to create theoretical models and figure out the observational consequences of those models.
This helps allow observers to look for data that can refute a model or help in choosing between several alternate or conflicting models. An example of this is the newly proposed cyclic universe theory which aims to disprove the big-bang theory. The cyclic universe theory represents a combination of standard physical concepts and ideas from the emerging fields of string theory and M-theory, which are ambitious efforts to develop a unified theory of all physical forces and particles. These theories rooted in complex mathematics offer a compelling graphic picture of the cyclic universe theory (Princeton University, 2000).
From the early approximate computations of planet movement to the determination of such movements for a period of several millions of years with accuracy to about 13 decimal places, mathematics has lent its hand. In recent years, the world has seen countless unmanned satellites launched into space to follow predetermined orbits precisely determined through the use of calculus. Powerful telescopes capable of seeing millions of miles across the galaxy have been developed through the use of computers. The developments both in technology and in astronomy are just some of the impact mathematics has made to modern science.
From simple arithmetical computations to complex computer computations in linear algebra, it is always at the forefront of change. Its importance is beyond reproach and its effects impossibly quantifiable. As civilization continues its growth and hunger for knowledge, mathematics shall guide it towards truth and realization.
Hiob, Erice (1998, June 11). Robotics: Using Transformation Matrices to Change from One Coordinate System to Another in Robotics. Retrieved December 9, 2007, from http://commons. bcit. ca/math/examples/robotics/linear_algebra/index. html