rt and Craft of Mathematical Problem Solving

Overview

Let an award-winning professor, and former champion “mathlete,” demonstrate how solving math problems can be fun. “Art and Craft of Mathematical Problem Solving” explores various strategies and techniques across 24 engaging lectures to enhance your problem-solving skills.

Course Instructor

Professor Paul Zeitz, a renowned educator and coach, guides you through mind-expanding challenges aimed at breaking down complex problems into manageable steps.

Video Lessons

1. Problems versus Exercises
   • Duration: 30 min
   • Description: Understand the differences between math problems and exercises and the importance of problem-solving techniques.

2. Strategies and Tactics
   • Duration: 29 min
   • Description: Learn effective strategies to tackle mathematical problems, including reasoning and logical thinking.

3. The Problem Solver’s Mind-Set
   • Duration: 33 min
   • Description: Explore cognitive approaches to problem-solving, enhancing creativity and confidence.

• Searching for Patterns
  • Duration: 29 min
  • Description: Investigate patterns in various problems, fostering discovery and conjecture.

5. Closing the Deal—Proofs and Tools
   • Duration: 33 min
   • Description: Master the art of making concise proofs for mathematical arguments using various strategies.

6. Pictures, Recasting, and Points of View
   • Duration: 29 min
   • Description: Employ visual representations and perspectives to simplify complex problems.

• The Great Simplifier—Parity
  • Duration: 29 min
  • Description: Use the concept of parity to solve engaging puzzles and mathematical challenges.

8. The Great Unifier—Symmetry
   • Duration: 29 min
   • Description: Discover how symmetry can help simplify problem-solving across various scenarios.

9. Symmetry Wins Games!
   • Duration: 31 min
   • Description: Devise winning strategies for games using the principles of symmetry.

10. Contemplate Extreme Values
    • Duration: 30 min
    • Description: Learn to identify minimal or maximal values in mathematical problems.

11. The Culture of Problem Solving
    • Duration: 30 min
    • Description: Explore the community of problem solvers and the cultural aspect of mathematical exploration.

12. Recasting Integers Geometrically
    • Duration: 27 min
    • Description: Approach the “chicken nuggets” problem by visualizing solutions geometrically.

13. Recasting Integers with Counting and Series
    • Duration: 32 min
    • Description: Tackle classical theorems using inventive and innovative thinking.

14. Things in Categories—The Pigeonhole Tactic
    • Duration: 30 min
    • Description: Apply the pigeonhole principle to find inevitabilities within various mathematical situations.

• The Greatest Unifier of All—Invariants
  • Duration: 31 min
  • Description: Explore how invariants can provide insight and simplify complex problems.

16. Squarer Is Better—Optimizing 3s and 2s
    • Duration: 31 min
    • Description: Solve problems using optimization techniques and mathematical intuition.

17. Using Physical Intuition—and Imagination
    • Duration: 31 min
    • Description: Empower your problem-solving with physical insights and imaginative approaches.

18. Geometry and the Transformation Tactic
    • Duration: 31 min
    • Description: Leverage geometric transformations to simplify problem-solving.

19. Building from Simple to Complex with Induction
    • Duration: 30 min
    • Description: Use inductive reasoning to tackle recursive problems.

20. Induction on a Grand Scale
    • Duration: 30 min
    • Description: Analyze the probability of primes using inductive methods.

21. Recasting Numbers as Polynomials—Weird Dice
    • Duration: 31 min
    • Description: Explore the intriguing concept of designing non-standard dice to maintain equal probabilities.

22. A Relentless Tactic Solves a Very Hard Problem
    • Duration: 30 min
    • Description: Use the pigeonhole principle creatively to explore complex mathematical structures.

23. Genius and Conway’s Infinite Checkers Problem
    • Duration: 32 min
    • Description: Analyze the challenges in Conway’s infamous checkers problem.

24. How versus Why—The Final Frontier
    • Duration: 34 min
    • Description: Reflect on the journey through problem-solving and explore deeper meanings behind mathematical solutions.