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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.

Interactive
quizzes

27

Concepts and
exercises

295+
  1. 1

    Introduction to Math Fundamentals

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

    1. Reverse Engineering Arithmetic

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

    2. Understanding Math Visually

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

    3. Cascading Deductions

      Solving these Sudoku-like puzzles will take both algebra and strategy.

  2. 2

    Numerical Reasoning

    Find the pattern, then make predictions.

    1. Included with
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      Take Care Where You Start

      Unpack a strategy that you'll use in every problem you encounter.

    2. Included with
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      Hypothesize Test Adapt

      Keep in mind that a hypothesis is NOT just a guess.

    3. Included with
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      Rewrite Redraw Rethink

      These problems aren't about elephants, they're about fractions.

    4. Included with
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      Wishful Thinking

      Meet the Calcdoku. Sudoku pales in comparison.

  3. 3

    Logical Reasoning

    Logic shows you how to win!

    1. Included with
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      Systematic Logical Thinking

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

    2. Included with
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      Werewolves of London

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

    3. Included with
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      Elimination Cascades

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

    4. Included with
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      Mad Hatter Puzzles

      You'll need to keep track of what other people might think you are thinking.

  4. 4

    Visually Understanding Algebra

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

    1. Included with
      Brilliant Premium

      Divisibility

      You won't believe this visual trick that makes number theory look obvious.

    2. Included with
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      The Distributive Property

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

    3. Included with
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      Difference of Squares

      This isn't how you learned this identity at school.

    4. Included with
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      Square Roots

      Now there is more than one right answer.

  5. 5

    Algebraic Reasoning

    Build and practice problem solving strategies with these algebra puzzles.

    1. Included with
      Brilliant Premium

      Choose Your Numbers Carefully

      Algebra is all about maintaining symmetry and balance.

    2. Included with
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      Algebraic Information

      Learn how to track down all the information you need from a problem.

    3. Included with
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      Rates and Ratios

      You'll need to reframe these problems to put the numbers in order.

    4. Included with
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      Advanced Cryptograms

      These puzzles are tough, but you have all the skills you need.

  6. 6

    What Comes Next?

    Connect the concepts you've learned in this course to new avenues of math and science.

    1. Included with
      Brilliant Premium

      Logic, Algebra, and Number Theory

      You've met the big players, but there's a lot more to come.

    2. Included with
      Brilliant Premium

      Geometry and Probability

      Explore the next steps in your mastery of mathematics.

    3. Included with
      Brilliant Premium

      Computer Science and Physical Science

      Explore the world and apply what you've learned.

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