# Mathematical Sciences

CIS 2 Computers and the Internet in Society SPRING 2009 Final Projects

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Mathematical Sciences deals with the use of applied mathematics for solving problems in all fields of science. By the very nature of Mathematics it is a universal constant way to explain the natural world quantified with numbers. Mathematical Sciences help society by providing the world with innovations from calculators to complex algorithms of computer encryption programs.

## History

Math has always been used to help solve problems. Originally most people started using it out of necessity to compute tax, measure objects and space, record trade, and even to explain astronomical occurrences. [1] Through the years math has been split into two sorts of categories: Applied and Pure Mathematics. Pure Mathematics focuses on proofs and mathematical theories while applied math is more of a practical and literal use of math for sciences and computation of real world quantities. Generally the fields of statistics and computer science are in the category of applied mathematics. Pure mathematics generally focuses on studying math simply because of its beauty and simplicity. Plato made an early distinction between pure and applied mathematics when he said that businessmen and generals "must learn the art of numbers or he will not know how to array his troops," compared to what was appropriate for philosophers "because he has to arise out of the sea of change and lay hold of true being." Pure Mathematics

## Current

Mathematics is an ongoing study that is still being vastly improved upon today. Every year, there are more than 7,000 proofs being added the the collective mathematics mind.

### Benefits

The benefits that arise from mathematical technological advancements are numerous. For one, mathematics is a very diverse and expressive field that is applicable in almost all aspects of life. Thus, benefits that arise from mathematical advancements are quite obvious due to the nature of mathematics itself. For one, calculators have improved life greatly by expediting long and tedious processes. The days where people had to do tedious calculations are long gone and have since been replaced with the ease of the calculator. An

In society, many gadgets that have been developed are considered to be beneficial in a mathematical aspect. For instance, phone calculators are commonly used now in place of a real calculator. These are used in moments where one does not have a calculator at hand, so they have to resort to their phone. The result of this is an increased chance of getting a computation right. Through this, one can see that developing mathematics in our society is greatly important and can lead to even more technological changes in other fields.

### Tools

#### Abacus

The first compact calculator is the abacus. The abacus was built from wood and beads. It was used in China in the ninth century. At the time the abacus was their “personal calculator” and served as the purpose we use a calculator today. Instead of actually computing the numbers, the abacus helps people keep track of the numbers and the person still has to compute it out themselves. It is proven that, a person who is good at the abacus, is able to do calculations just as fast as someone using a calculator. It was so popular back then that most people owned one and the use of an abacus spread throughout China. Though calculators are invented, some countries still have people using the abacus. [2] The abacus helped out ancient civilizations and led to the development of more sophisticated tools such as the calculator.

#### Calculators

After the abacus, a French man named Blaise Pascal, invented the first adding machine, in 1642. It was driven by gears and was only able to add and subtract. Only until 1886 was the adding machine able to go commercially, developed by William Seward Burroughs. Otto Steiger was then able to invent “The Millionare” which could add, subtract, and multiply! Texas Instrument, a company that is very well known today, for making calculators, was able to create a hand-held pocket calculator in 1966. The three men that were in the project to create the hand-held pocket calculator were Jerry D. Merryman, James H. Van Tassle and Jack St. Clair Kilby. This new invention had changed the way people had to do math. The first calculators would for $1000, but as soon as the IC (integrated circuit) calculators came out, it only sold for$125. Now-a-days, computers are so high-tech people barely have to think for their math problems. You could simply just type in your hard calculus problem and your scientific calculator could spit out an answer in less than a minute. Though the price hasn’t changed much, it has effected our lives more, with the fact it could do anything. [3]

With the advent of graphic calculators, life got a lot more simpler. Graphing calculators were revolutionary in the sense that not only can we do complex computations nearly instantaneously, but now we can see them visually and interpret more from them. The first graphing calculator was invented in 1985 and was called the Casio FX7000G. It was capable of carrying out simple equations graphically. These days however, the line between calculator and handheld computer is becoming more and more blurred. Some calculators even have the ability to play video games. As the years go by, more and more functions are being added to calculators.

#### Online Calculators

Those without a calculator are able to use Online Calculators, which do pretty much the same as a pocket calculator. You are now able to find online calculators that could do simple and hard math problems. Some websites that have online calculators are http://integrals.wolfram.com/index.jsp and http://www.math.com/students/calculators/calculators.html. You could simply type in a math problem and the answer would come out.

### Developments

Proofs are being worked on constantly and to date, there are at least 50,000+ types of algorithms and models. Sites such as Wolfram|Alpha are an ongoing collaboration and database with mathematicians.

Professor Craig Davis of the University of Michigan discovers a new algorithm that may reduce congestion problems on freeway on-ramps. This is an example of applied mathematics benefiting society. Statistical reasoning can aid in efficiency in transportation whether it be how the engine works to how the metering systems help stop congestion. [4]

## Future

The future of Mathematical Sciences looks promising for society. Computer Science applications are yielding new ways to interact with technology and other people in a faster, more secure mode of information transportation. Math allows us to understand our world so that we may live more efficiently. Math allowed humans to land on the moon, it helped us make hybrid cars, design computer systems, and much more. Computers themselves are just a glorified calculator that adds and subtracts at enormous rates. The future of Mathematical Sciences will lead society into an efficient age of new technology and telecommunication.