Foundations of Mathematics: Math 220
Term paper topics from the textbook
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Infinite products.
Non-Euclidean geometry.
Irrational numbers.
Strange sets.
Pathological functions.
Permutations.
Groups (see an article by Bryan Hayes).
Bernoulli numbers.
Additional term paper topics
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The golden ratio.
Fibonacci numbers.
Polygonal numbers.
Pascal’s Triangle and its applications.
Rational election procedures (Can you set up a voting procedure that cannot be manipulated?).
Tilings (for example, the chess problem of the knights).
Latin squares.
Fractal patterns.
Cryptography (secret codes).
Error-correcting codes, especially linear or matrix codes.
The five color problem (All maps can be colored using at most five colors so that no two
countries with a common borderline have the same color. Actually, four colors are enough,
but that is beyond this course).
Investigate and explain a paradox. For example:
– The Prisoner’s Dilemma (How to get the smallest sentence for both).
– The Surprise Examination Paradox (Can there be an announced surprise?).
– Newcomb’s Paradox.
– The Petersburg Paradox.
– Zeno’s Paradoxes.
The Königsberg bridge problem (Eulerian Circuits).
P-adic integers.
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