19/08/2013 17:32

 I. Numbers (6 lectures)

  • Prime numbers
  • Interesting properties of prime numbers without proofs
  • Ramanujan's work on the Prime Number Theorem
  • Euclid's division algorithm
  • Mathematical illustration through intuitive examples
  • Visualisation through tiling analogy
  • Encryption and Prime numbers
  • Gentle introduction of 2 x 2 matrices
    Constructing the RSA Algorithm

a Project Themes

  • Ramanujan's work
  • Implementations of RSA algorithms
  • Other methods of encryption

a II. Data and patterns (6 lectures)

  • Historical perspective and importance of data
  • Kepler's law for planetary orbits from Tycho Brahe's astronomical observation
  • Ramanujan's work on Prime numbers through data
  • Data collection techniques
  • Formulation of problem – goals, targets
  • Methods to collect data – questionnaire, observations, recording, etc.
  • How much of data is enough for the given problem
  • Population and sample

a Project Themes

  • Collecting and organising data in various situations through practical methods, from the
    internet and from other sources.
  • Use of spreadsheets for practical work related to the above concepts.

a III. Statistics (8 lectures)

  • Organisation of data
  • Frequency table
  • Grouping
  • Visualisation of data
  • Pictorially displaying data: dot plots, bar graphs, line graphs, pie charts
  • Misinterpretation of data by distorting the figures: Scaling and axis manipulation,
    Line graphs and cropping
  • Analysis of data
  • Mean, median, mode, variance, standard deviation.
  • Histogram, skewed distribution
  • Comparing two distributions

a Project Themes

  • Statistical analysis of daily life data
  • Statistical analysis of stock market data
  • Statistical analysis of weather data
  • Statistical analysis of data for better governance

a IV. Probability (4 lectures)

  • Interpreting probability, Sample Space, Events
  • Understanding the tossing of a coin and throwing of dice for large number of trials Probability in a situation where there are equally-likely outcomes
  • Probability of two independent events

a V. Project Themes

  • Compute probabilities from insufficient information
  • Validity of computed probability