http://school.maths.uwa.edu.au/~gregg/
Below is an index of lectures, with lecture notes and problems, Greg Gamble has given during his first session of 3 lectures in 2007 to UWA Academy for Young Mathematicians. Except for problems that were solved in the lecture, solutions will only appear after students have submitted their attempts. The notes and problems or problems with solutions below are provided in .pdf format, which requires you to have Acrobat Reader installed on your machine. If you find a mistake I'd certainly like to know. Please email me and tell me about it.
Solutions to all problems are now included. The prize of a Heaven chocolate bar for a solution to Problem 9 was won by Jason Kong. Congratulations Jason.
All solutions to the inequalities of the first and second problems are included. Take special note of the solution to Problem 3. The proof must start with the hypotheses and end with what was to be proved. The biggest mistake students make is to produce an upside-down proof. See the second dangerous bend on page 2 of the Mathematical Induction notes. (Often the argument does work both ways, and this is the case in Problem 3.)
Note that the last problem was somewhat harder than the rest, since it needed more than the ordinary induction.
Last updated: 1 August, 2009.
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Greg Gamble http://school.maths.uwa.edu.au/~gregg/ |
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