The Point of it All

There will be a point in the semester when you start to learn about these things called Vector Spaces and what it means to be in a Space. Likely, it will seem needlessly theoretical, and you might wonder; So what?

One of the many ways to solve math problems is to generalize. To find problems with a similiar "structure", or to say these 2 diasperate ideas are actually equivelent is a powerful tool

Linear Algebra is a formalization of many similiar and weird forms of math; It acts as a glue. The language of linearity unifies many of the mathematical ideas you've seen up until this point.

From the familiar geometry, cartesian plane, and thus undefined space in which we do calculus that you're used to; To solutions of polynomial equations, and matrices; Ideas of mappings, and functions; How to generalize distance, size, and angles; signal processing, and endless others. Linear Algebra can describe it all... ish.

You can think of this class as a slight preview to the world of math theory. Learning the unifying ideas between different types of math allows endless problem solving in the domain of your chosing.

Don't mean to pressure you to pick apple... but you should :-)

Jack

Something to think about: if 3 lines intersect in 3D, what does it mean for a system of linear equations to model that; what else could that system describe? Hint: it's a lot