Now that the field axioms have been established, we can formally define the rational numbers. Most elementary school students refer to them as “fractions.” You can read this lesson here.

# math

## Math From Scratch 24: Defining the Rational Numbers

October 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

## Math From Scratch 23: The Field Axioms

September 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

The second volume of *Math From Scratch* is here, with the intent to reach the definition of the real numbers. We will cover some Euclidean geometry along the way. This lesson covers the axioms of an algebraic field.

## Math From Scratch 22: RSA Encryption

June 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

One of the most common applications of advanced mathematics is in encryption. The RSA encryption algorithm is the most common version, and is the basis of the security that underlies the https protocols used to connect users to online retailers, banks, and so forth. This also concludes the first volume of the *Math From Scratch*, which can be obtained in a single document through Graphicly. Join us when we return in September with the goal of defining rational, irrational and real numbers.

## Math From Scratch 21: Totients

May 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

The Euler Totient function is the focus of this month’s lesson, and is the final piece of the puzzle required before we reach the RSA encryption algorithm in June.

## Math From Scratch 20: The Chinese Remainder Theorem

April 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

We are finally able to cover the Chinese Remainder Theorem, one of the oldest recorded mathematical theorems and one that is of great importance to many computer science applications.

## Math From Scratch 19: Solving Linear Diophantine Equations

March 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

We are now equipped to define and solve linear diophantine equations. We are on track to cover RSA encryption algorithms in June.

## Math From Scratch 18: The Euclidean Algorithm

February 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

Our teaching tidbits and Math From Scratch are overlapping for the first time with the Euclidean algorithm. If all goes as planned, RSA encryption algorithms will be derived and explained in June.

## Math From Scratch 17: Modular Arithmetic

January 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

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.

## Math From Scratch 16: Divisibility Rules (for base 10)

December 1, 2011 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

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 25: Infinite Processes

November 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

We have reached the point where we can properly introduce infinite processes, and show that the set of rational numbers cannot include all of the numbers we’ll need. You can read this lesson here.