Our informal math program consisted of a series of lectures designed by Dr. Desh Ranjan . Topics that were covered included:

Geometry. Greek Geometers and a historical perspective.

Co-ordinate geometry.

  • Co-ordinate systems.
  • Equations describing general straight lines:
  • Slopes and intercept.
  • Straight line passing through two given points.
  • Intersection of lines, solving linear equations.
  • Describing triangles --
    • via three lines;
    • via three points.
    • Converting one to another.
    • The centroid of a triangle.
  • The two sides of a straight line.
  • The inside and outside of a triangle.
  • Straight line passing through a given point parallel/perpendicular to another given line.
  • Co-ordinates of equidistant points on a straight line.
  • Equation describing circles.
    • Determining if a given point is inside a circle.
    • Circle passing through three given points.
    • Incircle and circumcircle of a triangle.

Fractals -- a different type of geometry.

  • Mathematics of fractals -- complex numbers.
  • Algebraic origins of complex numbers -- Square root of -1.
  • Geometric representation of complex numbers: modulus and phase.
  • Operations with complex numbers -- addition, multiplication.
  • The Mandelbrot set.
  • Mandelbrot set -- more details.
  • Displaying Mandelbrot set at various detail levels.
  • Other fractals.
Chance and probability.
  • Rolling a dice and flipping a coin.
  • Games of chance in casinos. Why gambling is not smart.
  • Simple probability calculations.
  • Monte Carlo method.
  • How to calculate the value of pi using randomness.

Sequences.

  • Pattern recognition -- notion of sequences.
  • Arithmetic sequences.
  • The geometric sequence and Zeno's paradox.
  • Fibonacci sequence
  • Fibonacci sequence and the Golden Ratio.
  • Golden Ratio in nature:
  • Fibonacci Spiral -- shells, pine cones, petals and leaf growth.
  • Towers of Hanoi -- Recursive thinking.