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?”

Locating Peaks and Valleys with Derivatives (Explaining Calculus #9)

We have gone through a couple of discussions now on how to actually calculate the value of a derivative. This is great, after all what good is a shiny new tool if you don’t know how to operate it? But we are done with that now. Now that we’ve gone through a tutorial with derivatives,Continue reading “Locating Peaks and Valleys with Derivatives (Explaining Calculus #9)”

Critical Thinking Toolkit: Inference to the Best Explanation

I’ve talked about deductive reasoning and inductive reasoning before. Both of these are important mechanisms we use for arriving at conclusions. The first makes use of the rules of logic – which we can essentially view as limiting ourselves to the definitions of words like true and false and not allowing ourselves any other resources.Continue reading “Critical Thinking Toolkit: Inference to the Best Explanation”