St. Mary’s College of Maryland Professor of Mathematics David Kung has released a new video lecture series titled “Mind-Bending Math: Riddles and Paradoxes.” The 24-lecture course teaches participants how to break down, examine, and solve famous riddles and paradoxes through basic logic and math principles.
“The brain needs exercise just like the body does,” says Kung. “Stretching your mind to try to solve a good puzzle helps improve your ability to focus—and to solve the problems that arise in your own life.”
Conundrums covered in the half-hour lectures run the gamut from simple to complex, including:
- Zeno’s paradoxes: “All motion is impossible,” said the ancient Greek philosopher Zeno, because an infinite number of intervals must be traversed to take even a single step. This and Zeno’s other paradoxes set the stage for two millennia of speculation about space and time.
- Liar’s Paradox: “This sentence is false.” A simple sentence, it traps you in an endless logical loop – with the conclusion that it is neither true nor false. Professor Kung traces the path from this simple idea to Kurt Gödel’s revolutionary theorems showing that no axiomatic system will ever prove all the true mathematical statements.
- Life in a 3-Torus: Imagine life in a cube where the left wall is glued to the right. Walk out one side – you’d come back in the other! Now glue the front wall to the back and the floor to the ceiling and you’re in a 3-torus. Watch as Professor Kung walks around this crazy space, even playing catch … with himself!
- Banach-Tarski Paradox: This most famous of all mathematical paradoxes shows that you can take a solid ball, split it up into six pieces, reassemble three of them into a complete ball the same size as the original, and reassemble the other three into another complete ball – also the same size as the original. Dr. Kung sketches the main ideas that prove this bit of mathematical alchemy.
Each lecture features a short segment called “Quick Conundrum” that presents a simple but perplexing phenomenon that you can easily explore at home. “The world is full of surprises,” says Kung, whose First Year Seminar course is based on the videos. “Spaghetti noodles don’t break like you think; autumn leaves don’t fall—they’re pushed; and light filters can turn subtraction into addition.”
Mind-Bending Math is the second of two online mathematics courses released by Kung through The Great Courses. The Great Courses provides lifelong learners with versatile courses in a multitude of fields. The courses are available on DVD, streaming, or video download at www.thegreatcourses.com. Kung’s first 12-lecture course, “How Music and Mathematics Relate,” has sold more than 44,000 copies since its release in 2013.
Kung earned his B.A. in mathematics and physics and his Ph.D. in mathematics from the University of Wisconsin, Madison. He joined the St. Mary’s College faculty in 2000 and became a full-time professor in 2012. His areas of expertise include harmonic analysis and mathematics education. He has led efforts to establish Emerging Scholars Programs at institutions across the country, and has won numerous teaching awards, including St. Mary’s College of Maryland’s Homer L. Dodge Award for Excellence in Teaching by Junior Faculty, and is the founder of the Southern Maryland Math Circle, an enrichment program for middle and high school students. In addition to his position at SMCM, he serves the Mathematical Association of America as Director of its professional development program for new mathematics faculty, Project NExT.
In addition to his academic pursuits, Kung is an accomplished violinist. He has studied with one of the pioneers of the innovative Suzuki method, attended the prestigious Interlochen music camp, and performed with the Madison Symphony Orchestra. He remains an active musician, playing chamber music with students, leading COSMIC (the local community orchestra), and serving on the board of the Southern Maryland Youth Symphony and Choir.