Maths in Computers

This article is based on the life experiences between mathematics and computers.

Definition

Mathematics is the fundamental thought process of every computing. Mathematics is the science that deals with the logic of shape, quantity and arrangement. The word comes from the Greek word "μάθημα" (máthema), meaning "science, knowledge, or learning", and is sometimes shortened to maths.

It is narrated well in the popular book "What is Mathematics" by Richard Courant and Herbert Robbins. It got published in 1941 by Oxford University Press.

Industry Use Case 

Here is a recent use case in cloud computing metric dashboard using "Trimmed Mean" mathematical concept.

What is Trimmed Mean?

Trimmed mean is computed by first ordering the data values from smallest to largest. It is by deleting a selected number of values from each end of the ordered list and finally computing the mean of the remaining values.

It is mathematically depicted as below:

Trimmed percentage is the percentage of values deleted from each end of the ordered list.

Where?

Last week, Amazon cloud platform (AWS) announced support for the trimmed mean statistic on CloudWatch metrics. System diagram of AWS cloud watch, is represented as below:

CloudWatch metrics already support statistics such as percentiles, which allow customers to monitor the worst value for a selected range, for example 95% or 99%, of the data. 

Trimmed mean statistics allow customers to monitor the average value for the selected percentage of data, giving a more accurate view of the users’ experience than a single percentile. Specifically, it is beneficial to monitor the performance indicators of system latency.

Why?

With trimmed mean statistics, customers gain visibility on the average performance of a metric without the noise of outliers. Trends in average performance represented by the trimmed mean can be either visualized or alerted. It is possible using CloudWatch Dashboards or setting the to set thresholds in alarms for proactive alerting.

AWS CloudWatch monitoring technical details are available at https://docs.aws.amazon.com/AmazonCloudWatch/latest/monitoring/getting-metric-statistics.html

How?

Let us look into the technical insights of how it's differential element.

For example, monitoring the tm99 would allow you to measure the average customer experience using 99% of the data and discarding only the highest 1% values, which are often skewed by outliers. 

Trimmed mean statistics helps to monitor the cloud hosted applications, which enables the customers to gain visibility on a more representative sample of performance metrics. Naturally, the common metrics are sensitive to variations which cannot be detected by monitoring percentiles.

Thus, it makes performance improvements visible by helping to address the worsening tendencies early in the proactive way.

Acknowledgement

The fast modern world is missing the deepest principle in human nature of "appreciation" along with its "demonstration".

Let us be grateful to people who makes us happy learning. Because, they are the charming gardeners who makes our soul blossom.

This chapter is dedicated to my close friend Dr. Vanniarajan Chellappan, who continue to inspire mathematically for four decades, since childhood.

Conclusion

Mathematics solves problems by using logic. Logic and reasoning are used by mathematicians to create general rules, which are an important part.

It is an essential & fundamental attribute of any computing in the world. To me, it aids to become a valid software engineer in IT career.