First up on my hit list is Linear Algebra - the prerequisite for any serious numerical work. This tool-set enables the manipulation of huge multi dimensional data-sets with simple scalable algorithms and numerical constructs . Any work involving computers is heavily dependent on these principles.
The name is exact in its description, the phrase "Linear" signifies the manipulation and study of straight lines and "Algebra" stems from the Arabic - al-jabr - which apparently means "the restoration of broken elements". We are all familiar with algebra in equations that generally contain the unknown quantity x to the power of something or other but also the most famous equation of all E=mc^2 . Algebraic equations rely on using known quantities to solve for variables of unknown quantity.
ie x + 9 =3 giving a value of x = -6
In linear algebra we concentrate on linear equations of the forms ax + by + c =0 or y=mx . We can use the power of Matrices, Vectors, Bases and Norms to solve systems of these linear functions. This can give us the ability to solve huge problems with large numbers of variables with the same techniques that we would use for a simple equation such as our example above.
At first glance it can all be very confusing, Vectors and Matrices are abstract concepts that take a bit of time to master . They are scary to look at, but are essentially simple once they are internalised. I wont be going into any depth on the fundamentals, as others have already explained these ideas beyond what i could ever hope to achieve. If you need a brush up, check out the links below. Over the next few posts, however, I do hope to share my own insights about Matrices and Vectors which are crucial to many areas of applied math such as Computer Graphics and Machine Learning.
In future posts, I will be covering some interesting properties of Vectors and Matrices that look and sound terrifying, but as with most things in mathematics, actually simple in practice.