1. Five Mathematical Algorithms That Help Us Get There
Presented by Yoni Nazarathy School 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 Dijkstra’s Algorithm
George Dantzig, 1940’s
231K hits on Google
Dijkstra’s Algorithm
Edsger Wybe Dijkstra, 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.)?
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

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

8. The Simplex Algorithm

9. The Simplex Algorithm

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

11. Dijkstra’s Algorithm

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.

16. Discussion….