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Below is the world's shortest intelligence test. See how many questions you can answer!
The pigeonhole principle: a counting concept with countless applications
Consider the following questions:
“I never understood that.”
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 ...
Which is bigger?: Set cardinality, injective functions, and bijections
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.