Places We Will Visit In Math 2790

• Brief Tour of the World: Methods and Proof (5 tours)
  
  • Parity
  • Pigeonhole Principle
  • Exploiting Symmetry
  • Proof by Contradiction
  • Mathematical Induction

• Brunswick, Germany: The Theory of Numbers (6 tours)
  
  • Sequences and Series
  • Sum of Cubes
  • Properties of Divisors
  • Perfect Numbers
  • Diophantine Equations
  • Pell's Equations
  • Modular Arithmetic
  • Quadratic Residues
  • Fermat's Last Theorem for n = 4

• Alexandria, Egypt: Euclidean Geometry (5 tours)
  
  • Comparing Areas To Solve Problems
  • The Internal Angle Bisector Theorem
  • Ceva's Theorem
  • Special Points in a Triangle
  • The Euler Line
  • An Incredible "Proof" That All Triangles Are Isosceles
  • Triangle theorems
  • Circle theorems
  • Properties of Cyclic Quadrilaterals
  • The Nine-Point Circle

• St. Petersburg, Russia: Combinatorics (5 tours)
  
  • Permutations and Combinations
  • Regular and Conditional Probability
  • Binomial Coefficients and Properties of Pascal's Triangle
  • Counting Methods and Techniques
  • Two Problems From the Price is Right game show
  • Fibonacci Numbers

• Budapest, Hungary: Mathematical Gems (2 tours)
  
  • Awesome problems with really simple solutions!