Math fundamentals

As soon as the keyword “math” comes-up during a conversation, people start to feel uneasy. There are a number of common strategies that people use to escape this subject of conversation. The most common approach is to say something like “I always hated math”, or “I am terrible at math”, which is a clear social cue that a change of subject is requested. Another approach is to generally be sympathetic to the idea of mathematics, so long as it appears in the third person: “she solved the equation” is fine but “I solved the equation” is not thinkable. The usual motivation for this mathematics pour les autres approach is that it is highly specialized knowledge that does not contain any true value for the general audience. A variant of the above is to believe that a special kind of brain is required in order to do math.

Mathematical knowledge is actually really cool. Knowing math is like having analytic superpowers. You can use the power of abstraction to see the math behind any real world situation. And once in the math world you can jot down some numbers and functions on a piece of paper and you can calculate the answer. Unfortunately, this is not the image that most people have of mathematics. Math is taught usually taught with a lot of focus placed on the mechanical steps. Mindlessly number crunching and following steps without understanding what they are doing is not cool. If this is how you learned about the basic ideas of math, I can't blame you if you hate it, as it is kind of boring.

Often times, my students ask me to review some basic notion from high school math which is needed for a more advanced topic. This chapter is a collection of short review articles that cover a lot of useful topics from high school math.

Topics math

This chapter should help you learn most of the useful concepts from the high school math curriculum, and in particular all the prerequisite topics for University-level math and physics courses.