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.

Interactive
quizzes

26

Concepts and
exercises

240+
  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.

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      Seeing Patterns

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

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      Describing Patterns

      Understand and create recursive and explicit descriptions of patterns.

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      Find the Formula

      Find and interpret the algebraic descriptions of patterns.

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      Using Variables

      Use variables to describe interrelated unknowns.

  3. 3

    Mathematical Logic

    Logic shows you how to win!

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      Logic Warmups

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

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      Humans and Werewolves

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

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      Implication

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

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      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.

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      Exploring Ratios

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

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      Rates

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

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      Percent Applications

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

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      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.

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      When It Gets Tough

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

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      Matchsticks and Coins

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

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      Logical Arithmetic

      These advanced cryptograms are more difficult than any you've seen in this course so far!

    4. Included with
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      The Arithmetic-Algebra Connection

      Extend basic arithmetic into surprising, beautiful, and useful patterns.