Subject: "Real-World" Application for Specific Mathematical Topics

Dear "Math Central":

My name is Jane Ann Musgrove and I am a teacher of secondary mathematics. As a teacher of mathematics, I am always asked "Where will we use this in the real world?". I am seeking ideas/sites via the internet where students can find answers to this type of question. Can you help me?

To be more specific, right now I am interested in finding careers where the employees would use the concepts of "Radicals", "Matrices", and "Logarithms". This information will be used by students to make presentations to the class on their findings from internet searches.

Thank you for your help.

Jane Ann Musgrove

Hi Jane Anne,
I did some Internet searching myself and found very little. I can give you a few ideas but I would be very interested in others that you or anyone else has. I would like to invite anyone reading this note who can add to the examples below to let me know by sending an email to TheCentralizer@MathCentral.uregina.ca

**Radicals:**
It is hard to imagine a "real-world" application of mathematics that doesn't involve some use of radicals. The distance between two points in two or three dimesnions involves a radical. It is an application of the theorem of Pythagoras. Solving an equation usually involves radicals. We show student quadratics that factor so that the roots are integers or rationals but this almost never happens in practice. Compound interest calculations often involve radicals.
**Logarithms:**
Logarithms are used in measuring many physical quantities. The scale that is used to measure earthquakes, the Richter Scale, involves a logarithm. Likewise the scale that is used to measure the loudness of sound in decibles involves a logarithm. They are often used in studying population growth and radioactive decay. Logarithms also arise in some financial calculations, for example those involving interest rates. Just last week I learned from a graduate student in geography that she was using logarithms to study the rate of melting of glaciers.
**Matrices:**
Matrices are ubiquitous. Medical imaging, CAT scans and MRI's, use matrices. Graphics are often placed on your computer screen using vectors and then moved (translated or rotated) using matrices. Matrices are used in the compression of electronic information, for example in the storage of fingerprint data. Matrices are used in modelling population growth. Another interesting application of matrices is in error correcting codes, that is identifying and correcting errors in electronic transmissions. In economics and operations research matrices are used optimization problems, for example in making the best use of resources, whether lobour or capital, in the manufacturing of a product.
Cheers,

Harley