Math Fundamentals (2020)

Dive into a comprehensive exploration of mathematical foundations in this 12-15 hour course. Master algebra and logic through pattern recognition and visual learning, eschewing rote memorization. Tackle Sudoku-like puzzles, develop numerical reasoning skills, and learn strategic problem-solving techniques. Engage with challenging concepts like Calcdoku, logical reasoning, and werewolf-themed logic puzzles. Discover new approaches to understanding algebra visually, explore divisibility tricks, and derive the quadratic formula using geometric methods. Practice algebraic reasoning, work with rates and ratios, and solve advanced cryptograms. Conclude by connecting these mathematical concepts to broader applications in computer science and physical sciences, setting the stage for further mathematical mastery.

• Introduction to Math Fundamentals: Explore the foundations of algebra and logic without any rote memorization.
• Reverse Engineering Arithmetic: Find the patterns and you'll be able to solve these puzzles.
• Understanding Math Visually: Algebra was never meant to be memorized. Learn a new way to see.
• Cascading Deductions: Solving these Sudoku-like puzzles will take both algebra and strategy.
• Numerical Reasoning: Find the pattern, then make predictions.
• Take Care Where You Start: Unpack a strategy that you'll use in every problem you encounter.
• Hypothesize Test Adapt: Keep in mind that a hypothesis is NOT just a guess.
• Rewrite Redraw Rethink: These problems aren't about elephants, they're about fractions.
• Wishful Thinking: Meet the Calcdoku. Sudoku pales in comparison.
• Reusable Insights: Building problem-solving skills takes practice – stay on the lookout for useful patterns.
• Logical Reasoning: Logic shows you how to win!
• Systematic Logical Thinking: You can't trust everything you hear, but you'll always have logic.
• Werewolves of London: Werewolves are predictably treacherous creatures. But they make for great puzzles.
• Elimination Cascades: Once you eliminate the impossible, whatever remains must be the truth.
• Mad Hatter Puzzles: You'll need to keep track of what other people might think you are thinking.
• Repairing Broken Puzzles: These puzzles can't be solved – until you fix them.
• Visually Understanding Algebra: A new way of learning the algebra and identities that you thought you knew.
• Divisibility: You won't believe this visual trick that makes number theory look obvious.
• The Distributive Property: If you replace algebra with geometry, you'll never need to factor again.
• Difference of Squares: This isn't how you learned this identity at school.
• Square Roots: Now there is more than one right answer.
• The Quadratic Formula: You've used it, you've memorized it, now derive it with squares.
• Algebraic Reasoning: Build and practice problem solving strategies with these algebra puzzles.
• Choose Your Numbers Carefully: Algebra is all about maintaining symmetry and balance.
• Algebraic Information: Learn how to track down all the information you need from a problem.
• Rates and Ratios: You'll need to reframe these problems to put the numbers in order.
• Advanced Cryptograms: These puzzles are tough, but you have all the skills you need.
• Number Courtyards: Some of these problems look impossible. They aren't.
• Advanced Design and Optimization: Evaluate and design calcdoku, operator search, and grid fill problems.
• What Comes Next?: Connect the concepts you've learned in this course to new avenues of math and science.
• Logic, Algebra, and Number Theory: You've met the big players, but there's a lot more to come.
• Geometry and Probability: Explore the next steps in your mastery of mathematics.
• Computer Science and Physical Science: Explore the world and apply what you've learned.