Antiderivatives (Explaining Calculus #15)

In the last post in the series on calculus, we talked about Riemann sums – which is just a fancy way of speaking of estimating the area of a complicated region by using lots of rectangles to obtain an approximately correct answer. The post that I must follow this up with, which for now seemsContinue reading “Antiderivatives (Explaining Calculus #15)”

The Natural Numbers and Zero (Types of Numbers #2)

I now begin the escapade into different sorts of numbers. This may seem rather a strange adventure to anyone who hasn’t listened to too many professional mathematicians talks, or anyone who is too far removed from high school education. I would guess that most people who have read this have some particular picture of numberContinue reading “The Natural Numbers and Zero (Types of Numbers #2)”

The Kalam Cosmological Argument: A Brief Overview

In a previous post, I have discussed the intuition behind cosmological arguments and gave several examples. One of these examples was the Kalam cosmological argument. By way of overview, a cosmological argument is, broadly speaking, one that reasons from facts about the universe we observe and metaphysical principles to argue that God, or at leastContinue reading “The Kalam Cosmological Argument: A Brief Overview”

Riemann Sums and Areas (Explaining Calculus #14)

At this point in calculus, we are taking what appears to be a sharp turn in a direction completely away from what we’ve been doing so far. We now turn to talking about areas. The Problem Geometry is one of the most important branches of all mathematics, both theoretical mathematics and applied mathematics. When middleContinue reading “Riemann Sums and Areas (Explaining Calculus #14)”

What are Cosmological Arguments?

Cosmological arguments are probably the most discussed and most intriguing area of natural theology. While there are a great variety of areas of philosophy that point towards God’s existence – we find that, for whatever reason, the realm of cosmological arguments seems to bring the most interest from both defenders and opponents of the arguments.Continue reading “What are Cosmological Arguments?”

Critical Thinking Toolkit: Straw Man Fallacy

Imagine the following scenario. A man walks up to an 80 year old with walking on his cane in the street, knocks him out with a single punch, then claims to be the best boxer who has ever lived. Sound silly? It should. This is an embodiment of what is known as the straw manContinue reading “Critical Thinking Toolkit: Straw Man Fallacy”

Why Ask Questions About Numbers? (Types of Numbers #1)

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”