Topics from “Pre-Calculus” (Explaining Calculus #1)

Before we can go into a discussion of calculus itself, it is important to set up some of the underlying concepts that calculus uses. You might view this as something analogous to learning the letters of the alphabet before you can start learning to read words and sentences. Without letters, you aren’t going to beContinue reading “Topics from “Pre-Calculus” (Explaining Calculus #1)”

Database: What Do History’s Great Mathematicians Think About God?

There is very often debate about whether science and religion are in conflict. I know from my own studies and will continue to affirm that these are not at all in conflict. There are quite a few ways to go about this, and I plan to take on every angle that I can. Since IContinue reading “Database: What Do History’s Great Mathematicians Think About God?”

Series: Databases of Resources

I am publishing this post as a preface to a sequence of posts that I will continue to update as long as I run this blog, and hope to continue updating for as long as I live – compilations of references on what I have studied during my life. I’ve decided to call these databasesContinue reading “Series: Databases of Resources”

Explaining Calculus (Intro)

In our day and age, this word strikes fear into many hearts. Much like ‘rocket science,’ it is used in our culture to represent anything that is extremely difficult or even something incomprehensible. I am talking about calculus. Those who have taken a course in this topic will have a good idea of what kindsContinue reading “Explaining Calculus (Intro)”

Critical Thinking Toolkit: A Priori Assumptions

This is one of the most important – perhaps the most important – of the many tools in the “critical thinking toolkit.” I don’t say this because I like this topic most among the topics I want to write about – although I do enjoy this topic a lot. The main reason I think thisContinue reading “Critical Thinking Toolkit: A Priori Assumptions”

Critical Thinking Toolkit: Ockham’s Razor

When we are in debates, very often there is more than one way to explain something. When we are presented with more than one way of explaining some aspect of reality – be it scientific, historical, religious, or anything else – these situations arise. When they do, we want to be able to differentiate betweenContinue reading “Critical Thinking Toolkit: Ockham’s Razor”

Critical Thinking Toolkit: Possible v.s Plausible

In our common experience, there are a plethora of alternative explanations of the realities we see around us. Some of these are highly likely, some fairly likely, some moderately likely, some that are reasonable but not strictly ‘likely’, and some that are extremely unlikely. There are a variety of situations that we might find ourselvesContinue reading “Critical Thinking Toolkit: Possible v.s Plausible”

The Fallacy of Equivocation

This is one of many brief articles I am writing about how to avoid fallacious patterns of thinking. Here, we briefly discuss the fallacy of equivocation. Before I try to define it, it will be helpful to see an example of the fallacy in action. (I take this example out of the Wikipedia page forContinue reading “The Fallacy of Equivocation”

Finding Patterns in the Fibonacci Sequence

This is the final post (at least for now) in a series on the Fibonacci numbers. We’ve gone through a proof of how to find an exact formula for all Fibonacci numbers, and how to find exact formulas for sequences of numbers that have a similar definition to the Fibonacci numbers. But, the fact thatContinue reading “Finding Patterns in the Fibonacci Sequence”

Finding the Fibonacci Numbers: A Similar Formula

In this series of posts about the Fibonacci sequence , a very famous sequence of numbers within mathematics, we have just concluded showing how you can take the recursive formula (which uses previous values of to compute the next values) and turn that formula into an exact formula that can skip right over the previousContinue reading “Finding the Fibonacci Numbers: A Similar Formula”