Math & Social Sciences

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History

Even these days, we have a tradition of 2 birthdays for an individual; one as per the Gregorian calendar &amp; the other by our local traditions. This kind of dual dates is not acceptable in studying history.

History is about looking at events of the past, see if they can be fitted into any pattern from which lessons can be drawn for the future. One of the crucial questions would be &ldquo;when&rdquo; did a particular event happen. The answers to that question were made easier by constructing a timeline of history and the idea came from the number line of math!

The number line is a totally arbitrary line where 0 can be marked anywhere as per our convenience. But the historical timeline has to have a fixed reference year which is agreed by everyone. In the chapter 24.2 on measurement of historical time we have talked about emperor Selucus Nicator who laid the seeds for identifying specific years along the timeline.

In the last millennium the world has got connected more and more through trade, migration and wars. Hence what happens in one part of the world, necessarily affects events in another part of the world. Hence using a historical timeline to study events happening at the same time in places which are geographically apart, improves understanding of history.

Archaeological excavations &amp; carbon dating are two important ways of fixing dates of past events. Excavations use geometrical diagrams both on the surface to document excavated material. The layers of earth which are dug out are also marked vertically on a scale which again is related to historical and even geological time.

Carbon dating helps find the age of any material by studying an atomic level emissions to work out what is called half-life. This is a product of both mathematics and physics.

Recently study of DNA sequences in humans is enabling scientists to work out details of past human migrations. DNA sequencing is math applied through computer software.

Geography

Geography is about understanding phenomena on the surface of the earth like winds, tides, pressure &amp; heat waves, seasons, vegetation etc. Scientific study of these necessitated the graphing of the surface of the earth using latitudes &amp; longitudes. These were enabled by using principles of both plane and spherical geometry.

The measuring of the contours of the Earth needed Trigonometry. The Everest was designated as the highest mountain peak without going anywhere near it! The outlines of any region on the earth, whether political or economic is represented by maps which use ideas of scaling.

The daily weather patterns around the earth are tracked continuously and displayed visually using specialized computer software.

The prediction of eclipses and comets is made possible by using complex math. The ubiquitous GPS which is used in most cars uses ideas of spherical trigonometry to locate the car within an accuracy of one metre.

The Earth is spherical. But maps that students study are drawn on plane surfaces. Students need to keep in mind the distortion of sizes of countries done in this process. Countries above & below the tropics of Cancer and Capricorn appear much bigger than actual. That is the reason there are different kinds of map projections.

Commerce 

The applications of math to commercial transactions are many. These will be covered under a separate section &ldquo;Math in Our Life&rdquo;.

Accounting 

Accounting is the mathematization of the commercial transactions in a family, organization or a country. It has also developed several tools for evaluating financial decisions.

Economics

Economics is the study of a society from the point of view of production, consumption, savings &amp; investments. It depends on understanding the psychological &amp; emotional forces which work at the level of the consumers. To that extent is more an art than a science.

Though the behaviour of an individual consumer cannot be predicted easily. Mathematicians have found, through statistics &amp; probability, that their behaviour at the mass level can be predicted with reasonable accuracy. Hence economists collect and study a lot of data with mathematical tools and try to make predictions.

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