Gems And Astonishments of Mathematics: Past and Present

MATH X 451.44

This advanced mathematics course, the first of a 2-part series, is a survey of mathematical problems that either remain unsolved or have been settled in fairly recent times. Great for devotees of mathematical reasoning.


What you can learn.

  • Understand why and how unique problem-solving approaches were created
  • Integrate recent mathematical developments to evaluate unsolved mathematical mysteries
  • Gain valuable problem-solving skills needed to be successful in future number and matrix theory classes
  • Explore real-life unsolved mathematical mysteries

About this course:

Mathematics has evolved over the centuries not only by building on the work of past generations, but also through unforeseen discoveries or conjectures that continue to tantalize, bewilder, and engage academics and the public alike.  This course, the first in a two-quarter sequence, is a survey of about two dozen problems—some dating back 400 years, but all readily stated and understood—that either remain unsolved or have been settled in fairly recent times.  Each of them, aside from presenting its own intrigue, has led to the development of novel mathematical approaches to problem solving.  Topics to be discussed include (Google away!): Conway’s Look and Say Sequences, Kepler’s Conjecture, Szilassi’s Polyhedron, the ABC Conjecture, Benford’s Law, Hadamard’s Conjecture, Parrondo’s Paradox, and the Collatz Conjecture.  The course should appeal to devotees of mathematical reasoning and those wishing to keep abreast of recent and continuing mathematical developments.
Suggested Prerequisites

It is advisable that you complete the following (or equivalent) since they are prerequisites for Gems And Astonishments of Mathematics: Past and Present.

Some exposure to advanced mathematical methods, particularly those pertaining to number theory and matrix theory.

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