http://school.maths.uwa.edu.au/~gregg/
Below is an index of lectures, with lecture notes and problems, Greg Gamble for lectures in 2009 to UWA Academy for Young Mathematicians. Notes and problems will be added once the lecture has happened. 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.
For homework please complete Problems 1-4. For some examples of the sort of formality with proofs I'd like to see in your solutions, see the solutions of last year's plane geometry problems.
A typo. has been corrected in the solution of Problem 1., where sin was unintentionally substituted for cos. Thanks to Jonathan for spotting it.
For homework please complete Problems 6, 9 and 10 from the previous session's Ceva's Theorem Problems sheet.
We didn't have time to cover this material in the lecture, but students are welcome to read the notes and submit attempts at the various problems. Solutions will appear for any problems for which at least one student submits an attempt. For an idea of how to go about the problems look at the example below.
For homework please complete Problems 1.-4. and 6. from the Trigonometry Problems of last week. Much of Problems 1.-4. was covered in the lecture. Your job is to fill in what wasn't done. The solutions for all the Trigonometry Problems are above.
This proves an inequality in 4 different ways in order to demonstrate how to use some standard inequalities to prove a particular inequality.
Last updated: 23 October, 2009.
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Greg Gamble http://school.maths.uwa.edu.au/~gregg/ |
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