In the previous post in this series, we set up a definition of the derivative of a function, which is a new function that tells us how the original function changes over time. Now that we have set up this idea of derivatives, we are going to enter into a period of showing how toContinue reading “Computing Derivatives: Part 1 (Explaining Calculus #6)”

# Category Archives: All Posts

## Derivatives, Tangent Lines, and Change (Explaining Calculus #5)

We’ve spent a few posts now developing the ideas of limits and continuity, two of the foundational ideas of calculus. We are now going to introduce the third foundational idea, the derivative. The derivative can be thought of as a way to capture the way that things change over time into one single formula. InContinue reading “Derivatives, Tangent Lines, and Change (Explaining Calculus #5)”

## Critical Thinking Toolkit: Clarifying Definitions

This is possibly the most important post I’ve written in my “Critical Thinking Toolkit” series so far. Ensuring we are clear on our definitions is so, so important. Every conversation we can ever have relies on definitions of certain important words, and so this tool always matters. Furthermore, when I look around in the worldContinue reading “Critical Thinking Toolkit: Clarifying Definitions”

## COVID Testing and Bayes’ Theorem

Yesterday, an interesting conundrum came to me. Sometimes, people take two COVID tests on the same day. Imagine that one came back negative and the other came back positive… which can and does happen. Here is the tricky question… which one do you trust? The positive or the negative? You might think there is noContinue reading “COVID Testing and Bayes’ Theorem”

## Database: What Do History’s Top Scientists Think About God?

This is now the third entry in a collection of inter-related database posts. The object of these posts is to collect data about the religious convictions of leading figures in the history of various intellectual disciplines. As of this moment, I have undergone this project for mathematicians and philosophers. This list is aimed at scientists.Continue reading “Database: What Do History’s Top Scientists Think About God?”

## Critical Thinking Toolkit: The Fallacy of Arguing from Ignorance

When debating important topics, whether with your friends, online with strangers, or in a public debate with spectators, there is always a high emphasis placed on proving your case. People ask why you believe what you do, ask you to show your evidence, ask you to give them your arguments. There is nothing wrong withContinue reading “Critical Thinking Toolkit: The Fallacy of Arguing from Ignorance”

## Understanding Continuity (Explaining Calculus #4)

In both life and academic science, we often come across things that change incrementally over time. If we are buying a fast car, we want to know how quickly that car accelerates from 0 to 60 miles per hour – and the answer is most certainly not zero seconds – we first have to hitContinue reading “Understanding Continuity (Explaining Calculus #4)”

## What is Living with ADHD Like?

I write about a wide variety of interests and issues on my blog. Most recently, I’ve been writing about calculus and general facts about academic argumentation and logic that are helpful for both day-to-day thinking and big picture questions. I’m also in the beginning of a long reading project that will eventually lead to aContinue reading “What is Living with ADHD Like?”

## Critical Thinking Toolkit: False Dilemma

Choices are important. Every day, we make lots of decisions about what to do and what to say. When decisions are especially important is when two possible paths we might take are totally opposite another or grind against one another. There is a certain tension that arises in decisions that carry a great deal ofContinue reading “Critical Thinking Toolkit: False Dilemma”

## Working With Limits (Explaining Calculus #3)

In a previous post, I spent time talking about what limits are on a conceptual level, and some details about how they work on a practical level. Now, I want to run through a few examples to show how computing limits actually works, and in particular a very special kind of situation – which youContinue reading “Working With Limits (Explaining Calculus #3)”