Do you remember when you first learned how to round numbers? For example, to round 687 to the nearest hundred, we notice it’s between 600 and 700. Since 687 is closer to 700 than it is to 600, we round up to 700. Maybe you even learned a rule: Look at the digit to the right of the one you’re rounding. If it’s 5 or greater, round up. If it’s 4 or less, round down. Rules can be good, but they can also be dangerous.
Continue reading “Dangers of Mathematical Rules”I’m an Author (Almost a Year Late)
With everything that happened last year, I managed to never write about my co-authorship of the Level 3 Puzzle Book put out by my company. It was the largest project I’ve been on, and the content I’m most proud of producing. Not only did I get to write and review close to half the puzzles in the book, I managed to learn the basics of InDesign and help compile the book into its final form.
I’m shocked I didn’t write about it late last Fall when it released, but I had other non-work ideas on my mind. This popped back into my head as we were cleaning our apartment in preparation for visitors, and I came across one of my copies of the book.
I recommend taking a look at the sample PDFs on the page linked above. They puzzles are dastardly. The Level 3 is only representative of the math prerequisites, but some of the puzzles themselves would stump our employees.
Evidence-Based Education Part 0
As part of a new role at work, I’ve been researching aspects of funding for education in the United States. A recurring phrase is evidence-based interactions. I’m going to explore some of the facets of this idea, from its definitions and origins, to potential ramifications of its increasing usage in education.
This post is a placeholder for those future investigations. The educational landscape is of interest to many people, and learning about some of the guiding tenets can help explain a lot of the situations states are finding themselves in. I’m excited to be diving in.
Socks and Underwear
Admittedly, this post is ripping off a conversation that happened on a work Slack channel the other week. Here’s the general idea: If you count in a particular way, there are 12 options for how to put on your underwear, and 12 (ordered) options for putting on socks and shoes. Since there are the same number of options, we can create a bijection between the two scenarios. In other words, each choice of underwear arrangement will correspond to exactly one choice for socks and shoes.
The question is what bijection is “natural”, for whatever definition of natural you choose to have in this strange scenario. Let’s explore it a bit.
Continue reading “Socks and Underwear”Geometric Series: The Basics
I was just tutoring someone in their Calculus 2 course, and we did a problem on geometric series. When I was a student, I remember memorizing several facts about geometric series without really grokking the algebraic details of why the formulas you come up with are so nice. Since it is fresh in my mind, I figured I’d go through the standard approach.
Continue reading “Geometric Series: The Basics”The Gold Standard for Math Typesetting on the Internet
Through a wonderful little game called TeXnique, I became aware of the online typesetting system KaTeX. Unlike MathJax, which is immensely finicky, slow, and has limited support for proper LaTeX, the KaTeX system supports scaling of rendered images, automatically detects the text color of my site and adapts as necessary, and has a fuller implementation of LaTeX commands.
Continue reading “The Gold Standard for Math Typesetting on the Internet”A Short Tribute to John Conway
John Conway passed away a few days ago. He was a favorite among mathematical educators and communicators. He was involved in a large array of interesting projects and results during his career, many that can easily fascinate even the most disinterested people when it comes to mathematics.
Here are a few things he worked on, listed roughly in the order in which I came across them in my mathematical life.
- Look-and-Say Sequence
- Game of Life
- Doomsday Algorithm
- Sporadic Groups (and far more generally, the classification of the finite simple groups)
- Surreal Numbers
Any of these are a treat to look into. Conway was a powerhouse of interesting and engaging ideas. Take a look at the Numberphile videos involving him for a slice of the world from his perspective.
Sniped by Math History
As with most nerds, I have a predisposition to being nerd sniped. Sometimes it’s a puzzle, but more often it’s simply an idea or the opportunity for a new project. After a conversation with a few coworkers, I’ve latched onto the idea of developing a summer course focused on the history of mathematics.
Continue reading “Sniped by Math History”