The Power of Mathematical Visualization

Overview

Discover the advantages of seeing math from an entirely new angle, guided by a brilliant and engaging teacher. “The Power of Mathematical Visualization” teaches you to understand complex mathematical concepts through visual methods, making learning enjoyable.

Course Instructor

Professor Peter Tanton, an expert in mathematical visualization, skillfully blends inspiration with rigorous mathematical thinking to enhance your appreciation of mathematics.

Video Lessons

• The Power of a Mathematical Picture
  • Duration: 34 min
  • Description: Explore the origins of mathematical visualization and its significance in understanding complex concepts.

2. Visualizing Negative Numbers
   • Duration: 29 min
   • Description: Learn to visualize negative numbers and parentheses to simplify algebraic expressions.

• Visualizing Ratio Word Problems
  • Duration: 29 min
  • Description: Tackle common ratio and proportion problems with visual aids like blocks and poker chips.

4. Visualizing Extraordinary Ways to Multiply
   • Duration: 30 min
   • Description: Discover innovative graphical methods to multiply numbers, breaking the traditional long-multiplication algorithm.

• Visualizing Area Formulas
  • Duration: 30 min
  • Description: Master area calculations with visual proofs that eliminate the need for memorization.

• The Power of Place Value
  • Duration: 33 min
  • Description: Understand how place value enables complex calculations through a visual approach.

7. Pushing Long Division to New Heights
   • Duration: 29 min
   • Description: Simplify long division through visualization, illuminating the rationale behind the algorithm.

• Pushing Long Division to Infinity
  • Duration: 30 min
  • Description: Solve polynomial division problems and explore infinite sums visually.

9. Visualizing Decimals
   • Duration: 32 min
   • Description: Connect decimals to fractions and learn how to convert between them using visual strategies.

• Pushing the Picture of Fractions
  • Duration: 30 min
  • Description: Investigate irrational numbers and the proof of the square root of two’s non-fractional nature.

11. Visualizing Mathematical Infinities
    • Duration: 30 min
    • Description: Explore Georg Cantor’s insights on the size relationships between infinite sets.

• Surprise! The Fractions Take Up No Space
  • Duration: 29 min
  • Description: Understand how fractions fit onto the number line, despite being infinite.

13. Visualizing Probability
    • Duration: 31 min
    • Description: Use visual models to make sense of probability problems involving chance events.

14. Visualizing Combinatorics: Art of Counting
    • Duration: 34 min
    • Description: Learn counting techniques through captivating combinatorial problems.

15. Visualizing Pascal’s Triangle
    • Duration: 32 min
    • Description: Uncover the beauty of Pascal’s triangle as it relates to algebra and probability.

16. Visualizing Random Movement, Orderly Effect
    • Duration: 31 min
    • Description: Investigate random walks and their applications to real-world phenomena.

• Visualizing Orderly Movement, Random Effect
  • Duration: 31 min
  • Description: Analyze how simple rules can lead to complex and chaotic outcomes.

18. Visualizing the Fibonacci Numbers
    • Duration: 34 min
    • Description: Study the Fibonacci sequence and its significance in mathematics and nature.

19. The Visuals of Graphs
    • Duration: 30 min
    • Description: Explore how graphing enhances the understanding of mathematical concepts.

• Symmetry: Revitalizing Quadratics Graphing
  • Duration: 31 min
  • Description: Use symmetry to simplify the graphing of quadratic functions.

21. Symmetry: Revitalizing Quadratics Algebra
    • Duration: 28 min
    • Description: Explore the importance of symmetry in solving quadratic equations.

22. Visualizing Balance Points in Statistics
    • Duration: 30 min
    • Description: Analyze data averages visually through graphical representations.

23. Visualizing Fixed Points
    • Duration: 33 min
    • Description: Investigate fixed-point theorems through visual understanding.

• Bringing Visual Mathematics Together
  • Duration: 32 min
  • Description: Conclude the course by integrating the concepts learned through visual mathematics.