Linear Algebra is a story told in two worlds, one geometric and one algebraic. The interplay between the two is beautiful and powerful. In this video we introduce the notion of a linear transformation and see how this simplification makes our lives far easier.
This video is the start of a one semester university level course on Linear Algebra that emphasizes both conceptual understanding as well as procedural fluency with the techniques of Linear Algebra. In this video, we get to see just the beginning of some of the big ideas of Linear Algebra.
Now it’s your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time – a lot of time! – sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
This video is part of a Linear Algebra course taught by Dr. Trefor Bazett