This is a first post in a series in which I’d like to discuss various different types of numbers that mathematicians study. This may sound strange – and that is fair. After all, aren’t all numbers just… numbers? Why would some numbers be so different from other numbers? What sense does that make? I’m honestlyContinue reading “Why Ask Questions About Numbers? (Types of Numbers #1)”

## The Importance of Derivatives and What Comes Next (Explaining Calculus #13)

This post doesn’t exactly introduce anything new about calculus. But, we must remember, it is important to reflect whenever we learn. Even in mathematics. In this post, I plan on achieving two main goals. One, we will reflect on what we’ve done so far by introducing the new ideas of limits and derivatives to ourContinue reading “The Importance of Derivatives and What Comes Next (Explaining Calculus #13)”

## Higher Order Derivatives and Their Applications (Explaining Calculus #12)

Up to this point, I’ve focused my efforts on derivatives of functions and what those derivatives mean. In particular, derivatives tell us about how things change over time – with derivatives, we can measure quantities like speed and growth. But derivatives are also functions, which means they have their own derivatives. Can we learn anythingContinue reading “Higher Order Derivatives and Their Applications (Explaining Calculus #12)”

## Database: Critical Thinking Toolkit

Up to this point, my database posts have been about compiling data from external sources. This database post is more organizational in nature. My goal here is to systematize the posts I’ve written in my series “Critical Thinking Toolkit”. The purpose of the series was to provide summary approaches to various areas of critical thinkingContinue reading “Database: Critical Thinking Toolkit”

## Summary of “Advice to Christian Philosophers” by Alvin Plantinga

Academia can be a wild place. Despite what people might think, there are often entire paradigm shifts between generations in academic circles. This has happened in philosophy – just two generations or so ago, things were wildly different, and things now are different from one generation ago. I now want to summarize famed Christian philosopherContinue reading “Summary of “Advice to Christian Philosophers” by Alvin Plantinga”

## Exponential Models (Explaining Calculus #11)

We’ve used calculus for a couple different applications at this point. I’d like to tack on another application to our list, perhaps the most important one – at least from the perspective of a society very reliant on technology, engineering, and science. The application I have in mind goes under the very broad title ofContinue reading “Exponential Models (Explaining Calculus #11)”

## Critical Thinking Toolkit: Necessity and Contingency

In moments of deeper thought, have you ever noticed that there seem to be certain features of the world that are quite arbitrary or random, while other things seem like there isn’t really any other way things could be? Have you ever wondered at why things are the way they are, instead of some otherContinue reading “Critical Thinking Toolkit: Necessity and Contingency”

## Optimizing Real-World Stuff (Explaining Calculus #10)

In the previous post in this series, I explained how you can use derivatives to locate maximizing and minimizing values for functions. Now, I will put that knowledge to use in concrete examples to show exactly how this works. Example 1: Building a Fence Imagine the following situation. You are a farmer, and you wantContinue reading “Optimizing Real-World Stuff (Explaining Calculus #10)”

## Critical Thinking Toolkit: The Correlation-Causation Fallacy

Here, I’d like to discuss two interconnected tendencies we human beings have. We like looking for patterns, and we like explaining things. These are both incredibly important features of the way we think as humans. But they are not identical. It is easy to get them confused, and we often do get them confused. ThisContinue reading “Critical Thinking Toolkit: The Correlation-Causation Fallacy”

## What Is Philosophy of Religion?

Have you ever watched a public debate or dialogue about religion? I certainly have – many in fact. I am quite interested in such conversations. Although I don’t usually like the heated ones – I like the philosophically informed ones. If you haven’t heard any of these types of conversations before, that might sound strange.Continue reading “What Is Philosophy of Religion?”