Collegemath
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Math is all about problems -- questions for which you don’t currently know the answer -- and problems can be really frustrating. That feeling of being stuck, for me, goes from a scattered confusion to a mind-numbing blankness. It’s really easy to shut down and give up, so the first step to solving any math problem is to persist! Don’t let the ...
In this post, we’re going to prove the most famous formula in all of science, E = mc^2! We’ll do this using a simplified version of Einstein’s original 1905 proof. In this post I will assume that you are familiar with special relativity and Lorentz transformations.
As a musician, I had always wondered why different instruments sound dis tinct from one another, despite being in-tune and playing the same note. Why is it so easy to distinguish someone singing a C major scale versus someone playing the same scale on the piano? Timbre, tone color, or tone quality of a sound are those characteristics separate from ...
Growing up, one of my favorite films was Studio Ghibli’s The Wind Rises—an animated historical drama about a 20th-century Japanese engineer named Jiro Horikoshi. Each time I rewatched it, I was always intrigued by a device that Jiro used for performing calculations. It consisted of two wooden rulers, with the top one able to slide freely. Somehow, ...
Below is the world's shortest intelligence test. See how many questions you can answer!
Consider the following questions:
“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?
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, but some of them are meant to distract. Let’s look at a strategy for answering initial value word problems.
Statistics is fun, I promise! But before we can start having all the fun, it is important to describe the distribution of our data. We will need to handle problems differently depending on the distribution.
One topic that seemed a bit mysterious and magic to me when I first learned calculus was implicit differentiation. In this post, we’ll start by reviewing some examples of implicit differentiation and then discuss why implicit differentiation works.
Probably the most common challenge that I see my students struggle with is understanding and writing out mathematical proofs. Although most higher-level college math and computer science courses rely heavily on proofs, there aren’t many courses that really prepare students before they’re thrown off the deep end. I wanted to discuss some tips and ...
Comparing finite set sizes, or cardinalities, is one of the first things we learn how to do in math. From a young age, we can answer questions like “Do you see more dogs or cats?” Your reasoning might sound like this: There are four dogs and two cats, and four is more than two, so there are more dogs than cats. In other words, the set of dogs is ...
There are many misconceptions when it comes to the subject of mathematics. One of the most common myths I encounter is related to the way one approaches learning math.
Induction. It's a mathematical concept that is no doubt familiar to any student taking an introductory proof class. It is also a concept that can bring complex feelings---the excitement of learning a new cool proof technique, the fear of being asked to prove something "obvious", or the confusion of where to start.
Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?