Here are some interesting mathematics seminar topics that combine puzzles, surprising results, and deeper mathematical concepts suitable for a master's degree:
1. The Mathematics of Rubik's Cube: Explore group theory, permutations, and algorithms to understand how the cube can be solved mathematically.
2. Mental Mathematics and Fast Calculations: Investigate methods for calculating large squares, cubes, and cube roots without a calculator, and explain the algebraic principles behind them.
3. The Monty Hall Problem: Explore probability theory and why switching doors increases the probability of winning from 1/3 to 2/3.
4. The Mathematics of Infinity: Discuss Cantor's diagonal argument, countable and uncountable sets, and why some infinities are larger than others.
5. The Four-Color Theorem: Explain why any planar map can be colored using no more than four colors without adjacent regions sharing the same color.
6. Cryptography and Number Theory: Explore how prime numbers, modular arithmetic, and mathematical algorithms are used to protect digital information.
My suggestion would be Mental Mathematics and Fast Calculations if you want an interactive seminar. You could begin by challenging the audience to calculate the cube of a large number without a calculator, demonstrate a mathematical shortcut, and then explain why the method works using algebra and number theory.
For a master's-level presentation, include a rigorous mathematical derivation or proof rather than focusing only on the calculation tricks.
