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# Mathematical Fundamentals

## The essential tools for mastering algebra, logic, and number theory!

In this course, we'll introduce the foundational ideas of algebra, number theory, and logic that come up in nearly every topic across STEM.

This course is ideal for anyone who's either starting or re-starting their math education. You'll learn many essential problem solving techniques and you'll need to think creatively and strategically to solve each challenge. Each exploration is designed to push your mathematical skills to the next level.

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1. 1

### Introduction

Explore the foundations of algebra and logic without any rote memorization.

1. #### Generalize

Algebra was never meant to be memorized. Learn a new way to see.

2. #### Rewrite, Rethink, Redraw

Explore fractal patterns and compound interest in the mathematics of fractions.

3. #### Thinking Forwards and Backwards

To solve new problems, you need to be able to think in several directions.

2. 2

### Logical Reasoning

Logic shows you how to win!

1. Included with

#### Reasoning from Results to Cause

You can't trust everything you hear, but you'll always have logic.

2. Included with

#### Werewolves of London

Werewolves are predictably treacherous creatures. But they make for great puzzles.

3. Included with

#### Eliminating the Impossible

Once you eliminate the impossible, whatever remains must be the truth.

4. Included with

#### A Treasure Hunt

The real treasures are the truths we find along the way.

3. 3

### Numerical Reasoning

Use the basics of arithmetic and algebra to uncover properties of numbers.

1. Included with

#### Strategic Arithmetic

Learn to sum 100 numbers at a glance with this one simple trick.

2. Included with

#### Dissecting Numbers

See the composition of numbers in a brand new light.

3. Included with

#### Divisible by 3

Dividing numbers in clever ways is the first step towards number theory.

4. Included with

#### Building Numbers to Spec

Bring your divisibility rules, because not just any numbers will do.

4. 4

### Contextual Reasoning

Mathematical reasoning about the real world.

1. Included with

#### Compare the Pair

Find the best deals in town by breaking down these problems.

2. Included with

#### Understanding Fractions

A high-stakes Segway race puts you on the fast lane to comparing rates and ratios.

3. Included with

#### Probability

The Lumps has hit Flatland. Can you use probabilities to separate fact from fiction?

4. Included with

#### Compound Interest

Questionable business practices and multiplying fractions greater than one are quick ways to get exponential growth.

5. 5

### Algebraic Reasoning

Build and practice problem solving strategies with these algebra puzzles.

1. Included with

#### Magical Variables

Writing down equations is often the easiest way to organize information and solve problems.

2. Included with

#### Reverse Engineering Arithmetic

Find the patterns and you'll be able to solve these problems.

3. Included with

#### Sums and Symmetry

Algebra is all about maintaining symmetry and balance.

4. Included with

#### How Much Altogether?

Mix, match, and compare unknown values – then put them to work.

6. 6

### Geometric Reasoning

A new way of learning the algebra and identities that you thought you knew.

1. Included with

#### Pythagoras' Theorem

A visual proof of the most famous theorem in all of mathematics.

2. Included with

#### The Distributive Property

If you replace algebra with geometry, you'll never need to factor again.

3. Included with