Overview

Delve into the mechanics of some of math’s greatest and most awe-inspiring achievements in this enlightening course. “Great Thinkers, Great Theorems” offers a journey through the powerful ideas that have shaped mathematics, showcasing landmark achievements akin to celebrated works of art.

Course Instructor

The course is presented by an award-winning professor, who guides you through the history and beauty of mathematics, exploring key theorems and the great minds behind them.

Video Lessons

1. Theorems as Masterpieces
   • Duration: 32 min
   • Description: Learn about great theorems that are masterpieces of mathematical thought and discover two methods of theorem proving.

2. Mathematics before Euclid
   • Duration: 31 min
   • Description: Investigate the mathematical traditions of ancient civilizations prior to Euclid.

3. The Greatest Mathematics Book of All
   • Duration: 29 min
   • Description: Explore Euclid’s “Elements,” the most influential mathematical text in history.

4. Euclid’s Elements-Triangles and Polygons
   • Duration: 32 min
   • Description: Delve into Euclid’s proof of the Pythagorean theorem and techniques for constructing regular polygons.

• Number Theory in Euclid
  • Duration: 29 min
  • Description: Examine Euclid’s significant contributions to number theory, including his proof of the infinitude of primes.

6. The Life and Works of Archimedes
   • Duration: 29 min
   • Description: Discover the fascinating life of Archimedes and his accomplishments in mathematics.

7. Archimedes’ Determination of Circular Area
   • Duration: 32 min
   • Description: Follow Archimedes’ solution to determining the area of a circle using indirect proofs.

8. Heron’s Formula for Triangular Area
   • Duration: 31 min
   • Description: Learn about Heron’s method for calculating the area of any triangle using just side lengths.

9. Al-Khwarizmi and Islamic Mathematics
   • Duration: 30 min
   • Description: Investigate the contributions of al-Khwarizmi to mathematics and the origins of algebra.

10. A Horatio Algebra Story
    • Duration: 29 min
    • Description: Explore the competitive environment of 16th-century Italian mathematics and Gerolamo Cardano’s innovations.

11. To the Cubic and Beyond
    • Duration: 32 min
    • Description: Follow Cardano’s journey to solving cubic equations and the contributions of his protégé, Ludovico Ferrari.

12. The Heroic Century
    • Duration: 31 min
    • Description: Discover the innovations of the 17th century, including the introduction of modern mathematical notation.

13. The Legacy of Newton
    • Duration: 30 min
    • Description: Examine Isaac Newton’s immense contributions to mathematics and science.

14. Newton’s Infinite Series
    • Duration: 31 min
    • Description: Explore Newton’s use of infinite series in calculus and its applications.

15. Newton’s Proof of Heron’s Formula
    • Duration: 32 min
    • Description: Analyze Newton’s own proof of the area formula for triangles.

• The Legacy of Leibniz
  • Duration: 31 min
  • Description: Investigate Gottfried Wilhelm Leibniz’s impact on calculus and his independent discovery of the subject.

17. The Bernoullis and the Calculus Wars
    • Duration: 31 min
    • Description: Explore the fierce debate between Newton and Leibniz and the Bernoulli brothers’ contributions.

18. Euler, the Master
    • Duration: 30 min
    • Description: Delve into Leonhard Euler’s prolific work and lasting impact on mathematics.

19. Euler’s Extraordinary Sum
    • Duration: 31 min
    • Description: Follow Euler’s groundbreaking solution to the Basel problem.

• Euler and the Partitioning of Numbers
  • Duration: 31 min
  • Description: Examine Euler’s theory on prime numbers and their partitioning.

• Gauss-the Prince of Mathematicians
  • Duration: 30 min
  • Description: Celebrate the legacy of Carl Friedrich Gauss and his contributions to mathematics.

22. The 19th Century-Rigor and Liberation
    • Duration: 31 min
    • Description: Explore key developments in mathematics during the 19th century.

23. Cantor and the Infinite
    • Duration: 29 min
    • Description: Learn about Georg Cantor’s revolutionary ideas on infinite sets and transfinite numbers.

24. Beyond the Infinite
    • Duration: 31 min
    • Description: Understand the implications of Cantor’s work on the nature of infinity and mathematics.