**SLR 511F: 10 MATHEMATICAL IDEAS EVERYONE SHOULD
KNOW and their everyday applications in the real world **

** John Clements.**

** SESSION #5, Mon. Oct. 3/11. I hope that you had a Happy Thanksgiving **

** SESSION #5 will **

** (a) complete TOPIC #7: The concept of PROOF **

** (b) explore TOPIC #2: Famous easy-to-understand problems – and their uses **

** (c) and then have another
look at Diana's interesting application of mathematics to rowing. **

** **

** TOPIC #2: Famous easy-to-understand problems – and their uses **

** **

** (i) GPS (Getting from A to J): The Dynamic Programming Principle vs the Greedy Algorithm
**

** **

** (ii) The Chinese Postman Problem (visiting edges): Graphs, Euler Circuits,
Loenhard Euler and Euler’s Theorem, The Seven bridges of Konigsberg**

** **

** (iii) The Travelling Salesman Problem (visiting vertices), Hamiltonian Circuits
– first studied by William Hamilton (1805-1865) NP Hard **

** **

** (iv) The Knapsack Problem: First studied by Tobias Dantzig (1884–1956)
NP HARD **

** **

** (v) The Four Color Problem Francis Guthrie made the conjecture in 1852,
but it remained unproven until 1976 **

** **

** (vi) OPERATIONS RESEARCH - HOW IS IT DONE?
LINEAR PROGRAMMING and the SIMPLEX METHOD
George Danzig. Movie: “Goodwill Hunting **

** **

** (vii) Game Theory, John Von Neumann, John Nash. Movie: “A Beautiful Mind” **

** **

** (vii) The Atomic Bomb Problem of 1945, Sir G. I. Taylor,
DIMENSIONAL ANALYSIS **

** Each of these problems will be examined briefly.**

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