Consider the following questions:

Mathematical proofs are what make math objective: while you could find a few examples that "prove" a mathematical statement, it is often more important to write a rigorous proof that holds true in all cases. Mathematicians have a few methods in their toolkit to tackle different proofs. In this post, we will learn how to write a proof by contradiction.

If you are reading this, I can tell you’ve mastered solving simple linear equations. You’ve mastered the art of balance. You know that whatever you do to one side of the equal sign, you must do to the other. You can perform inverse operations until the cows come home, and you are a pro at isolating the variable. I bet you even check your work by plugging your answer back into the original equation, math whiz kid that you are. You could solve the following problem without breaking a sweat.

Today, we are going to learn how to solve linear algebraic equations like 3y + 3 = 18 or 5x - 4 = 16. If these equations make you feel a bit queasy, have no fear! I am going to break the process down into five simple steps. 

“I never understood that.”

If at some point you ever want to buy property near water, a variation of this question will undoubtedly pass through your head: what are the chances that my {insert name of your expensive piece of property close to water} floods?

Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.

We’ve all been there: on a homework set or in an exam, you turn to the final page and, to your dismay, it’s a wall of text. The dreaded Word Problem. Some of the words are useful, some of them are meant to distract. Let’s look at a strategy for answering initial value word problems.

I’m writing this blog post because when I first came across Taylor series I found that a lot of my previous intuitions for mathematics were suddenly inadequate. It took time for me to build intuition not only for how these things work but why they are important. I hope this post will be illuminating for those just beginning to learn about Taylor series and also those who have some experience with them but haven’t quite wrapped their heads around them yet.

Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by