Overview

Experience the thrilling pursuit of a mathematical proof in this course suitable for everyone from high school students to math lovers. Mathematical proof is the gold standard of knowledge, establishing truths that endure through time. This course includes 24 lectures filled with engaging proofs and concepts, taught by Professor Bruce H. Edwards of the University of Florida, who brings excitement to the world of mathematics.

Course Instructor

Professor Bruce H. Edwards, an award-winning educator and author of widely utilized textbooks, guides you through the art of mathematical argument, showcasing how proof illuminates the abstract order behind all things.

Video Lessons

1. What Are Proofs, and How Do I Do Them?
   • Duration: 32 min
   • Description: Learn the basics of mathematical proofs and enhance your proving skills.

• The Root of Proof-A Brief Look at Geometry
  • Duration: 31 min
  • Description: Discover Euclid’s theorems and explore the importance of proofs in mathematics.

• The Building Blocks-Introduction to Logic
  • Duration: 30 min
  • Description: Study the fundamental connectors in logic and their role in mathematical statements.

4. More Blocks-Negations and Implications
   • Duration: 30 min
   • Description: Delve into negations and implications, crucial components of mathematical theorems.

• Existence and Uniqueness-Quantifiers
  • Duration: 30 min
  • Description: Explore the role of quantifiers in defining mathematical concepts and sequences.

• The Simplest Road-Direct Proofs
  • Duration: 31 min
  • Description: Learn direct proof techniques using hypotheses to reach conclusions.

• Let’s Go Backward-Proofs by Contradiction
  • Duration: 31 min
  • Description: Understand proof by contradiction, including Euclid’s proof of the square root of 2.

• Let’s Go Both Ways-If-and-Only-If Proofs
  • Duration: 31 min
  • Description: Examine isosceles triangles as an example of “if-and-only-if” theorems in mathematics.

• The Language of Mathematics-Set Theory
  • Duration: 30 min
  • Description: Discover elementary set theory and learn to manipulate sets through proofs.

10. Bigger and Bigger Sets-Infinite Sets
    • Duration: 32 min
    • Description: Investigate properties and paradoxes of infinite sets, including uncountable reals.

• Mathematical Induction
  • Duration: 31 min
  • Description: Use mathematical induction as a powerful tool for proving theorems about integers.

• Deeper and Deeper-More Induction
  • Duration: 31 min
  • Description: Explore the equality of 0.99999… and apply induction to geometrical series.

• Strong Induction and the Fibonacci Numbers
  • Duration: 30 min
  • Description: Apply strong induction to prime numbers and the Fibonacci sequence.

• I Exist Therefore I Am-Existence Proofs
  • Duration: 31 min
  • Description: Analyze existence proofs, demonstrating the necessity of certain mathematical objects.

• I Am One of a Kind-Uniqueness Proofs
  • Duration: 31 min
  • Description: Prove the uniqueness of mathematical results by exploring contradictions.

16. Let Me Count the Ways-Enumeration Proofs
    • Duration: 31 min
    • Description: Learn about the Four Color theorem and the enumeration of cases in proofs.

17. Not True! Counterexamples and Paradoxes
    • Duration: 30 min
    • Description: Discover how to disprove conjectures using counterexamples and famous paradoxes.

• When 1 = 2-False Proofs
  • Duration: 31 min
  • Description: Examine common errors in proofs and the history of attempts to prove notable conjectures.

• A Picture Says It All-Visual Proofs
  • Duration: 32 min
  • Description: Explore the role of visual arguments in proofs, including Garfield’s proof of the Pythagorean theorem.

20. The Queen of Mathematics-Number Theory
    • Duration: 29 min
    • Description: Study the captivating field of number theory by proving theories about prime numbers.

21. Primal Studies-More Number Theory
    • Duration: 31 min
    • Description: Probe further into prime numbers and attempt to prove significant conjectures.

• Fun with Triangular and Square Numbers
  • Duration: 30 min
  • Description: Use diverse proof techniques to explore square and triangular numbers.

• Perfect Numbers and Mersenne Primes
  • Duration: 31 min
  • Description: Investigate relationships between perfect numbers and Mersenne primes.

• Let’s Wrap It Up-The Number e
  • Duration: 32 min
  • Description: Conclude with properties of the number e and challenge yourself with proofs of its rationality.