Applications of Mathematics in Real Life

Applications of Mathematics in Real Life Situations

1.0 Application of Matrices

Matrix concepts can be applied in various fields such as:

• Quantum Mechanics
• 3D Games
• Animations
• Cryptography and Others.

We shall analyze the last one which is Encryption in further details.

Encryption is indeed an important measure of security when there are transactions of data between parties.

Firstly, we shall make use of the AB = X and B = A^-1X concept, where the matrix A is the Encoder and the inverse of A is the Decoder.

As messages are mainly sent in letters, we have a set a relationship between letters from the message and numbers in our matrix.

For our example we will take the following relationship.

Now let’s encode our message which is “BAD”.

Referring to our relationship table, it becomes “3, 2, 5”.

We decide for a coding matrix A, which can be 5 2 4

6 1 0

2 7 2

As it is a 3*3 matrix, we can encode 3 numbers at a time.

Encrypting the first 3 numbers, 10, 0, 13 (Matrix B) using matrix multiplications:

5 2 4 3 39

6 1 0 2 = 20

2 7 2 5 30

39, 20, 30 becomes the Encrypted Message which should be decoded now using inverse of matrix A.

Inverse of A = 1/73 12/73 -2/73 39 3

-6/73 1/73 12/73 20 = 2

20/73 -31/146 -7/146 30 5

Decoding the message gives us back 3, 2, 5 which can be referred back to the relationship table to get the message sent.

Note: For this example

• We need to have a matrix A which does have an inverse, we need to cater for the blank – space hence we can allocate a “0” for it
• The coding matrix as well as the number letter relationship is independent that is for some other encryption A can be 3 while B is 4 and so on.

Conclusion: Matrices do play a major role in not only Encryption of Messages to avoid misuse of data, but in other fields mentioned above as well.

2.0 Application of Statistics

“We live in the Information Age…” is a common saying in today’s world. It is a true fact as in our era as we make use of information in every field to be able to get an idea of what is actually happening and what we can do to not only to reduce problems of the past but devise ways and techniques for much proper less time consuming, less complicated, less costly and more beneficial processes to obtain output

Statistics are the ways we can achieve the above by manipulating the data in their own ways to obtain a set of conclusions which will help us take many crucial decisions.

We can also agree to the fact that indeed statistics are being used in many vast and important fields which will be illustrated below:

1. Weather Forecast/Emergencies Precautions

We make use of statistics to a very great extent in weather forecasting. This is so as almost every forecasting is based on data and information gathered from previous ones and in addition with other related data.

For example: In reference to the amount of rainfall or cyclones obtained from previous years, we can have a close overview for the current year and hence take necessary precautions

2. Medical Studies/Prediction of Diseases/Genetics

Statistics have a huge role in medical fields nowadays. By referring to data and information on other past patients, we can learn more and extract new remedies and treatment not only to make the medical field prospect but help needy peoples.

Also, using genetic data, some parents might come to know well before the coming problems with their expected children hence can prevent the possible problems accordingly.

For example: Using information recorded from past patients suffering from a particular disease in a particular season, expected patients with the same disease can be protected using vaccinations well before.

3. Politics

To achieve a well organized political structure for the country’s well being, the potential people needs to be elected and based on their contribution, their work and their reputation on previous data, the obtain their chances to be candidates in next elections.

4. Consumer Goods/Stock Market/Quality Testing

Many wholesalers, retailers and even small scaled businessmen nowadays do keep tracks of both their purchases and sales which constantly being referred to be able to extract many important conclusions for better decision making and productivity.

For example: If a certain commodity’s sales rises during a particular festive season, the businessman will know from statistics that he should have the item in stock for his own profit.

In addition, it is crucial acknowledge what is happening in the economy of the country, hence statistics is a blessing here also as it gives us feedback and predictions for the future.

Companies too use statistics to test whether their products are as per their customer’s wants and needs. To do so, they make use of product batches and hence it is time consuming for them to check for all the products.

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Conclusion: In the light of the above, we have seen that statistics are merely predictions; hence we cannot rely completely on statistics. However, they allow us to have better overviews of what is expected and hence we prepare accordingly to eliminate errors and mistakes.

3.0 Application of Regression and Correlation

Regression and Correlation is used with sets of data, most commonly 2 sets of data to conclude about one main point, the relationship between the data.

Regression deals mainly with the graphs of best fits for the data to be able to obtain the Correlation between them.

Example:

The Correlation: Positive Linear Correlation

The study also includes the Correlation degree or measure namely the Pearson Product Moment Correlation Coefficient, which lies between -1 and 1.

Regression and Correlation is used in everyday life in various situations namely:

1. In Businesses

Firstly, to compare the previous sale figures such as to have better understandings for future sales.

Moreover, companies are able to see how the varied prices on commodities have an effect on sales and clients requirements.

Also, also the regression predictions will allow the companies to eliminate future problems and risk hence obtaining better business models with proper decision makings.

2. In Regression Testing

As defined by the Internet, Regression Testing is to verify that modified code does not break the existing functionality of the application and works within the requirements of the system.

Therefore, it is a much easier and quicker way to find mistakes in systems to be able to implement new designed and modified ones.

3. In Medical Fields

According to Paul I. M. Schmitz (1970-1986), in the biomedical field, data in binary form such as disease/no disease or survival/death are very common. In these applications a multivariate normal distribution for the x-variables in both the disease group and the non-disease group was assumed.

In pregnancy cases, the IQ of the unborn child is mainly based on predictions from regressions.

Hence it is clear that regression played an important part in medical fields.

4. In Education / Candidates Selection / World War

Many institutions such as Harvard use regression models to be able to select the students that are eligible. Students also turn to counselors which uses the same techniques to predict the best school for the latter.

For selecting best candidates for employment, companies do make use of regression methods. In the same way, during world wars, regression made it simple to pick the most capable soldiers to increase their winning chances.

Conclusion: Like Statistics, Regression is of great importance when it comes to have predictions for the future to be able to make better decisions.

4.0 References

Matrix Encryption [Online] Available from http://www.austincc.edu/lrosen/1314/webact2/webact2.htm [Accessed: 26th – 29th November 2014].

Maths Worksheet Center [Online] Available from http://www.mathworksheetscenter.com/mathtips/statsareimportant.html [Accessed: 30th November – 3^rd December 2014]

What Are Some Ways Linear Regression Can Be Applied in Business Settings? [Online] Available from http://smallbusiness.chron.com/ways-linear-regression-can-applied-business-settings-35431.html [Accessed: 26th – 05th November 2014].

Pearson’s Product Moment Correlation Coefficient [Online] Available from http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient [Accessed: 5th November 2014].

Numbers Numerical Methods For Bioscience Students [Online] Available from http://web.anglia.ac.uk/numbers/graphsCharts.html [Accessed: 7th December 2014]

Testing Basic Interview Questions [Online] Available from http://testingbasicinterviewquestions.blogspot.com/2012/01/what-is-regression-testing-explain-it.html [Accessed: 7th December 2014]

Regression Models [Online] Available from http://www.psychstat.missouristate.edu/introbook/sbk16m.htm [Accessed: 7th December 2014]

Paul I. M. Schmitz. (1970-1986) Developments In Logistic Regression Methodology. 1.p.2.1 [Online] Available from file:///C:/Users/User/Downloads/860423_SCHMITZ,%20Paulus%20Ignatius%20Maria.pdf [Accessed: 7^th December 2014]