Tags: Moore And Parker Critical ThinkingStanford Admission EssayChoosing A Topic For A Research PaperCaderousse EssayMultiple Multiple Choice QuestionsCause And Effect Essay On Healthy DietEssays About Raymond CarverSolved Problems On Fourier TransformParis Essay In French
The Bill & Melinda Gates Foundation is a Strategic Partner. It’s a question many students will ask while grappling with a particularly complex calculus problem – and their teachers will probably echo while setting or marking tests. Many fields of mathematics germinated from the study of real world problems, before the underlying rules and concepts were identified.These rules and concepts were then defined as abstract structures.
People no longer have to depend on real world objects, as was once the case, to solve a mathematical puzzle.
They can now generalise to have wider applications or by matching it to other structures can illuminate similar phenomena.
If he had stones left over, it means some sheep had wandered away or perhaps been stolen.
This one-to-one correspondence helped the shepherd to keep track of his flock.
That process of moving from the concrete to the abstract scenario is known, appropriately enough, as abstraction.
Through abstraction, the underlying essence of a mathematical concept can be extracted.
It means we’re able to handle any amount of sheep, regardless of how many stones we have.
We’ve moved from real-world objects – stones, sheep – to the abstract.
Results in one field can suggest concepts and ideas to be explored in a related field.
Occasionally, methods and techniques developed in one field can be directly applied to another field to create similar results. Some of the mathematical subjects taught at university level – Calculus, Real Analysis, Linear Algebra, Topology, Category Theory, Functional Analysis and Set Theory among them – are very advanced examples of abstraction. They’re often tough to visualise and their rules rather unintuitive to manipulate or reason with.