Five Mathematical Algorithms That Help Us Get There

So you do mathematical research…. What is that about? Isn’t everything in math known?

But who cares? Answer 1: It is beautiful, exciting, challenging and promoting thought. Answer

Today’s talk The Simplex Algorithm George Dantzig, 1940’s 231 K hits on Google Dijkstra’s

What’s special about 1945— 1965? Answer 1: Post war + cold war Answer 2:

Where are these used (for e. g. )? Kalman Simplex Dijkstra You take a

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

The Simplex Algorithm http: //demonstrations. wolfram. com/ASimple. Standard. Linear. Programming. Scenario/

Dijkstra’s Algorithm Question: What does it do? Answer: It finds the shortest path between

Dijkstra’s Algorithm http: //demonstrations. wolfram. com/Dijkstras. Algorithm/

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

The Viterbi Algorithm Question: What does it do? Answer: It finds the most likely

The Fast Fourier Transform Question: What does it do? Answer: It computes a discrete

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

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?

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.

Today’s talk The Simplex Algorithm George Dantzig, 1940’s 231 K hits on Google Dijkstra’s Algorithm Edsger Wybe Dijkstra, 1950’s 258 K hits on Google The Viterbi Algorithm Andrew Viterbi, 1960’s. And others… 301 K hits on Google The Kalman Filter Rudolf Kalman, late 1950’s. 1. 3 M hits on Google The Fast Fourier Transform (FFT) James Cooley and John Tukey, 1960’s 1. 7 M hits on Google

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

Where are these used (for e. g. )? Kalman Simplex 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

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

The Simplex Algorithm

The Simplex Algorithm http: //demonstrations. wolfram. com/ASimple. Standard. Linear. Programming. Scenario/

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

Dijkstra’s Algorithm http: //demonstrations. wolfram. com/Dijkstras. Algorithm/

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

The Kalman Filter

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

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

Discussion….