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. Cryptograms

Which numbers fill the holes in these algebra puzzles?

2. Is it Possible?

Solve Sudoku-like puzzles that require algebra as well as logic.

3. Challenge Set

Use three warm-ups to limber up, and then give your brain a workout with two tougher challenges.

2. 2

Patterns & Variables

Find the pattern, then make predictions.

1. Included with

Seeing Patterns

Is there order, repetition, or regularity in these visual patterns?

2. Included with

Describing Patterns

Understand and create recursive and explicit descriptions of patterns.

3. Included with

Find the Formula

Find and interpret the algebraic descriptions of patterns.

4. Included with

Using Variables

Use variables to describe interrelated unknowns.

3. 3

Mathematical Logic

Logic shows you how to win!

1. Included with

Logic Warmups

Get your analytical and critical thinking skills warmed-up and ready for some strenuous exercise!

2. Included with

Humans and Werewolves

Apply logic to determine the secret identities of the entities in each challenge.

3. Included with

Implication

Understand the behavior of "If...then..." statements within the framework of formal logic.

4. Included with

Find the Order

Are the small clues in each of these challenges enough information to figure out the whole situation?

4. 4

Ratios & Percentages

The mathematics of comparisons: ratios, percentages, and fractions.

1. Included with

Exploring Ratios

Learn how to use rewriting fractions as a problem-solving shortcut.

2. Included with

Rates

It's easy to answer these rate and speed questions incorrectly if you're not careful!

3. Included with

Percent Applications

Use these problems to expose and correct a few common misconceptions about percentages.

4. Included with

Percent Puzzles

Put your intuition for ratios and percentages to the test in some tricky scenarios!

5. 5

When It Gets Tough

Demonstrate what you've learned with these difficult problems.

1. Included with

When It Gets Tough

Break down and tackle difficult problems that require the creative, coordinated use of multiple techniques.

2. Included with

Matchsticks and Coins

Get ready to first solve these manipulation challenges, and then to prove that your solutions are ideal.

3. Included with