Adv Math Topics 1
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COURSE OVERVIEW. This Course is divided into Part I and II.
Part I. History of Numbers (0.5 credit)
Just like languages, numbers have a history. But if anything is taught in our schools about this rich history, it typically begins with White western philosophers from ancient Greece, and ignores roots that plunge deeper into time, and spread across a broad range of cultures. The History of Numbers goes all the way back to prehistoric times, explores these ancient multicultural roots, and brings us up to our modern Hindu-Arabic number system. Along the way we learn about the uses and properties of numbers. It starts with the original use of numerals: to count. But then moves on to the development of positional number systems, different bases besides our own base 10, the concepts of zero and infinity, irrational numbers such as pi and the golden ratio, and the counterintuitive negative and imaginary numbers.
History of Numbers is organized around these four modules:
1. Historical Counting Systems
2. Positional Systems and Numbers in Different Bases
3. Zero and Irrational Numbers
4. Negative Numbers and Imaginary Numbers
Part II. A. Critical Thinking and B. Weird Geometry (0.5 credit)
Still under construction - coming soon!
A. Critical Thinking and Problem Solving
Both refer to how we should stick to facts to solve problems. But “word problems" rarely resemble real life, and you are often told which procedure to use, and given the information you need. Yet in real life, we must figure out a procedure, and what information we will need. This requires critical thinking because the information available may be unclear, incomplete, or even intentionally misleading. Many problems require proportional reasoning, and the ability to understand the really large (such as the universe, Jeff Bezos' net worth) and really small (such as viruses, atoms).
Critical Thinking and Problem Solving is organized around these two modules:
5. Proportional Reasoning
6. Understanding Really Big and Small Things
B. Weird Geometry (Under Construction)
Some topics in geometry ARE weird, and fun to learn about! But these are rarely covered in a standard geometry course, or perhaps only touched upon. Here I tried to choose what I find to be among the most intriguing of topics: the concept of dimensions. In this section we will explore both higher dimensions, and the dimensions in between 0, 1, 2, 3 .... Along the way we learn more about measurement in different dimensions, and about the logarithm as a way to calculate the dimension of a fractal.
Weird Geometry is organized around these two modules:
7. Dimensions - 0D (point), 1D (line segment), 2D (square), 3D (cube), 4D (tesseract), and beyond ...
8. Fractals and Fractional Dimensions