It turns out there needed to be more groundwork than I had anticipated before hitting the Chinese Remainder Theorem. This lesson introduces modular arithmetic, and the Chinese Remainder Theorem will be covered later. I will also be taking a detour to cover all of the math inherent to RSA encryption algorithms in the coming months.
Tag Archives: math
Math From Scratch 16: Divisibility Rules (for base 10)
The results for testing numbers for divisibility in base 10 are laid out here. It appears we’ll be reaching the rational numbers at some point in the spring of 2012.
Math From Scratch 15: The Fundamental Theorem of Arithmetic
The fifteenth lesson of the Math From Scratch series, dealing with the Fundamental Theorem of Arithmetic, is available here.
Math From Scratch 14: Defining Division With Remainder
The next chapter in the Math From Scratch series is available here. We can now define a division algorithm involving remainder.
Math From Scratch 13: Metric Spaces Other Than Canada
We can finally define distances, which allows us to establish the number line. Those tools are presented in lesson 13: Metric Spaces Other Than Canada.
Math From Scratch 12: Other Bases
With the bases representation theorem established, we can examine the bases that are common to computer science, and how they have plagued some of the more adept Nintendo players of by generation. Lesson 12: Other Bases.
Math From Scratch 11: Introducing Base 10
In our eleventh lesson, we can formally justify the number representation we inherited from Arab mathematicians so many centuries ago. I hope you enjoy All Your Bases Are Belong To Us.
Teaching Tidbit: Multiplying Left to Right
Some regions have seen a trend towards multiplying numbers from left to right instead of right to left in recent years. An explanation of how this “works” and my own personal critique of the methods can be found here.
Math From Scratch 0010: Introduction to Rings
Our tenth lesson introduces ring theory, which allows us to define several familiar concepts: One Algebra To Rule Them All. Remember, past lessons can all be found by clicking on the “math from scratch” tag below.
Math From Scratch 0009: Cosets and Lagrange’s Theorem
Part nine of a number that I hope will be finite: Cosets and Cardinality. Remember, past lessons can all be found by clicking on the “math from scratch” tag below. Also, try as I might, I couldn’t find a natural ZZ Top reference to work into this lesson dealing with Lagrange’s Theorem. Suggestions are welcome in the space below.