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