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Majoring in Mathematics (view source)
Revision as of 05:09, October 5, 2009
, 05:09, October 5, 2009→Major Topics of Study
A motivating question: failure of unique factorization in certain number fields (with explicit examples)
A motivating question: failure of unique factorization in certain number fields (with explicit examples)
=== Geometry and Topology ===
=== Geometry ===
# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better.
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?
=== Topology ===
# Konigsberg bridge problem, with complete solution.
# Konigsberg bridge problem, with complete solution.
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better)
# Connection between topological spaces and algebraic groups
# Double-bubble conjecture (a nice result, easy to state and wave hands about "curvature", and with a connection to CP!)
# Double-bubble conjecture (a nice result, easy to state and wave hands about "curvature", and with a connection to CP!)