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Five Mathematical Algorithms That Help Us Get There

Learn about five important mathematical algorithms that we use in our daily lives. Discover how the Simplex Algorithm, Dijkstra's Algorithm, the Viterbi Algorithm, the Kalman Filter, and the Fast Fourier Transform have shaped various fields. Presented by Yoni Nazarathy from the School of Mathematics and Physics at The University of Queensland.

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Five Mathematical Algorithms That Help Us Get There

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  1. Five Mathematical Algorithms That Help Us Get There Presented by Yoni NazarathySchool Of Mathematics and Physics, The University of Queensland

  2. So you do mathematical research…. • What is that about? • Isn’t everything in math known?Answer: In pure math there are still very basic open problems. For example, the twin-prime conjecture…. (3,5), (5,7), (11,13), (17,19), (29,31), (41,43),….,(617,619),…Does it go on forever?

  3. But who cares? • Answer 1: It is beautiful, exciting, challenging and promoting thought. • Answer 2: Pure math often translates itself down the road to applied math. • Question: “Applied math”? Can you give me an example where it is used in my life? • Answer: I’ll tell you about five mathematical algorithms which we use on a daily basis.

  4. Today’s talk • The Simplex Algorithm • George Dantzig, 1940’s • 231K hits on Google • Dijkstra’s Algorithm • EdsgerWybeDijkstra, 1950’s • 258K hits on Google • The Viterbi Algorithm • Andrew Viterbi, 1960’s. And others… • 301K hits on Google • The Kalman Filter • Rudolf Kalman, late 1950’s. • 1.3M hits on Google • The Fast Fourier Transform (FFT) • James Cooley and John Tukey, 1960’s • 1.7M hits on Google

  5. What’s special about 1945—1965? • Answer 1: Post war + cold war • Answer 2: The computer… • Some questions: • What is an algorithm? • Did algorithms exist prior to computers? • What is the first algorithm developed on this planet? Alan Turing

  6. Where are these used (for e.g.)? Simplex Kalman Dijkstra You take a flight from Brisbane to Sydney, navigate in Sydney using Google maps, take a photo using your phone and then make a phone call… Viterbi FFT

  7. The Simplex Algorithm Question: What does it do? Answer: It optimizes:

  8. The Simplex Algorithm

  9. The Simplex Algorithm http://demonstrations.wolfram.com/ASimpleStandardLinearProgrammingScenario/

  10. Dijkstra’s Algorithm Question: What does it do? Answer: It finds the shortest path between u and v in:

  11. Dijkstra’s Algorithm http://demonstrations.wolfram.com/DijkstrasAlgorithm/

  12. The Kalman Filter Question: What does it do? Answer: It estimates x(t) based on y(t) from:

  13. The Kalman Filter

  14. The Viterbi Algorithm Question: What does it do? Answer: It finds the most likely sequence of hidden states:

  15. The Fast Fourier Transform Question: What does it do? Answer: It computes a discrete Fourier transform fast. http://demonstrations.wolfram.com/FourierSeriesOfSimpleFunctions/

  16. Discussion….

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