Probability & Probability Distributions Physical, Biological & Social Sciences The Monty Hall problem Radiocarbon dating Monte Carlo simulations Gravity, orbits & escape velocity Random walks Mathematical methods in economics Insurance and calculating risks Biostatistics Poisson distribution and queues Genetics Determination of by probability Crystallography Lotteries Computing centres of mass theorem Elliptical orbits Bayes’ Birthday paradox Logarithmic scales decibel, Richter, etc – Normal distribution and natural phenomena Fibonacci sequence and spirals in nature Predicting an eclipse Change in BMI for a person over time Games & Game Theory Concepts of equilibrium in economics The prisoner’s dilemma Sudoku Miscellaneous Paper folding Gambler’s fallacy Poker and other card games Designing bridges in chess Methods of approximating Knight’s tour Mathematical card tricks paradox Curry’s – ‘missing’ square Topology & Networks Barcodes Knots Applications of parabolas Steiner problem Music notes, pitches, scales, etc – Chinese postman problem Voting systems Travelling Salesman Problem by Edwin Abbott (book) Flatland Königsberg bridge problem Terminal velocity Handshake problem Towers of Hanoi puzzle Möbius strip Photography Klein bottle Art of M.C. Escher Harmonic mean Sundials Logic & Sets Navigational systems Codes and ciphers (film) A Beautiful Mind Set theory and The abacus different ‘size’ infinities Mathematical induction (strong) Construction of calendars Proof by contradiction Slide rules Proving that a number is irrational Different number systems Mathematics of juggling Global positioning system (GPS) Numerical Analysis Airline routes Linear programming Fixed point iteration Methods of approximating Applications of iteration method Newton’s Estimating size of large crowds Generating the number e rule of signs Descartes’ Methods for solving differential equations Compiled by: Tim Garry
Probability & Probability Distributions The Monty Hall problem Monte Carlo simulations Random walks Insurance and calculating risks Poisson distribution and queues Determination of by probability Lotteries Bayes’ theorem Birthday paradox Normal distribution and natural phenomena Games & Game Theory The prisoner’s dilemma Sudoku Gambler’s fallacy Poker and other card games Knight’s tour in chess Topology & Networks Knots Steiner problem Chinese postman problem Travelling Salesman Problem Königsberg bridge problem Handshake problem Möbius strip Klein bottle Logic & Sets Codes and ciphers Set theory and different ‘size’ infinities Mathematical induction (strong) Proof by contradiction Proving that a number is irrational Numerical Analysis Linear programming Fixed point iteration Methods of approximating Applications of iteration Newton’s method Estimating size of large crowds Generating the number e Descartes’ rule of signs Methods for solving differential equations Compiled by: Tim Garry Physical, Biological & Social Sciences Radiocarbon dating Gravity, orbits & escape velocity Mathematical methods in economics Biostatistics Genetics Crystallography Computing centres of mass Elliptical orbits Logarithmic scales – decibel, Richter, etc Fibonacci sequence and spirals in nature Predicting an eclipse Change in BMI for a person over time Concepts of equilibrium in economics Miscellaneous Paper folding Designing bridges Methods of approximating Mathematical card tricks Curry’s paradox – ‘missing’ square Barcodes Applications of parabolas Music – notes, pitches, scales, etc Voting systems Flatland by Edwin Abbott (book) Terminal velocity Towers of Hanoi puzzle Photography Art of M.C. Escher Harmonic mean Sundials Navigational systems A Beautiful Mind (film) The abacus Construction of calendars Slide rules Different number systems Mathematics of juggling Global positioning system (GPS) Airline routes
ib_maths_hl__sl_exploration_200_ideas.docx