## Overview

Here is a story that isn’t true:

When I was a young child I invented a machine (not true) that was nothing more than a series of boxes that could hold dots. And these dots would, upon certain actions, explode. And with this machine, in this non-true story, I realized I could explain true things! In one fell swoop I explained all the mathematics of arithmetic I learnt in grade school (true), all of the polynomial algebra I was to learn in high-school (true), elements of calculus and number theory I was to learn in university (true), and begin to explore unanswered research questions intriguing mathematicians to this day (also true)!

Let me share this story with you. See how simple and elegant ideas connect to elegant and profound ideas in mathematics as a whole. See how these ideas will COMPLETELY REVOLUTIONIZE your thinking of school arithmetic and algebra and beyond!

This course will knock your socks off!

## Lessons

 1.0 School Arithmetic and Algebra made Ridiculously Easy! 1.1 Base Machines 1.2 What these Machines are Doing 1.3 A Peek at a Weird Machine 1.4 Arithmetic in a $$1 \leftarrow 10$$ Machine 1.5 Subtraction 1.6 Division 1.7 Arithmetic in an $$1 \leftarrow x$$ Machine 1.8 A Problem? 1.9 An Infinite Process: The Geometric Series Formula
 2.0 Going to Decimals and $$x$$-mals 2.1 Introducing Decimals 2.2 Division and Repeating Decimals 2.3 $$x$$-mals 2.4 Some Irrational Thoughts 2.5 ADDENDUM: Some Fun Extra $$1 \leftarrow 10$$ Questions
 3.0 Wild and Weird Explorations 3.1 On Base One-and-a-Half 3.2 Base Two? Base Three? 3.3 Changing the Order of Explosions 3.4 Negative Bases? Irrational Bases? Going Wild!
 4.0 Connections to the COMMON CORE STATE STANDARDS and MATH CIRCLE WORK 4.1 Common Core State Standards 4.2 MATH CIRCLES for Students and for Teachers
 5.0 Where did these ideas come from? 5.1 To answer …

## Books

Take your understanding to the next level with easy to understand books by James Tanton.

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## Guides & Solutions

Dive deeper into key topics through detailed, easy to follow guides and solution sets.

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