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Majoring in Mathematics (view source)
Revision as of 03:34, October 6, 2009
, 03:34, October 6, 2009move a couple problems, reorganize
=== Geometry ===
=== Geometry ===
# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?
# Double-bubble conjecture (a nice result, easy to state and wave hands about "curvature", and with a connection to CP!)
=== Topology ===
=== Topology ===
# Konigsberg bridge problem, with complete solution.
# Konigsberg bridge problem, with complete solution.
# Connection between topological spaces and algebraic groups
# 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!)
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better.
A motivating problem: how can we prove that a sphere and a torus are different?
A motivating problem: how can we prove that a sphere and a torus are different?
=== Analysis ===
=== Analysis ===
Hard problem: What does an integral really mean? Babble a bit about integrating the characteristic function of Q.
Hard problem: What does an integral really mean? Babble a bit about integrating the characteristic function of Q.
=== Probability and Statistics ===
# Discussion of Benford's law, application to recognizing fraud.
# Understanding the concept of the "random variable"
# Proving the Central Limit Theorem
Motivating problem: Deriving conclusions from rarely occurring events, such as multiple no-hitters by the same pitcher. Specifically, how many no-hitters must a pitcher toss before one can conclude from that evidence alone that he is a great pitcher?
=== Other fields ===
=== Other fields ===